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Chapter 11: Adding and Subtracting Whole Numbers and Decimals

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Adding and Subtracting Whole Numbers and Decimals in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Adding whole numbers (Adding whole numbers is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Subtracting whole numbers (Subtracting whole numbers is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Adding decimals (A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.)
  • Regrouping in addition (Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Regrouping in subtraction (Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Mental addition strategies (A rate compares two quantities measured in different units.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

11.1 Adding whole numbers

Adding whole numbers is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In 824,897, what is the value of the digit 2 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 20,000

Worked Example 2

Problem: In 647,916, what is the value of the digit 7 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 7,000

Worked Example 3

Problem: In 94,732, what is the value of the digit 3 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 30

Worked Example 4

Problem: In 166,619, what is the value of the digit 1 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 100,000

Worked Example 5

Problem: In 801,734, what is the value of the digit 1 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 1,000

Worked Example 6

Problem: In 281,313, what is the value of the digit 8 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 80,000

Worked Example 7

Problem: In 106,493, what is the value of the digit 9 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 90

Worked Example 8

Problem: In 877,150, what is the value of the digit 8 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 800,000

Worked Example 9

Problem: In 314,276, what is the value of the digit 1 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 10,000

Worked Example 10

Problem: In 549,593, what is the value of the digit 9 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 90

Practice Exercise

Create one new Grade 6 problem about Adding whole numbers. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

11.2 Subtracting whole numbers

Subtracting whole numbers is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: In 574,311, what is the value of the digit 4 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 4,000

Worked Example 2

Problem: In 26,666, what is the value of the digit 6 in the 100 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 600

Worked Example 3

Problem: In 19,175, what is the value of the digit 0 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 0

Worked Example 4

Problem: In 278,775, what is the value of the digit 7 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 70,000

Worked Example 5

Problem: In 580,335, what is the value of the digit 8 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 80,000

Worked Example 6

Problem: In 258,808, what is the value of the digit 8 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 8,000

Worked Example 7

Problem: In 85,848, what is the value of the digit 5 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 5,000

Worked Example 8

Problem: In 522,087, what is the value of the digit 5 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 500,000

Worked Example 9

Problem: In 75,344, what is the value of the digit 3 in the 100 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 300

Worked Example 10

Problem: In 385,820, what is the value of the digit 3 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 300,000

Practice Exercise

Create one new Grade 6 problem about Subtracting whole numbers. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

11.3 Adding decimals

A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 45.888 + 18.217.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 64.105

Worked Example 2

Problem: Calculate 85.252 + 5.198.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 90.45

Worked Example 3

Problem: Calculate 91.076 + 1.551.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 92.627

Worked Example 4

Problem: Calculate 3.904 + 14.684.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 18.588

Worked Example 5

Problem: Calculate 43.073 + 13.461.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 56.534

Worked Example 6

Problem: Calculate 69.542 + 1.145.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 70.687

Worked Example 7

Problem: Calculate 9.065 + 10.273.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 19.338

Worked Example 8

Problem: Calculate 26.395 + 16.644.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 43.039

Worked Example 9

Problem: Calculate 28.92 + 14.859.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 43.779

Worked Example 10

Problem: Calculate 58.185 + 16.826.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 75.011

Practice Exercise

Create one new Grade 6 problem about Adding decimals. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is lining up the last digits instead of lining up decimal points and place values.

11.4 Subtracting decimals

A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 85.786 - 16.643.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 69.143

Worked Example 2

Problem: Calculate 59.779 - 13.32.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 46.459

Worked Example 3

Problem: Calculate 50.858 - 17.51.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 33.348

Worked Example 4

Problem: Calculate 5.575 - 16.483.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: -10.908

Worked Example 5

Problem: Calculate 99.685 - 2.159.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 97.526

Worked Example 6

Problem: Calculate 79.812 - 4.638.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 75.174

Worked Example 7

Problem: Calculate 17.683 - 5.698.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 11.985

Worked Example 8

Problem: Calculate 31.183 - 8.961.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 22.222

Worked Example 9

Problem: Calculate 39.341 - 11.483.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 27.858

Worked Example 10

Problem: Calculate 32.037 - 15.932.

  1. Line up or track place values carefully.
  2. Perform the operation.
  3. Estimate to check the result.

Very beginner explanation: Decimal calculations are reliable when each place value is kept aligned.

Answer: 16.105

Practice Exercise

Create one new Grade 6 problem about Subtracting decimals. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is lining up the last digits instead of lining up decimal points and place values.

11.5 Aligning decimal places

A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: What digit is in the tenths place of 9.772?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 7

Worked Example 2

Problem: What digit is in the tenths place of 50.168?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 1

Worked Example 3

Problem: What digit is in the tenths place of 74.789?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 7

Worked Example 4

Problem: What digit is in the tenths place of 57.611?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 6

Worked Example 5

Problem: What digit is in the tenths place of 17.254?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 2

Worked Example 6

Problem: What digit is in the tenths place of 88.182?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 1

Worked Example 7

Problem: What digit is in the tenths place of 50.014?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 0

Worked Example 8

Problem: What digit is in the tenths place of 53.265?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 2

Worked Example 9

Problem: What digit is in the tenths place of 38.558?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 5

Worked Example 10

Problem: What digit is in the tenths place of 1.477?

  1. The first digit to the right of the decimal point is the tenths digit.

Very beginner explanation: Decimal places move right from tenths to hundredths to thousandths.

Answer: 4

Practice Exercise

Create one new Grade 6 problem about Aligning decimal places. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is lining up the last digits instead of lining up decimal points and place values.

11.6 Regrouping in addition

Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Regrouping in addition to analyze the values 25 and 3. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Regrouping in addition to analyze the values 26 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Regrouping in addition to analyze the values 15 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Regrouping in addition to analyze the values 18 and 12. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Regrouping in addition to analyze the values 16 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Regrouping in addition to analyze the values 22 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Regrouping in addition to analyze the values 27 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Regrouping in addition to analyze the values 26 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Regrouping in addition to analyze the values 8 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Regrouping in addition to analyze the values 26 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Regrouping in addition. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

11.7 Regrouping in subtraction

Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Regrouping in subtraction to analyze the values 15 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Regrouping in subtraction to analyze the values 8 and 8. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Regrouping in subtraction to analyze the values 14 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Regrouping in subtraction to analyze the values 4 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Regrouping in subtraction to analyze the values 15 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Regrouping in subtraction to analyze the values 6 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Regrouping in subtraction to analyze the values 20 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Regrouping in subtraction to analyze the values 3 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Regrouping in subtraction to analyze the values 13 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Regrouping in subtraction to analyze the values 5 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Regrouping in subtraction. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

11.8 Mental addition strategies

A rate compares two quantities measured in different units. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: 14 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 14 ÷ 7 = 2.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 2 per group

Worked Example 2

Problem: 10 units are used in 5 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 10 ÷ 5 = 2.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 2 per group

Worked Example 3

Problem: 84 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 84 ÷ 7 = 12.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 12 per group

Worked Example 4

Problem: 20 units are used in 10 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 20 ÷ 10 = 2.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 2 per group

Worked Example 5

Problem: 30 units are used in 10 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 30 ÷ 10 = 3.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 3 per group

Worked Example 6

Problem: 56 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 56 ÷ 7 = 8.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 8 per group

Worked Example 7

Problem: 72 units are used in 9 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 72 ÷ 9 = 8.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 8 per group

Worked Example 8

Problem: 6 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 6 ÷ 3 = 2.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 2 per group

Worked Example 9

Problem: 64 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 64 ÷ 8 = 8.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 8 per group

Worked Example 10

Problem: 8 units are used in 4 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 8 ÷ 4 = 2.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 2 per group

Practice Exercise

Create one new Grade 6 problem about Mental addition strategies. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

11.9 Mental subtraction strategies

A rate compares two quantities measured in different units. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: 117 units are used in 13 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 117 ÷ 13 = 9.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 9 per group

Worked Example 2

Problem: 32 units are used in 4 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 32 ÷ 4 = 8.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 8 per group

Worked Example 3

Problem: 24 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 24 ÷ 3 = 8.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 8 per group

Worked Example 4

Problem: 16 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 16 ÷ 8 = 2.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 2 per group

Worked Example 5

Problem: 18 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 18 ÷ 3 = 6.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 6 per group

Worked Example 6

Problem: 40 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 40 ÷ 8 = 5.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 5 per group

Worked Example 7

Problem: 50 units are used in 5 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 50 ÷ 5 = 10.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 10 per group

Worked Example 8

Problem: 60 units are used in 10 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 60 ÷ 10 = 6.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 6 per group

Worked Example 9

Problem: 35 units are used in 7 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 35 ÷ 7 = 5.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 5 per group

Worked Example 10

Problem: 48 units are used in 8 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 48 ÷ 8 = 6.

Very beginner explanation: A unit rate tells the amount for one unit of the second quantity.

Answer: 6 per group

Practice Exercise

Create one new Grade 6 problem about Mental subtraction strategies. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

11.10 Estimating sums and differences

Estimating sums and differences is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 49,426 - 16,413.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 33,013

Worked Example 2

Problem: Calculate 15,323 - 10,468.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 4,855

Worked Example 3

Problem: Calculate 29,181 - 7,285.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 21,896

Worked Example 4

Problem: Calculate 32,281 - 11,647.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 20,634

Worked Example 5

Problem: Calculate 76,491 - 10,402.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 66,089

Worked Example 6

Problem: Calculate 11,387 - 10,815.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 572

Worked Example 7

Problem: Calculate 87,109 - 18,780.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 68,329

Worked Example 8

Problem: Calculate 64,992 - 7,275.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 57,717

Worked Example 9

Problem: Calculate 81,111 - 5,995.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 75,116

Worked Example 10

Problem: Calculate 56,927 - 16,952.

  1. Align place values.
  2. Regroup when needed.
  3. Estimate to check.

Very beginner explanation: Keeping ones with ones, tens with tens, and so on prevents place-value errors.

Answer: 39,975

Practice Exercise

Create one new Grade 6 problem about Estimating sums and differences. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

11.11 Money applications

Money applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A goal requires saving $20 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $120

Worked Example 2

Problem: A goal requires saving $25 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $150

Worked Example 3

Problem: A goal requires saving $30 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $180

Worked Example 4

Problem: A goal requires saving $35 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $210

Worked Example 5

Problem: A goal requires saving $40 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $240

Worked Example 6

Problem: A goal requires saving $45 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $270

Worked Example 7

Problem: A goal requires saving $50 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $300

Worked Example 8

Problem: A goal requires saving $55 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $330

Worked Example 9

Problem: A goal requires saving $60 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $360

Worked Example 10

Problem: A goal requires saving $65 each month for 6 months. How much will be saved?

  1. Multiply monthly saving by number of months.

Very beginner explanation: Breaking a goal into regular steps makes progress easier to plan and track.

Answer: $390

Practice Exercise

Create one new Grade 6 problem about Money applications. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

11.12 Measurement applications

Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Measurement applications to analyze the values 11 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Measurement applications to analyze the values 27 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Measurement applications to analyze the values 17 and 8. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Measurement applications to analyze the values 10 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Measurement applications to analyze the values 8 and 11. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Measurement applications to analyze the values 10 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Measurement applications to analyze the values 16 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Measurement applications to analyze the values 9 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Measurement applications to analyze the values 29 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Measurement applications to analyze the values 2 and 8. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Measurement applications. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

11.13 Checking with inverse operations

A ratio compares two quantities by division. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Simplify the ratio 10:8.

  1. Find the greatest common factor, 2.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 5:4

Worked Example 2

Problem: Simplify the ratio 6:14.

  1. Find the greatest common factor, 2.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 3:7

Worked Example 3

Problem: Simplify the ratio 11:4.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 11:4

Worked Example 4

Problem: Simplify the ratio 6:13.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 6:13

Worked Example 5

Problem: Simplify the ratio 7:8.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 7:8

Worked Example 6

Problem: Simplify the ratio 4:8.

  1. Find the greatest common factor, 4.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 1:2

Worked Example 7

Problem: Simplify the ratio 9:6.

  1. Find the greatest common factor, 3.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 3:2

Worked Example 8

Problem: Simplify the ratio 10:3.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 10:3

Worked Example 9

Problem: Simplify the ratio 11:7.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 11:7

Worked Example 10

Problem: Simplify the ratio 5:6.

  1. Find the greatest common factor, 1.
  2. Divide both parts by the same factor.

Very beginner explanation: A ratio is simplified the same way as a fraction.

Answer: 5:6

Practice Exercise

Create one new Grade 6 problem about Checking with inverse operations. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

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30 Review Questions and Answers

Q1. What is important to understand about Adding whole numbers?

Answer: Adding whole numbers is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q2. What is important to understand about Subtracting whole numbers?

Answer: Subtracting whole numbers is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q3. What is important to understand about Adding decimals?

Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.

Q4. What is important to understand about Subtracting decimals?

Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.

Q5. What is important to understand about Aligning decimal places?

Answer: A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.

Q6. What is important to understand about Regrouping in addition?

Answer: Regrouping in addition is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q7. What is important to understand about Regrouping in subtraction?

Answer: Regrouping in subtraction is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q8. What is important to understand about Mental addition strategies?

Answer: A rate compares two quantities measured in different units.

Q9. What is important to understand about Mental subtraction strategies?

Answer: A rate compares two quantities measured in different units.

Q10. What is important to understand about Estimating sums and differences?

Answer: Estimating sums and differences is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q11. What is important to understand about Money applications?

Answer: Money applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q12. What is important to understand about Measurement applications?

Answer: Measurement applications is a Grade 6 mathematics idea in Adding and Subtracting Whole Numbers and Decimals. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. What is important to understand about Checking with inverse operations?

Answer: A ratio compares two quantities by division.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q16. Why do units matter?

Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.

Q17. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q23. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q24. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q25. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q26. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q27. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q28. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.

Q29. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.

Q30. Why should you compare an exact answer with an estimate?

Answer: The estimate gives a quick reasonableness check for the exact calculation.