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Chapter 12: Multiplying 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 Multiplying 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

  • Multiplication facts and fluency (Multiplication facts and fluency is a Grade 6 mathematics idea in Multiplying 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.)
  • Multiplication properties (Multiplication properties is a Grade 6 mathematics idea in Multiplying 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.)
  • Multiplying multi-digit whole numbers (Multiplying multi-digit whole numbers is a Grade 6 mathematics idea in Multiplying 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.)
  • Partial products (Partial products is a Grade 6 mathematics idea in Multiplying 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.)
  • Multiplying a decimal by a whole number (A decimal uses place value to show parts of one, such as tenths, hundredths, and thousandths.)
  • Place value in decimal products (Place value is the value a digit has because of its position in a number.)

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.

12.1 Multiplication facts and fluency

Multiplication facts and fluency is a Grade 6 mathematics idea in Multiplying 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: 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 facts and fluency. 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.

12.2 Multiplication properties

Multiplication properties is a Grade 6 mathematics idea in Multiplying 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: 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 properties. 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.

12.3 Multiplying multi-digit whole numbers

Multiplying multi-digit whole numbers is a Grade 6 mathematics idea in Multiplying 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 728,974, 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 2

Problem: In 797,747, what is the value of the digit 9 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: 90,000

Worked Example 3

Problem: In 472,892, what is the value of the digit 8 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: 800

Worked Example 4

Problem: In 131,648, 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 5

Problem: In 888,035, 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 6

Problem: In 186,109, what is the value of the digit 0 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: 0

Worked Example 7

Problem: In 647,346, what is the value of the digit 4 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: 40,000

Worked Example 8

Problem: In 704,549, what is the value of the digit 5 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: 500

Worked Example 9

Problem: In 735,194, what is the value of the digit 3 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: 30,000

Worked Example 10

Problem: In 868,730, what is the value of the digit 6 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: 60,000

Practice Exercise

Create one new Grade 6 problem about Multiplying multi-digit 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.

12.4 Partial products

Partial products is a Grade 6 mathematics idea in Multiplying 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 200 × 42.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 8,400

Worked Example 2

Problem: Calculate 70 × 27.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 1,890

Worked Example 3

Problem: Calculate 276 × 5.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 1,380

Worked Example 4

Problem: Calculate 237 × 33.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 7,821

Worked Example 5

Problem: Calculate 245 × 27.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 6,615

Worked Example 6

Problem: Calculate 73 × 39.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 2,847

Worked Example 7

Problem: Calculate 274 × 43.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 11,782

Worked Example 8

Problem: Calculate 165 × 6.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 990

Worked Example 9

Problem: Calculate 315 × 37.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 11,655

Worked Example 10

Problem: Calculate 258 × 28.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 7,224

Practice Exercise

Create one new Grade 6 problem about Partial products. 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.

12.5 Multiplying a decimal by a whole number

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: In 196,602, 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 2

Problem: In 216,115, what is the value of the digit 6 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: 6,000

Worked Example 3

Problem: In 791,529, 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 4

Problem: In 377,303, 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 5

Problem: In 371,080, what is the value of the digit 8 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: 80

Worked Example 6

Problem: In 139,480, what is the value of the digit 8 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: 80

Worked Example 7

Problem: In 617,685, what is the value of the digit 8 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: 80

Worked Example 8

Problem: In 898,170, what is the value of the digit 1 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: 100

Worked Example 9

Problem: In 101,449, what is the value of the digit 4 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: 400

Worked Example 10

Problem: In 84,466, 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

Practice Exercise

Create one new Grade 6 problem about Multiplying a decimal by a whole number. 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.

12.6 Multiplying 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 70.656 × 17.485.

  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: 1236.48

Worked Example 2

Problem: Calculate 62.252 × 16.655.

  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: 1039.608

Worked Example 3

Problem: Calculate 56.507 × 3.54.

  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: 197.774

Worked Example 4

Problem: Calculate 60.214 × 14.387.

  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: 867.082

Worked Example 5

Problem: Calculate 89.303 × 0.929.

  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: 80.373

Worked Example 6

Problem: Calculate 17.181 × 19.326.

  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: 331.593

Worked Example 7

Problem: Calculate 59.439 × 5.453.

  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: 326.914

Worked Example 8

Problem: Calculate 81.45 × 3.662.

  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: 301.365

Worked Example 9

Problem: Calculate 46.798 × 0.662.

  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: 32.759

Worked Example 10

Problem: Calculate 35.293 × 6.598.

  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: 232.934

Practice Exercise

Create one new Grade 6 problem about Multiplying 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.

12.7 Place value in decimal products

Place value is the value a digit has because of its position in a number. 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 162,659, what is the value of the digit 5 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: 50

Worked Example 2

Problem: In 510,538, 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 3

Problem: In 831,135, 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 114,266, 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 5

Problem: In 41,620, 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 6

Problem: In 33,368, 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 7

Problem: In 846,732, what is the value of the digit 7 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: 700

Worked Example 8

Problem: In 554,296, 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 238,724, 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 10

Problem: In 584,723, 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

Practice Exercise

Create one new Grade 6 problem about Place value in decimal products. 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.

12.8 Estimating products

Estimating products is a Grade 6 mathematics idea in Multiplying 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 159 × 25.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 3,975

Worked Example 2

Problem: Calculate 54 × 12.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 648

Worked Example 3

Problem: Calculate 301 × 6.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 1,806

Worked Example 4

Problem: Calculate 98 × 33.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 3,234

Worked Example 5

Problem: Calculate 122 × 33.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 4,026

Worked Example 6

Problem: Calculate 260 × 43.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 11,180

Worked Example 7

Problem: Calculate 118 × 25.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 2,950

Worked Example 8

Problem: Calculate 23 × 27.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 621

Worked Example 9

Problem: Calculate 232 × 4.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 928

Worked Example 10

Problem: Calculate 72 × 39.

  1. Break one factor into place-value parts if helpful.
  2. Multiply each part.
  3. Add partial products.
  4. Estimate to check.

Very beginner explanation: Multiplication combines equal groups and can be decomposed using place value.

Answer: 2,808

Practice Exercise

Create one new Grade 6 problem about Estimating products. 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.

12.9 Area-model multiplication

The mode is the value that appears most often. 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 Area-model multiplication. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is using the wrong formula or forgetting square units for area.

12.10 Money multiplication

Money multiplication is a Grade 6 mathematics idea in Multiplying 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: 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 Money multiplication. 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.

12.11 Measurement multiplication

Measurement multiplication is a Grade 6 mathematics idea in Multiplying 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: 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 Measurement multiplication. 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.

12.12 Checking multiplication

Checking multiplication is a Grade 6 mathematics idea in Multiplying 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: 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 Checking multiplication. 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 Multiplication facts and fluency?

Answer: Multiplication facts and fluency is a Grade 6 mathematics idea in Multiplying 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 Multiplication properties?

Answer: Multiplication properties is a Grade 6 mathematics idea in Multiplying 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 Multiplying multi-digit whole numbers?

Answer: Multiplying multi-digit whole numbers is a Grade 6 mathematics idea in Multiplying 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.

Q4. What is important to understand about Partial products?

Answer: Partial products is a Grade 6 mathematics idea in Multiplying 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.

Q5. What is important to understand about Multiplying a decimal by a whole number?

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

Q6. What is important to understand about Multiplying 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 Place value in decimal products?

Answer: Place value is the value a digit has because of its position in a number.

Q8. What is important to understand about Estimating products?

Answer: Estimating products is a Grade 6 mathematics idea in Multiplying 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.

Q9. What is important to understand about Area-model multiplication?

Answer: The mode is the value that appears most often.

Q10. What is important to understand about Money multiplication?

Answer: Money multiplication is a Grade 6 mathematics idea in Multiplying 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 Measurement multiplication?

Answer: Measurement multiplication is a Grade 6 mathematics idea in Multiplying 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 Checking multiplication?

Answer: Checking multiplication is a Grade 6 mathematics idea in Multiplying 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. Why should you show your steps?

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

Q14. Why is estimation useful?

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

Q15. Why do units matter?

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

Q16. When should you round?

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

Q17. How can you check an answer?

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

Q18. What should you identify first in a word problem?

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

Q19. What makes a final answer complete?

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

Q20. What should you do if an answer seems unreasonable?

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

Q21. Why are diagrams useful?

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

Q22. Why are tables useful?

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

Q23. Why are graphs useful?

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

Q24. Why should you explain your reasoning?

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

Q25. Why can more than one strategy be correct?

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

Q26. What should you do before using a formula or rule?

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

Q27. How does practice help in mathematics?

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

Q28. 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.

Q29. Why should you compare an exact answer with an estimate?

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

Q30. What does representing mathematics mean?

Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.