EASYTUTORGUIDE

Practical tutorials, tools, courses, digital skills, and business promotion.

Free Learning
Google Translate — English / فارسی / العربية
EasyTutorGuide LogoLearn, Build, & Grow

Chapter 14: Order of Operations and Multi-Operation Problems

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
Advertisement area — AdSense / Auto Ads

Chapter Overview

This chapter teaches Order of Operations and Multi-Operation Problems in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Grouping symbols (Grouping symbols is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Multiplication and division first (Multiplication and division first is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Addition and subtraction after multiplication and division (Addition and subtraction after multiplication and division is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Left-to-right rules (Left-to-right rules is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Order of operations with whole numbers (A ratio compares two quantities by division.)
  • Order of operations with decimals (A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.)

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.

14.1 Grouping symbols

Grouping symbols is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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: Evaluate 11 + 10 × 6.

  1. Do multiplication before addition.
  2. 10 × 6 = 60.
  3. Then add 11.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 71

Worked Example 2

Problem: Evaluate 3 + 3 × 7.

  1. Do multiplication before addition.
  2. 3 × 7 = 21.
  3. Then add 3.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 24

Worked Example 3

Problem: Evaluate 10 + 4 × 6.

  1. Do multiplication before addition.
  2. 4 × 6 = 24.
  3. Then add 10.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 34

Worked Example 4

Problem: Evaluate 12 + 6 × 9.

  1. Do multiplication before addition.
  2. 6 × 9 = 54.
  3. Then add 12.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 66

Worked Example 5

Problem: Evaluate 5 + 2 × 3.

  1. Do multiplication before addition.
  2. 2 × 3 = 6.
  3. Then add 5.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 11

Worked Example 6

Problem: Evaluate 10 + 6 × 4.

  1. Do multiplication before addition.
  2. 6 × 4 = 24.
  3. Then add 10.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 34

Worked Example 7

Problem: Evaluate 10 + 9 × 9.

  1. Do multiplication before addition.
  2. 9 × 9 = 81.
  3. Then add 10.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 91

Worked Example 8

Problem: Evaluate 4 + 9 × 6.

  1. Do multiplication before addition.
  2. 9 × 6 = 54.
  3. Then add 4.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 58

Worked Example 9

Problem: Evaluate 6 + 4 × 5.

  1. Do multiplication before addition.
  2. 4 × 5 = 20.
  3. Then add 6.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 26

Worked Example 10

Problem: Evaluate 9 + 3 × 7.

  1. Do multiplication before addition.
  2. 3 × 7 = 21.
  3. Then add 9.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 30

Practice Exercise

Create one new Grade 6 problem about Grouping symbols. 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.

14.2 Multiplication and division first

Multiplication and division first is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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: Find 1% of 80.

  1. Think of 1% as 1/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 0.8

Worked Example 2

Problem: Find 5% of 120.

  1. Think of 5% as 5/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6

Worked Example 3

Problem: Find 10% of 64.

  1. Think of 10% as 10/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6.4

Worked Example 4

Problem: Find 20% of 250.

  1. Think of 20% as 20/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 50

Worked Example 5

Problem: Find 25% of 96.

  1. Think of 25% as 25/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 24

Worked Example 6

Problem: Find 50% of 40.

  1. Think of 50% as 50/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 20

Worked Example 7

Problem: Find 75% of 200.

  1. Think of 75% as 75/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 150

Worked Example 8

Problem: Find 15% of 60.

  1. Think of 15% as 15/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 9

Worked Example 9

Problem: Find 30% of 150.

  1. Think of 30% as 30/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 45

Worked Example 10

Problem: Find 40% of 90.

  1. Think of 40% as 40/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 36

Practice Exercise

Create one new Grade 6 problem about Multiplication and division first. 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.

14.3 Addition and subtraction after multiplication and division

Addition and subtraction after multiplication and division is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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: Find 1% of 80.

  1. Think of 1% as 1/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 0.8

Worked Example 2

Problem: Find 5% of 120.

  1. Think of 5% as 5/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6

Worked Example 3

Problem: Find 10% of 64.

  1. Think of 10% as 10/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 6.4

Worked Example 4

Problem: Find 20% of 250.

  1. Think of 20% as 20/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 50

Worked Example 5

Problem: Find 25% of 96.

  1. Think of 25% as 25/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 24

Worked Example 6

Problem: Find 50% of 40.

  1. Think of 50% as 50/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 20

Worked Example 7

Problem: Find 75% of 200.

  1. Think of 75% as 75/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 150

Worked Example 8

Problem: Find 15% of 60.

  1. Think of 15% as 15/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 9

Worked Example 9

Problem: Find 30% of 150.

  1. Think of 30% as 30/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 45

Worked Example 10

Problem: Find 40% of 90.

  1. Think of 40% as 40/100.
  2. Multiply the quantity by the percent as a decimal or fraction.

Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.

Answer: 36

Practice Exercise

Create one new Grade 6 problem about Addition and subtraction after multiplication and division. 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.

14.4 Left-to-right rules

Left-to-right rules is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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: Evaluate 10 + 4 × 4.

  1. Do multiplication before addition.
  2. 4 × 4 = 16.
  3. Then add 10.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 26

Worked Example 2

Problem: Evaluate 12 + 6 × 3.

  1. Do multiplication before addition.
  2. 6 × 3 = 18.
  3. Then add 12.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 30

Worked Example 3

Problem: Evaluate 6 + 5 × 3.

  1. Do multiplication before addition.
  2. 5 × 3 = 15.
  3. Then add 6.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 21

Worked Example 4

Problem: Evaluate 8 + 8 × 4.

  1. Do multiplication before addition.
  2. 8 × 4 = 32.
  3. Then add 8.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 40

Worked Example 5

Problem: Evaluate 11 + 5 × 3.

  1. Do multiplication before addition.
  2. 5 × 3 = 15.
  3. Then add 11.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 26

Worked Example 6

Problem: Evaluate 7 + 5 × 8.

  1. Do multiplication before addition.
  2. 5 × 8 = 40.
  3. Then add 7.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 47

Worked Example 7

Problem: Evaluate 4 + 4 × 6.

  1. Do multiplication before addition.
  2. 4 × 6 = 24.
  3. Then add 4.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 28

Worked Example 8

Problem: Evaluate 12 + 6 × 2.

  1. Do multiplication before addition.
  2. 6 × 2 = 12.
  3. Then add 12.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 24

Worked Example 9

Problem: Evaluate 9 + 10 × 4.

  1. Do multiplication before addition.
  2. 10 × 4 = 40.
  3. Then add 9.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 49

Worked Example 10

Problem: Evaluate 8 + 10 × 8.

  1. Do multiplication before addition.
  2. 10 × 8 = 80.
  3. Then add 8.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 88

Practice Exercise

Create one new Grade 6 problem about Left-to-right rules. 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.

14.5 Order of operations with whole numbers

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: Compare 281,763 and 281,267.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 281,763 > 281,267

Worked Example 2

Problem: Compare 366,978 and 368,449.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 366,978 < 368,449

Worked Example 3

Problem: Compare 263,874 and 262,737.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 263,874 > 262,737

Worked Example 4

Problem: Compare 58,795 and 61,617.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 58,795 < 61,617

Worked Example 5

Problem: Compare 451,561 and 455,473.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 451,561 < 455,473

Worked Example 6

Problem: Compare 722,815 and 722,430.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 722,815 > 722,430

Worked Example 7

Problem: Compare 730,427 and 727,284.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 730,427 > 727,284

Worked Example 8

Problem: Compare 875,669 and 870,970.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 875,669 > 870,970

Worked Example 9

Problem: Compare 981,713 and 978,543.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 981,713 > 978,543

Worked Example 10

Problem: Compare 53,886 and 56,721.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 53,886 < 56,721

Practice Exercise

Create one new Grade 6 problem about Order of operations with 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.

14.6 Order of operations with 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: Compare 54.736 and 13.632.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 54.736 > 13.632

Worked Example 2

Problem: Compare 32.383 and 16.811.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 32.383 > 16.811

Worked Example 3

Problem: Compare 29.483 and 2.391.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 29.483 > 2.391

Worked Example 4

Problem: Compare 10.975 and 16.367.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 10.975 < 16.367

Worked Example 5

Problem: Compare 91.4 and 3.624.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 91.4 > 3.624

Worked Example 6

Problem: Compare 61.746 and 8.461.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 61.746 > 8.461

Worked Example 7

Problem: Compare 60.693 and 1.858.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 60.693 > 1.858

Worked Example 8

Problem: Compare 76.785 and 8.643.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 76.785 > 8.643

Worked Example 9

Problem: Compare 90.042 and 14.885.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 90.042 > 14.885

Worked Example 10

Problem: Compare 51.692 and 6.898.

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and thousandths.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 51.692 > 6.898

Practice Exercise

Create one new Grade 6 problem about Order of operations with 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.

14.7 Order of operations with fractions

A fraction represents equal parts of a whole, set, or quantity. 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: Compare 1/2 and 1/3.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 1/2 > 1/3

Worked Example 2

Problem: Compare 2/3 and 1/4.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 2/3 > 1/4

Worked Example 3

Problem: Compare 3/5 and 2/7.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 3/5 > 2/7

Worked Example 4

Problem: Compare 5/8 and 1/6.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 5/8 > 1/6

Worked Example 5

Problem: Compare 7/10 and 3/5.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 7/10 > 3/5

Worked Example 6

Problem: Compare 4/9 and 5/12.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 4/9 > 5/12

Worked Example 7

Problem: Compare 5/6 and 1/8.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 5/6 > 1/8

Worked Example 8

Problem: Compare 3/4 and 7/9.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 3/4 < 7/9

Worked Example 9

Problem: Compare 2/5 and 4/15.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 2/5 > 4/15

Worked Example 10

Problem: Compare 7/12 and 5/18.

  1. Use a common denominator, decimal value, or benchmark fraction.

Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.

Answer: 7/12 > 5/18

Practice Exercise

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

Common Mistake

A common mistake is combining numerators and denominators without first applying the correct fraction rule.

14.8 Multi-operation expressions

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 8:11.

  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: 8:11

Worked Example 2

Problem: Simplify the ratio 3:5.

  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: 3:5

Worked Example 3

Problem: Simplify the ratio 7:9.

  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: 7:9

Worked Example 4

Problem: Simplify the ratio 6:15.

  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: 2:5

Worked Example 5

Problem: Simplify the ratio 4:4.

  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: 1:1

Worked Example 6

Problem: Simplify the ratio 7:15.

  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: 7:15

Worked Example 7

Problem: Simplify the ratio 8:5.

  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: 8:5

Worked Example 8

Problem: Simplify the ratio 10:5.

  1. Find the greatest common factor, 5.
  2. Divide both parts by the same factor.

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

Answer: 2:1

Worked Example 9

Problem: Simplify the ratio 4:12.

  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: 1:3

Worked Example 10

Problem: Simplify the ratio 4:9.

  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: 4:9

Practice Exercise

Create one new Grade 6 problem about Multi-operation expressions. 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.

14.9 Translating words into expressions

An algebraic expression combines numbers, variables, and operations without an equals sign. 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: Evaluate 3x + 4 when x = 5.

  1. Replace x with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 2

Problem: Evaluate 2n + 7 when n = 6.

  1. Replace n with 6.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 19

Worked Example 3

Problem: Evaluate 5a - 3 when a = 4.

  1. Replace a with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 17

Worked Example 4

Problem: Evaluate 4p + 1 when p = 8.

  1. Replace p with 8.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 33

Worked Example 5

Problem: Evaluate 6m - 5 when m = 3.

  1. Replace m with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 13

Worked Example 6

Problem: Evaluate 2.5x + 1 when x = 4.

  1. Replace x with 4.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 11

Worked Example 7

Problem: Evaluate 7q + 2 when q = 2.

  1. Replace q with 2.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 16

Worked Example 8

Problem: Evaluate 3r - 1 when r = 9.

  1. Replace r with 9.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 9

Problem: Evaluate 4y + 6 when y = 5.

  1. Replace y with 5.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 26

Worked Example 10

Problem: Evaluate 8k - 4 when k = 3.

  1. Replace k with 3.
  2. Follow order of operations.
  3. Calculate carefully.

Very beginner explanation: Substitution replaces a variable with a known value before calculating.

Answer: 20

Practice Exercise

Create one new Grade 6 problem about Translating words into expressions. 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.

14.10 Multi-step word problems

Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems to analyze the values 25 and 5. 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems to analyze the values 20 and 13. 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems to analyze the values 14 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems to analyze the values 9 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems to analyze the values 3 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems to analyze the values 28 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems to analyze the values 26 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems to analyze the values 9 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems to analyze the values 24 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: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multi-step word problems. 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.

14.11 Estimating before calculating

Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 14 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 13 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 11 and 5. 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 11 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 19 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 30 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 17 and 10. 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 10 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 3 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating to analyze the values 5 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: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating. 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.

14.12 Calculator checks

Calculator checks is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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: Evaluate 8 + 6 × 8.

  1. Do multiplication before addition.
  2. 6 × 8 = 48.
  3. Then add 8.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 56

Worked Example 2

Problem: Evaluate 10 + 4 × 8.

  1. Do multiplication before addition.
  2. 4 × 8 = 32.
  3. Then add 10.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 42

Worked Example 3

Problem: Evaluate 6 + 6 × 2.

  1. Do multiplication before addition.
  2. 6 × 2 = 12.
  3. Then add 6.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 18

Worked Example 4

Problem: Evaluate 9 + 3 × 4.

  1. Do multiplication before addition.
  2. 3 × 4 = 12.
  3. Then add 9.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 21

Worked Example 5

Problem: Evaluate 12 + 2 × 6.

  1. Do multiplication before addition.
  2. 2 × 6 = 12.
  3. Then add 12.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 24

Worked Example 6

Problem: Evaluate 5 + 5 × 9.

  1. Do multiplication before addition.
  2. 5 × 9 = 45.
  3. Then add 5.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 50

Worked Example 7

Problem: Evaluate 2 + 7 × 6.

  1. Do multiplication before addition.
  2. 7 × 6 = 42.
  3. Then add 2.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 44

Worked Example 8

Problem: Evaluate 11 + 8 × 3.

  1. Do multiplication before addition.
  2. 8 × 3 = 24.
  3. Then add 11.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 35

Worked Example 9

Problem: Evaluate 2 + 6 × 2.

  1. Do multiplication before addition.
  2. 6 × 2 = 12.
  3. Then add 2.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 14

Worked Example 10

Problem: Evaluate 8 + 2 × 3.

  1. Do multiplication before addition.
  2. 2 × 3 = 6.
  3. Then add 8.

Very beginner explanation: Order of operations makes sure everyone interprets the same expression consistently.

Answer: 14

Practice Exercise

Create one new Grade 6 problem about Calculator checks. 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.

14.13 Common order-of-operations mistakes

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 4:11.

  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: 4:11

Worked Example 2

Problem: Simplify the ratio 2:9.

  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: 2:9

Worked Example 3

Problem: Simplify the ratio 2:5.

  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: 2:5

Worked Example 4

Problem: Simplify the ratio 7:7.

  1. Find the greatest common factor, 7.
  2. Divide both parts by the same factor.

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

Answer: 1:1

Worked Example 5

Problem: Simplify the ratio 2:9.

  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: 2:9

Worked Example 6

Problem: Simplify the ratio 10:15.

  1. Find the greatest common factor, 5.
  2. Divide both parts by the same factor.

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

Answer: 2:3

Worked Example 7

Problem: Simplify the ratio 8:8.

  1. Find the greatest common factor, 8.
  2. Divide both parts by the same factor.

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

Answer: 1:1

Worked Example 8

Problem: Simplify the ratio 5:7.

  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: 5:7

Worked Example 9

Problem: Simplify the ratio 4:4.

  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: 1:1

Worked Example 10

Problem: Simplify the ratio 9:9.

  1. Find the greatest common factor, 9.
  2. Divide both parts by the same factor.

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

Answer: 1:1

Practice Exercise

Create one new Grade 6 problem about Common order-of-operations mistakes. 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.

Advertisement area — AdSense / Auto Ads

30 Review Questions and Answers

Q1. What is important to understand about Grouping symbols?

Answer: Grouping symbols is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Multiplication and division first?

Answer: Multiplication and division first is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Addition and subtraction after multiplication and division?

Answer: Addition and subtraction after multiplication and division is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q4. What is important to understand about Left-to-right rules?

Answer: Left-to-right rules is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q5. What is important to understand about Order of operations with whole numbers?

Answer: A ratio compares two quantities by division.

Q6. What is important to understand about Order of operations with decimals?

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

Q7. What is important to understand about Order of operations with fractions?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q8. What is important to understand about Multi-operation expressions?

Answer: A ratio compares two quantities by division.

Q9. What is important to understand about Translating words into expressions?

Answer: An algebraic expression combines numbers, variables, and operations without an equals sign.

Q10. What is important to understand about Multi-step word problems?

Answer: Multi-step word problems is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Estimating before calculating?

Answer: Estimating before calculating is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Calculator checks?

Answer: Calculator checks is a Grade 6 mathematics idea in Order of Operations and Multi-Operation Problems. 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 Common order-of-operations mistakes?

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.