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Chapter 26: Remainders and Fraction Remainders

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 Remainders and Fraction Remainders in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

26.1 Meaning of 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 93 ÷ 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: 13 remainder 2

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 10 ÷ 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 remainder 1

Worked Example 4

Problem: Calculate 118 ÷ 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 6

Worked Example 5

Problem: Calculate 19 ÷ 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 remainder 1

Worked Example 6

Problem: Calculate 53 ÷ 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: 6 remainder 5

Worked Example 7

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 8

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 9

Problem: Calculate 97 ÷ 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: 13 remainder 6

Worked Example 10

Problem: Calculate 35 ÷ 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 8

Practice Exercise

Create and solve one new example of Meaning of 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.

26.2 Remainders in sharing situations

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 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 2

Problem: Calculate 43 ÷ 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: 5 remainder 3

Worked Example 3

Problem: Calculate 15 ÷ 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: 7 remainder 1

Worked Example 4

Problem: Calculate 73 ÷ 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 1

Worked Example 5

Problem: Calculate 94 ÷ 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: 18 remainder 4

Worked Example 6

Problem: Calculate 29 ÷ 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: 14 remainder 1

Worked Example 7

Problem: Calculate 102 ÷ 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: 17

Worked Example 8

Problem: Calculate 35 ÷ 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: 7

Worked Example 9

Problem: Calculate 101 ÷ 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: 11 remainder 2

Worked Example 10

Problem: Calculate 111 ÷ 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: 13 remainder 7

Practice Exercise

Create and solve one new example of Remainders in sharing situations. 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.

26.3 Remainders in grouping situations

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 126 ÷ 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 6

Worked Example 2

Problem: Calculate 19 ÷ 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 remainder 1

Worked Example 3

Problem: Calculate 63 ÷ 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 3

Worked Example 4

Problem: Calculate 92 ÷ 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 4

Worked Example 5

Problem: Calculate 110 ÷ 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 5

Worked Example 6

Problem: Calculate 115 ÷ 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 3

Worked Example 7

Problem: Calculate 67 ÷ 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 remainder 3

Worked Example 8

Problem: Calculate 37 ÷ 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: 6 remainder 1

Worked Example 9

Problem: Calculate 97 ÷ 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: 19 remainder 2

Worked Example 10

Problem: Calculate 110 ÷ 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 2

Practice Exercise

Create and solve one new example of Remainders in grouping situations. 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.

26.4 Writing a remainder as a fraction

A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. 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 11 ÷ 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 remainder 2

Worked Example 2

Problem: Calculate 12 ÷ 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

Worked Example 3

Problem: Calculate 60 ÷ 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

Worked Example 4

Problem: Calculate 136 ÷ 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: 19 remainder 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 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 7

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 8

Problem: Calculate 20 ÷ 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: 10

Worked Example 9

Problem: Calculate 105 ÷ 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

Worked Example 10

Problem: Calculate 101 ÷ 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 3

Practice Exercise

Create and solve one new example of Writing a remainder as a fraction. 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.

26.5 Simplifying a remainder fraction when possible

A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. 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 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 3

Problem: Calculate 62 ÷ 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 6

Worked Example 4

Problem: Calculate 95 ÷ 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: 19

Worked Example 5

Problem: Calculate 68 ÷ 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: 13 remainder 3

Worked Example 6

Problem: Calculate 131 ÷ 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 5

Worked Example 7

Problem: Calculate 92 ÷ 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: 13 remainder 1

Worked Example 8

Problem: Calculate 19 ÷ 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: 6 remainder 1

Worked Example 9

Problem: Calculate 24 ÷ 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

Worked Example 10

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

Practice Exercise

Create and solve one new example of Simplifying a remainder fraction when possible. 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.

26.6 Choosing whether to round or keep a fraction

A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered. 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: A model has 4 equal parts and 1 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 1/4

Worked Example 2

Problem: A model has 2 equal parts and 2 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 2/2

Worked Example 3

Problem: A model has 2 equal parts and 1 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 1/2

Worked Example 4

Problem: A model has 6 equal parts and 5 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 5/6

Worked Example 5

Problem: A model has 3 equal parts and 1 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 1/3

Worked Example 6

Problem: A model has 10 equal parts and 10 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 10/10

Worked Example 7

Problem: A model has 6 equal parts and 1 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 1/6

Worked Example 8

Problem: A model has 3 equal parts and 2 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 2/3

Worked Example 9

Problem: A model has 8 equal parts and 7 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 7/8

Worked Example 10

Problem: A model has 6 equal parts and 3 are selected. What fraction is selected?

  1. Count all equal parts for the denominator.
  2. Count selected parts for the numerator.

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 3/6

Practice Exercise

Create and solve one new example of Choosing whether to round or keep a fraction. 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.

26.7 Remainders in measurement problems

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 126 ÷ 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: 14

Worked Example 2

Problem: Calculate 104 ÷ 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: 17 remainder 2

Worked Example 3

Problem: Calculate 82 ÷ 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: 9 remainder 1

Worked Example 4

Problem: Calculate 51 ÷ 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 2

Worked Example 5

Problem: Calculate 181 ÷ 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 1

Worked Example 6

Problem: Calculate 147 ÷ 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: 18 remainder 3

Worked Example 7

Problem: Calculate 123 ÷ 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: 17 remainder 4

Worked Example 8

Problem: Calculate 130 ÷ 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 4

Worked Example 9

Problem: Calculate 43 ÷ 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 1

Worked Example 10

Problem: Calculate 92 ÷ 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: 18 remainder 2

Practice Exercise

Create and solve one new example of Remainders in measurement 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.

26.8 Remainders in fair 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 61 ÷ 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 1

Worked Example 2

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 3

Problem: Calculate 59 ÷ 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: 6 remainder 5

Worked Example 4

Problem: Calculate 99 ÷ 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: 19 remainder 4

Worked Example 5

Problem: Calculate 152 ÷ 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: 16 remainder 8

Worked Example 6

Problem: Calculate 44 ÷ 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 2

Worked Example 7

Problem: Calculate 23 ÷ 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: 7 remainder 2

Worked Example 8

Problem: Calculate 130 ÷ 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 2

Worked Example 9

Problem: Calculate 70 ÷ 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 7

Worked Example 10

Problem: Calculate 10 ÷ 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

Practice Exercise

Create and solve one new example of Remainders in fair 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.

26.9 Checking remainder size

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 29 ÷ 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: 14 remainder 1

Worked Example 2

Problem: Calculate 52 ÷ 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 7

Worked Example 3

Problem: Calculate 32 ÷ 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: 16

Worked Example 4

Problem: Calculate 146 ÷ 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: 18 remainder 2

Worked Example 5

Problem: Calculate 50 ÷ 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: 10

Worked Example 6

Problem: Calculate 102 ÷ 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: 17

Worked Example 7

Problem: Calculate 27 ÷ 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: 3 remainder 3

Worked Example 8

Problem: Calculate 10 ÷ 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

Worked Example 9

Problem: Calculate 124 ÷ 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: 17 remainder 5

Worked Example 10

Problem: Calculate 25 ÷ 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: 4 remainder 1

Practice Exercise

Create and solve one new example of Checking remainder size. 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.

26.10 Connecting quotient and divisor

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 78 ÷ 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

Worked Example 2

Problem: Calculate 127 ÷ 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: 14 remainder 1

Worked Example 3

Problem: Calculate 30 ÷ 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 2

Worked Example 4

Problem: Calculate 40 ÷ 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: 8

Worked Example 5

Problem: Calculate 73 ÷ 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: 12 remainder 1

Worked Example 6

Problem: Calculate 51 ÷ 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: 10 remainder 1

Worked Example 7

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 8

Problem: Calculate 29 ÷ 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: 7 remainder 1

Worked Example 9

Problem: Calculate 47 ÷ 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: 5 remainder 7

Worked Example 10

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

Practice Exercise

Create and solve one new example of Connecting quotient and divisor. 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.

26.11 Reasonableness of remainder answers

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 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 2

Problem: Calculate 51 ÷ 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 3

Worked Example 3

Problem: Calculate 25 ÷ 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: 3 remainder 1

Worked Example 4

Problem: Calculate 87 ÷ 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: 14 remainder 3

Worked Example 5

Problem: Calculate 26 ÷ 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 remainder 2

Worked Example 6

Problem: Calculate 6 ÷ 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: 3

Worked Example 7

Problem: Calculate 27 ÷ 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: 4 remainder 3

Worked Example 8

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 9

Problem: Calculate 46 ÷ 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 1

Worked Example 10

Problem: Calculate 39 ÷ 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

Practice Exercise

Create and solve one new example of Reasonableness of remainder answers. 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.

26.12 Mixed remainder problems

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 40 ÷ 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

Worked Example 2

Problem: Calculate 33 ÷ 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: 16 remainder 1

Worked Example 3

Problem: Calculate 26 ÷ 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 remainder 2

Worked Example 4

Problem: Calculate 154 ÷ 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 1

Worked Example 5

Problem: Calculate 115 ÷ 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 3

Worked Example 6

Problem: Calculate 73 ÷ 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 1

Worked Example 7

Problem: Calculate 40 ÷ 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 1

Worked Example 8

Problem: Calculate 7 ÷ 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: 3 remainder 1

Worked Example 9

Problem: Calculate 86 ÷ 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: 17 remainder 1

Worked Example 10

Problem: Calculate 75 ÷ 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: 18 remainder 3

Practice Exercise

Create and solve one new example of Mixed remainder 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.

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30 Review Questions and Answers

Q1. What is important to understand about Meaning of a remainder?

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

Q2. What is important to understand about Remainders in sharing situations?

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

Q3. What is important to understand about Remainders in grouping situations?

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

Q4. What is important to understand about Writing a remainder as a fraction?

Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.

Q5. What is important to understand about Simplifying a remainder fraction when possible?

Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.

Q6. What is important to understand about Choosing whether to round or keep a fraction?

Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.

Q7. What is important to understand about Remainders in measurement problems?

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

Q8. What is important to understand about Remainders in fair sharing?

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

Q9. What is important to understand about Checking remainder size?

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

Q10. What is important to understand about Connecting quotient and divisor?

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

Q11. What is important to understand about Reasonableness of remainder answers?

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

Q12. What is important to understand about Mixed remainder problems?

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

Q13. How would you explain Meaning of a remainder?

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

Q14. How would you explain Remainders in sharing situations?

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

Q15. How would you explain Remainders in grouping situations?

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

Q16. How would you explain Writing a remainder as a fraction?

Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.

Q17. How would you explain Simplifying a remainder fraction when possible?

Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.

Q18. How would you explain Choosing whether to round or keep a fraction?

Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.

Q19. How would you explain Remainders in measurement problems?

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

Q20. How would you explain Remainders in fair sharing?

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

Q21. How would you explain Checking remainder size?

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

Q22. How would you explain Connecting quotient and divisor?

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

Q23. How would you explain Reasonableness of remainder answers?

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

Q24. How would you explain Mixed remainder problems?

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 Meaning of a remainder?

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 Remainders in sharing situations?

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 Remainders in grouping situations?

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

Q28. What should a beginner check when working with Writing a remainder as a fraction?

Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.

Q29. What should a beginner check when working with Simplifying a remainder fraction when possible?

Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.

Q30. What should a beginner check when working with Choosing whether to round or keep a fraction?

Answer: A fraction names equal parts of a whole, set, or length. The denominator names how many equal parts make the whole, and the numerator tells how many parts are being considered.