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Chapter 13: Dividing 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 Dividing 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

  • Division facts and fact families (Division facts and fact families is a Grade 6 mathematics idea in Dividing 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.)
  • Dividing by one-digit divisors (Dividing by one-digit divisors is a Grade 6 mathematics idea in Dividing 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.)
  • Dividing three-digit numbers (Dividing three-digit numbers is a Grade 6 mathematics idea in Dividing 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.)
  • Dividing by two-digit divisors (Dividing by two-digit divisors is a Grade 6 mathematics idea in Dividing 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.)
  • Remainders (Remainders is a Grade 6 mathematics idea in Dividing 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.)
  • Decimal dividends (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.

13.1 Division facts and fact families

Division facts and fact families is a Grade 6 mathematics idea in Dividing 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 1377 ÷ 17.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 81

Worked Example 2

Problem: Calculate 316 ÷ 17.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 18 remainder 10

Worked Example 3

Problem: Calculate 2373 ÷ 21.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 113

Worked Example 4

Problem: Calculate 220 ÷ 2.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 110

Worked Example 5

Problem: Calculate 432 ÷ 12.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 36

Worked Example 6

Problem: Calculate 47 ÷ 2.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 23 remainder 1

Worked Example 7

Problem: Calculate 943 ÷ 23.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 41

Worked Example 8

Problem: Calculate 732 ÷ 5.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 146 remainder 2

Worked Example 9

Problem: Calculate 702 ÷ 9.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 78

Worked Example 10

Problem: Calculate 1692 ÷ 14.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 120 remainder 12

Practice Exercise

Create one new Grade 6 problem about Division facts and fact families. 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.

13.2 Dividing by one-digit divisors

Dividing by one-digit divisors is a Grade 6 mathematics idea in Dividing 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 940 ÷ 10.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 94

Worked Example 2

Problem: Calculate 534 ÷ 22.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 24 remainder 6

Worked Example 3

Problem: Calculate 792 ÷ 11.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 72

Worked Example 4

Problem: Calculate 1438 ÷ 10.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 143 remainder 8

Worked Example 5

Problem: Calculate 1064 ÷ 19.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 56

Worked Example 6

Problem: Calculate 91 ÷ 5.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 18 remainder 1

Worked Example 7

Problem: Calculate 822 ÷ 6.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 137

Worked Example 8

Problem: Calculate 588 ÷ 7.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 84

Worked Example 9

Problem: Calculate 901 ÷ 17.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 53

Worked Example 10

Problem: Calculate 1954 ÷ 17.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 114 remainder 16

Practice Exercise

Create one new Grade 6 problem about Dividing by one-digit divisors. 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.

13.3 Dividing three-digit numbers

Dividing three-digit numbers is a Grade 6 mathematics idea in Dividing 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 2682 ÷ 18.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 149

Worked Example 2

Problem: Calculate 2018 ÷ 21.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 96 remainder 2

Worked Example 3

Problem: Calculate 1386 ÷ 18.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 77

Worked Example 4

Problem: Calculate 1023 ÷ 22.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 46 remainder 11

Worked Example 5

Problem: Calculate 357 ÷ 7.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 51

Worked Example 6

Problem: Calculate 571 ÷ 9.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 63 remainder 4

Worked Example 7

Problem: Calculate 294 ÷ 6.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 49

Worked Example 8

Problem: Calculate 2692 ÷ 23.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 117 remainder 1

Worked Example 9

Problem: Calculate 1968 ÷ 24.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 82

Worked Example 10

Problem: Calculate 921 ÷ 20.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 46 remainder 1

Practice Exercise

Create one new Grade 6 problem about Dividing three-digit 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.

13.4 Dividing by two-digit divisors

Dividing by two-digit divisors is a Grade 6 mathematics idea in Dividing 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 710 ÷ 10.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 71

Worked Example 2

Problem: Calculate 1818 ÷ 13.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 139 remainder 11

Worked Example 3

Problem: Calculate 304 ÷ 19.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 16

Worked Example 4

Problem: Calculate 43 ÷ 3.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 14 remainder 1

Worked Example 5

Problem: Calculate 864 ÷ 18.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 48

Worked Example 6

Problem: Calculate 872 ÷ 17.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 51 remainder 5

Worked Example 7

Problem: Calculate 1365 ÷ 13.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 105

Worked Example 8

Problem: Calculate 1406 ÷ 10.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 140 remainder 6

Worked Example 9

Problem: Calculate 2400 ÷ 24.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 100

Worked Example 10

Problem: Calculate 162 ÷ 3.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 54

Practice Exercise

Create one new Grade 6 problem about Dividing by two-digit divisors. 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.

13.5 Remainders

Remainders is a Grade 6 mathematics idea in Dividing 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 1885 ÷ 13.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 145

Worked Example 2

Problem: Calculate 2932 ÷ 25.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 117 remainder 7

Worked Example 3

Problem: Calculate 1840 ÷ 20.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 92

Worked Example 4

Problem: Calculate 858 ÷ 9.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 95 remainder 3

Worked Example 5

Problem: Calculate 492 ÷ 6.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 82

Worked Example 6

Problem: Calculate 217 ÷ 2.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 108 remainder 1

Worked Example 7

Problem: Calculate 630 ÷ 15.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 42

Worked Example 8

Problem: Calculate 719 ÷ 16.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 44 remainder 15

Worked Example 9

Problem: Calculate 1365 ÷ 15.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 91

Worked Example 10

Problem: Calculate 1124 ÷ 17.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 66 remainder 2

Practice Exercise

Create one new Grade 6 problem about Remainders. 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.

13.6 Decimal dividends

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 76.496 ÷ 18.6.

  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: 4.113

Worked Example 2

Problem: Calculate 18.053 ÷ 2.3.

  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: 7.849

Worked Example 3

Problem: Calculate 56.593 ÷ 11.3.

  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: 5.008

Worked Example 4

Problem: Calculate 49.895 ÷ 16.4.

  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: 3.042

Worked Example 5

Problem: Calculate 94.007 ÷ 5.9.

  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: 15.933

Worked Example 6

Problem: Calculate 41.646 ÷ 12.6.

  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: 3.305

Worked Example 7

Problem: Calculate 65.712 ÷ 5.0.

  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: 13.142

Worked Example 8

Problem: Calculate 34.91 ÷ 9.8.

  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: 3.562

Worked Example 9

Problem: Calculate 48.95 ÷ 16.2.

  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: 3.022

Worked Example 10

Problem: Calculate 84.818 ÷ 14.0.

  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: 6.058

Practice Exercise

Create one new Grade 6 problem about Decimal dividends. 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.

13.7 Decimal quotients

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 68.343 ÷ 2.9.

  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: 23.567

Worked Example 2

Problem: Calculate 78.329 ÷ 6.6.

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

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

Answer: 11.868

Worked Example 3

Problem: Calculate 13.973 ÷ 3.9.

  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: 3.583

Worked Example 4

Problem: Calculate 72.694 ÷ 19.0.

  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: 3.826

Worked Example 5

Problem: Calculate 4.04 ÷ 19.3.

  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: 0.209

Worked Example 6

Problem: Calculate 39.022 ÷ 5.2.

  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: 7.504

Worked Example 7

Problem: Calculate 33.292 ÷ 8.4.

  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: 3.963

Worked Example 8

Problem: Calculate 60.236 ÷ 18.1.

  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: 3.328

Worked Example 9

Problem: Calculate 67.711 ÷ 1.2.

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

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

Answer: 56.426

Worked Example 10

Problem: Calculate 53.324 ÷ 10.6.

  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: 5.031

Practice Exercise

Create one new Grade 6 problem about Decimal quotients. 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.

13.8 Dividing decimals by whole numbers

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 161,916, 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 787,922, what is the value of the digit 7 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: 700,000

Worked Example 3

Problem: In 475,425, 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 4

Problem: In 98,181, 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 5

Problem: In 352,082, 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 480,205, what is the value of the digit 8 in the 10,000 place?

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

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

Answer: 80,000

Worked Example 7

Problem: In 170,612, what is the value of the digit 7 in the 10,000 place?

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

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

Answer: 70,000

Worked Example 8

Problem: In 224,489, what is the value of the digit 2 in the 10,000 place?

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

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

Answer: 20,000

Worked Example 9

Problem: In 85,149, what is the value of the digit 8 in the 10,000 place?

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

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

Answer: 80,000

Worked Example 10

Problem: In 46,366, 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 Dividing decimals by whole numbers. 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.

13.9 Estimating quotients

Estimating quotients is a Grade 6 mathematics idea in Dividing 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 2000 ÷ 20.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 100

Worked Example 2

Problem: Calculate 464 ÷ 5.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 92 remainder 4

Worked Example 3

Problem: Calculate 608 ÷ 16.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 38

Worked Example 4

Problem: Calculate 176 ÷ 4.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 44

Worked Example 5

Problem: Calculate 1311 ÷ 23.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 57

Worked Example 6

Problem: Calculate 97 ÷ 6.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 16 remainder 1

Worked Example 7

Problem: Calculate 598 ÷ 13.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 46

Worked Example 8

Problem: Calculate 2000 ÷ 24.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 83 remainder 8

Worked Example 9

Problem: Calculate 943 ÷ 23.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 41

Worked Example 10

Problem: Calculate 392 ÷ 5.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 78 remainder 2

Practice Exercise

Create one new Grade 6 problem about Estimating quotients. 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.

13.10 Money division

Money division is a Grade 6 mathematics idea in Dividing 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 1056 ÷ 24.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 44

Worked Example 2

Problem: Calculate 2397 ÷ 18.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 133 remainder 3

Worked Example 3

Problem: Calculate 2500 ÷ 20.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 125

Worked Example 4

Problem: Calculate 1160 ÷ 25.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 46 remainder 10

Worked Example 5

Problem: Calculate 72 ÷ 2.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 36

Worked Example 6

Problem: Calculate 1794 ÷ 13.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 138

Worked Example 7

Problem: Calculate 2120 ÷ 20.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 106

Worked Example 8

Problem: Calculate 920 ÷ 8.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 115

Worked Example 9

Problem: Calculate 195 ÷ 3.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 65

Worked Example 10

Problem: Calculate 3343 ÷ 23.

  1. Estimate the quotient.
  2. Divide using place value.
  3. Record any remainder.
  4. Multiply back to check.

Very beginner explanation: Division separates a quantity into equal groups or finds how many equal groups fit.

Answer: 145 remainder 8

Practice Exercise

Create one new Grade 6 problem about Money 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.

13.11 Rate applications

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

Beginner Note

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

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: 84 units are used in 12 equal groups. Find the unit rate.

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

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

Answer: 7 per group

Worked Example 2

Problem: 104 units are used in 13 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 104 ÷ 13 = 8.

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

Answer: 8 per group

Worked Example 3

Problem: 9 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 9 ÷ 3 = 3.

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

Answer: 3 per group

Worked Example 4

Problem: 33 units are used in 3 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 33 ÷ 3 = 11.

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

Answer: 11 per group

Worked Example 5

Problem: 35 units are used in 5 equal groups. Find the unit rate.

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

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

Answer: 7 per group

Worked Example 6

Problem: 75 units are used in 15 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 75 ÷ 15 = 5.

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

Answer: 5 per group

Worked Example 7

Problem: 77 units are used in 11 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 77 ÷ 11 = 7.

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

Answer: 7 per group

Worked Example 8

Problem: 50 units are used in 10 equal groups. Find the unit rate.

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

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

Answer: 5 per group

Worked Example 9

Problem: 35 units are used in 5 equal groups. Find the unit rate.

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

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

Answer: 7 per group

Worked Example 10

Problem: 66 units are used in 6 equal groups. Find the unit rate.

  1. Divide the first quantity by the second.
  2. 66 ÷ 6 = 11.

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

Answer: 11 per group

Practice Exercise

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

Common Mistake

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

13.12 Checking division with multiplication

Checking division with multiplication is a Grade 6 mathematics idea in Dividing 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 division with 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 Division facts and fact families?

Answer: Division facts and fact families is a Grade 6 mathematics idea in Dividing 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 Dividing by one-digit divisors?

Answer: Dividing by one-digit divisors is a Grade 6 mathematics idea in Dividing 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 Dividing three-digit numbers?

Answer: Dividing three-digit numbers is a Grade 6 mathematics idea in Dividing 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 Dividing by two-digit divisors?

Answer: Dividing by two-digit divisors is a Grade 6 mathematics idea in Dividing 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 Remainders?

Answer: Remainders is a Grade 6 mathematics idea in Dividing 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.

Q6. What is important to understand about Decimal dividends?

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

Q7. What is important to understand about Decimal quotients?

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

Q8. What is important to understand about Dividing decimals by whole numbers?

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

Q9. What is important to understand about Estimating quotients?

Answer: Estimating quotients is a Grade 6 mathematics idea in Dividing 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.

Q10. What is important to understand about Money division?

Answer: Money division is a Grade 6 mathematics idea in Dividing 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 Rate applications?

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

Q12. What is important to understand about Checking division with multiplication?

Answer: Checking division with multiplication is a Grade 6 mathematics idea in Dividing 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.