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Chapter 24: Two-Digit by One-Digit Division

Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 4Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Two-Digit by One-Digit Division in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

24.1 Division as sharing

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 13 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 4 remainder 1

Worked Example 2

Problem: Calculate 48 ÷ 5.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 9 remainder 3

Worked Example 3

Problem: Calculate 41 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 13 remainder 2

Worked Example 4

Problem: Calculate 77 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 9 remainder 5

Worked Example 5

Problem: Calculate 62 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 15 remainder 2

Worked Example 6

Problem: Calculate 111 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 18 remainder 3

Worked Example 7

Problem: Calculate 18 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 9

Worked Example 8

Problem: Calculate 29 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 4 remainder 1

Worked Example 9

Problem: Calculate 25 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 12 remainder 1

Worked Example 10

Problem: Calculate 79 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 19 remainder 3

Practice Exercise

Create and solve one new example of Division as sharing. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.2 Division as grouping

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 55 ÷ 5.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 11

Worked Example 2

Problem: Calculate 44 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 14 remainder 2

Worked Example 3

Problem: Calculate 24 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 8

Worked Example 4

Problem: Calculate 26 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 13

Worked Example 5

Problem: Calculate 15 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 5

Worked Example 6

Problem: Calculate 98 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 16 remainder 2

Worked Example 7

Problem: Calculate 30 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 15

Worked Example 8

Problem: Calculate 121 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 15 remainder 1

Worked Example 9

Problem: Calculate 142 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 17 remainder 6

Worked Example 10

Problem: Calculate 94 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 11 remainder 6

Practice Exercise

Create and solve one new example of Division as grouping. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.3 Using multiplication facts to divide

Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 5 × 3.

  1. Break 5 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 15

Worked Example 2

Problem: Calculate 5 × 3.

  1. Break 5 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 15

Worked Example 3

Problem: Calculate 12 × 5.

  1. Break 12 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 60

Worked Example 4

Problem: Calculate 5 × 4.

  1. Break 5 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 20

Worked Example 5

Problem: Calculate 3 × 4.

  1. Break 3 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 12

Worked Example 6

Problem: Calculate 2 × 5.

  1. Break 2 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 10

Worked Example 7

Problem: Calculate 7 × 5.

  1. Break 7 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 35

Worked Example 8

Problem: Calculate 4 × 9.

  1. Break 4 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 36

Worked Example 9

Problem: Calculate 3 × 9.

  1. Break 3 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 27

Worked Example 10

Problem: Calculate 2 × 7.

  1. Break 2 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 14

Practice Exercise

Create and solve one new example of Using multiplication facts to divide. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.4 Using arrays to divide

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 61 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 7 remainder 5

Worked Example 2

Problem: Calculate 17 ÷ 5.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 3 remainder 2

Worked Example 3

Problem: Calculate 57 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 8 remainder 1

Worked Example 4

Problem: Calculate 160 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 20

Worked Example 5

Problem: Calculate 50 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 12 remainder 2

Worked Example 6

Problem: Calculate 112 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 12 remainder 4

Worked Example 7

Problem: Calculate 35 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 17 remainder 1

Worked Example 8

Problem: Calculate 15 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 5

Worked Example 9

Problem: Calculate 100 ÷ 5.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 20

Worked Example 10

Problem: Calculate 69 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 7 remainder 6

Practice Exercise

Create and solve one new example of Using arrays to divide. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.5 Partial quotients

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 15 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 5

Worked Example 2

Problem: Calculate 134 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 16 remainder 6

Worked Example 3

Problem: Calculate 45 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 6 remainder 3

Worked Example 4

Problem: Calculate 25 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 6 remainder 1

Worked Example 5

Problem: Calculate 47 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 11 remainder 3

Worked Example 6

Problem: Calculate 73 ÷ 5.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 14 remainder 3

Worked Example 7

Problem: Calculate 183 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 20 remainder 3

Worked Example 8

Problem: Calculate 38 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 12 remainder 2

Worked Example 9

Problem: Calculate 32 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 3 remainder 5

Worked Example 10

Problem: Calculate 50 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 16 remainder 2

Practice Exercise

Create and solve one new example of Partial quotients. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.6 Breaking apart the dividend

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 173 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 19 remainder 2

Worked Example 2

Problem: Calculate 51 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 17

Worked Example 3

Problem: Calculate 44 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 7 remainder 2

Worked Example 4

Problem: Calculate 9 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 3

Worked Example 5

Problem: Calculate 117 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 16 remainder 5

Worked Example 6

Problem: Calculate 101 ÷ 5.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 20 remainder 1

Worked Example 7

Problem: Calculate 17 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 5 remainder 2

Worked Example 8

Problem: Calculate 62 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 8 remainder 6

Worked Example 9

Problem: Calculate 13 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 4 remainder 1

Worked Example 10

Problem: Calculate 80 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 20

Practice Exercise

Create and solve one new example of Breaking apart the dividend. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.7 Division with no remainder

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 49 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 16 remainder 1

Worked Example 2

Problem: Calculate 48 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 5 remainder 3

Worked Example 3

Problem: Calculate 27 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 13 remainder 1

Worked Example 4

Problem: Calculate 60 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 10

Worked Example 5

Problem: Calculate 32 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 10 remainder 2

Worked Example 6

Problem: Calculate 56 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 18 remainder 2

Worked Example 7

Problem: Calculate 42 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 10 remainder 2

Worked Example 8

Problem: Calculate 128 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 18 remainder 2

Worked Example 9

Problem: Calculate 55 ÷ 5.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 11

Worked Example 10

Problem: Calculate 159 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 19 remainder 7

Practice Exercise

Create and solve one new example of Division with no remainder. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.8 Division with a remainder

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 23 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 5 remainder 3

Worked Example 2

Problem: Calculate 52 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 13

Worked Example 3

Problem: Calculate 49 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 16 remainder 1

Worked Example 4

Problem: Calculate 116 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 19 remainder 2

Worked Example 5

Problem: Calculate 25 ÷ 5.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 5

Worked Example 6

Problem: Calculate 62 ÷ 5.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 12 remainder 2

Worked Example 7

Problem: Calculate 110 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 12 remainder 2

Worked Example 8

Problem: Calculate 11 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 5 remainder 1

Worked Example 9

Problem: Calculate 68 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 17

Worked Example 10

Problem: Calculate 99 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 14 remainder 1

Practice Exercise

Create and solve one new example of Division with a remainder. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.9 Estimating a quotient

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 13 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 6 remainder 1

Worked Example 2

Problem: Calculate 17 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 8 remainder 1

Worked Example 3

Problem: Calculate 47 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 6 remainder 5

Worked Example 4

Problem: Calculate 164 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 20 remainder 4

Worked Example 5

Problem: Calculate 78 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 8 remainder 6

Worked Example 6

Problem: Calculate 55 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 13 remainder 3

Worked Example 7

Problem: Calculate 22 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 5 remainder 2

Worked Example 8

Problem: Calculate 41 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 20 remainder 1

Worked Example 9

Problem: Calculate 93 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 15 remainder 3

Worked Example 10

Problem: Calculate 158 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 17 remainder 5

Practice Exercise

Create and solve one new example of Estimating a quotient. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.10 Word problems

Word problems is an important Grade 4 mathematics idea in Two-Digit by One-Digit Division. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Word problems using the numbers 2 and 4.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Worked Example 2

Problem: Create a simple Grade 4 example about Word problems using the numbers 10 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Worked Example 3

Problem: Create a simple Grade 4 example about Word problems using the numbers 11 and 8.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Worked Example 4

Problem: Create a simple Grade 4 example about Word problems using the numbers 17 and 10.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Worked Example 5

Problem: Create a simple Grade 4 example about Word problems using the numbers 9 and 11.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Worked Example 6

Problem: Create a simple Grade 4 example about Word problems using the numbers 18 and 4.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Worked Example 7

Problem: Create a simple Grade 4 example about Word problems using the numbers 7 and 12.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Worked Example 8

Problem: Create a simple Grade 4 example about Word problems using the numbers 8 and 6.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Worked Example 9

Problem: Create a simple Grade 4 example about Word problems using the numbers 15 and 8.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Worked Example 10

Problem: Create a simple Grade 4 example about Word problems using the numbers 11 and 17.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Word problems.

Practice Exercise

Create and solve one new example of Word problems. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.11 Checking with multiplication

Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 7 × 4.

  1. Break 7 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 28

Worked Example 2

Problem: Calculate 2 × 3.

  1. Break 2 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 6

Worked Example 3

Problem: Calculate 9 × 6.

  1. Break 9 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 54

Worked Example 4

Problem: Calculate 2 × 8.

  1. Break 2 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 16

Worked Example 5

Problem: Calculate 9 × 6.

  1. Break 9 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 54

Worked Example 6

Problem: Calculate 4 × 6.

  1. Break 4 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 24

Worked Example 7

Problem: Calculate 4 × 6.

  1. Break 4 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 24

Worked Example 8

Problem: Calculate 11 × 4.

  1. Break 11 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 44

Worked Example 9

Problem: Calculate 9 × 6.

  1. Break 9 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 54

Worked Example 10

Problem: Calculate 10 × 8.

  1. Break 10 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 80

Practice Exercise

Create and solve one new example of Checking with multiplication. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

24.12 Choosing a division strategy

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 37 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 4 remainder 1

Worked Example 2

Problem: Calculate 60 ÷ 3.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 20

Worked Example 3

Problem: Calculate 55 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 7 remainder 6

Worked Example 4

Problem: Calculate 18 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 3

Worked Example 5

Problem: Calculate 64 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 16

Worked Example 6

Problem: Calculate 82 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 13 remainder 4

Worked Example 7

Problem: Calculate 111 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 15 remainder 6

Worked Example 8

Problem: Calculate 113 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 14 remainder 1

Worked Example 9

Problem: Calculate 18 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 4 remainder 2

Worked Example 10

Problem: Calculate 20 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 3 remainder 2

Practice Exercise

Create and solve one new example of Choosing a division strategy. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

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30 Review Questions and Answers

Q1. What is important to understand about Division as sharing?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q2. What is important to understand about Division as grouping?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q3. What is important to understand about Using multiplication facts to divide?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q4. What is important to understand about Using arrays to divide?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q5. What is important to understand about Partial quotients?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q6. What is important to understand about Breaking apart the dividend?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q7. What is important to understand about Division with no remainder?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q8. What is important to understand about Division with a remainder?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q9. What is important to understand about Estimating a quotient?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q10. What is important to understand about Word problems?

Answer: Word problems is an important Grade 4 mathematics idea in Two-Digit by One-Digit Division. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q11. What is important to understand about Checking with multiplication?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q12. What is important to understand about Choosing a division strategy?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q13. How would you explain Division as sharing?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q14. How would you explain Division as grouping?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q15. How would you explain Using multiplication facts to divide?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q16. How would you explain Using arrays to divide?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q17. How would you explain Partial quotients?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q18. How would you explain Breaking apart the dividend?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q19. How would you explain Division with no remainder?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q20. How would you explain Division with a remainder?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q21. How would you explain Estimating a quotient?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q22. How would you explain Word problems?

Answer: Word problems is an important Grade 4 mathematics idea in Two-Digit by One-Digit Division. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q23. How would you explain Checking with multiplication?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q24. How would you explain Choosing a division strategy?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q25. What should a beginner check when working with Division as sharing?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q26. What should a beginner check when working with Division as grouping?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q27. What should a beginner check when working with Using multiplication facts to divide?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q28. What should a beginner check when working with Using arrays to divide?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q29. What should a beginner check when working with Partial quotients?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q30. What should a beginner check when working with Breaking apart the dividend?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.