EASYTUTORGUIDE

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

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

Chapter 25: Three-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
Advertisement area — AdSense / Auto Ads

Chapter Overview

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

25.1 Breaking apart hundreds tens and ones

Breaking apart hundreds tens and ones is an important Grade 4 mathematics idea in Three-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 Breaking apart hundreds tens and ones using the numbers 3 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 Breaking apart hundreds tens and ones.

Worked Example 2

Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 18 and 2.

  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 Breaking apart hundreds tens and ones.

Worked Example 3

Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 4 and 5.

  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 Breaking apart hundreds tens and ones.

Worked Example 4

Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 8 and 5.

  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 Breaking apart hundreds tens and ones.

Worked Example 5

Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 15 and 15.

  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 Breaking apart hundreds tens and ones.

Worked Example 6

Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 14 and 20.

  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 Breaking apart hundreds tens and ones.

Worked Example 7

Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 16 and 14.

  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 Breaking apart hundreds tens and ones.

Worked Example 8

Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 7 and 20.

  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 Breaking apart hundreds tens and ones.

Worked Example 9

Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 18 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 Breaking apart hundreds tens and ones.

Worked Example 10

Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 11 and 7.

  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 Breaking apart hundreds tens and ones.

Practice Exercise

Create and solve one new example of Breaking apart hundreds tens and ones. 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.

25.2 Using place value 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 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 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 86 ÷ 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: 10 remainder 6

Worked Example 4

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 5

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 6

Problem: Calculate 16 ÷ 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 1

Worked Example 7

Problem: Calculate 91 ÷ 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 1

Worked Example 8

Problem: Calculate 121 ÷ 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: 13 remainder 4

Worked Example 9

Problem: Calculate 15 ÷ 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

Worked Example 10

Problem: Calculate 59 ÷ 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: 9 remainder 5

Practice Exercise

Create and solve one new example of Using place value 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.

25.3 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 36 ÷ 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: 18

Worked Example 2

Problem: Calculate 69 ÷ 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 remainder 1

Worked Example 3

Problem: Calculate 44 ÷ 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 4

Worked Example 4

Problem: Calculate 93 ÷ 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 3

Worked Example 5

Problem: Calculate 16 ÷ 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

Worked Example 6

Problem: Calculate 36 ÷ 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: 18

Worked Example 7

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 8

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 9

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 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 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.

25.4 Long-division structure for beginners

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 39 ÷ 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 3

Worked Example 2

Problem: Calculate 91 ÷ 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 1

Worked Example 3

Problem: Calculate 125 ÷ 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 6

Worked Example 4

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 5

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 6

Problem: Calculate 61 ÷ 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 5

Worked Example 7

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 8

Problem: Calculate 54 ÷ 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

Worked Example 9

Problem: Calculate 23 ÷ 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: 3 remainder 2

Worked Example 10

Problem: Calculate 41 ÷ 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 5

Practice Exercise

Create and solve one new example of Long-division structure for beginners. 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.

25.5 Division with zero in the 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 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

Worked Example 2

Problem: Calculate 52 ÷ 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 remainder 1

Worked Example 3

Problem: Calculate 65 ÷ 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

Worked Example 4

Problem: Calculate 22 ÷ 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 1

Worked Example 5

Problem: Calculate 94 ÷ 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 3

Worked Example 6

Problem: Calculate 30 ÷ 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

Worked Example 7

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 8

Problem: Calculate 90 ÷ 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 2

Worked Example 9

Problem: Calculate 15 ÷ 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

Worked Example 10

Problem: Calculate 47 ÷ 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 5

Practice Exercise

Create and solve one new example of Division with zero in the 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.

25.6 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 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 2

Problem: Calculate 46 ÷ 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 2

Worked Example 3

Problem: Calculate 31 ÷ 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 3

Worked Example 4

Problem: Calculate 52 ÷ 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 remainder 1

Worked Example 5

Problem: Calculate 87 ÷ 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: 10 remainder 7

Worked Example 6

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 7

Problem: Calculate 141 ÷ 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: 15 remainder 6

Worked Example 8

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 9

Problem: Calculate 124 ÷ 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: 20 remainder 4

Worked Example 10

Problem: Calculate 49 ÷ 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 4

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.

25.7 Estimating 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 104 ÷ 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 4

Worked Example 2

Problem: Calculate 86 ÷ 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 2

Worked Example 3

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 4

Problem: Calculate 36 ÷ 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

Worked Example 5

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 6

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 7

Problem: Calculate 69 ÷ 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 remainder 1

Worked Example 8

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

Worked Example 9

Problem: Calculate 72 ÷ 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

Worked Example 10

Problem: Calculate 16 ÷ 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 1

Practice Exercise

Create and solve one new example of Estimating 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.

25.8 Sharing contexts

Sharing contexts is an important Grade 4 mathematics idea in Three-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 Sharing contexts using the numbers 18 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 Sharing contexts.

Worked Example 2

Problem: Create a simple Grade 4 example about Sharing contexts using the numbers 13 and 2.

  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 Sharing contexts.

Worked Example 3

Problem: Create a simple Grade 4 example about Sharing contexts using the numbers 10 and 18.

  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 Sharing contexts.

Worked Example 4

Problem: Create a simple Grade 4 example about Sharing contexts using the numbers 12 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 Sharing contexts.

Worked Example 5

Problem: Create a simple Grade 4 example about Sharing contexts using the numbers 10 and 14.

  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 Sharing contexts.

Worked Example 6

Problem: Create a simple Grade 4 example about Sharing contexts using the numbers 12 and 13.

  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 Sharing contexts.

Worked Example 7

Problem: Create a simple Grade 4 example about Sharing contexts using the numbers 5 and 5.

  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 Sharing contexts.

Worked Example 8

Problem: Create a simple Grade 4 example about Sharing contexts using the numbers 12 and 2.

  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 Sharing contexts.

Worked Example 9

Problem: Create a simple Grade 4 example about Sharing contexts using the numbers 2 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 Sharing contexts.

Worked Example 10

Problem: Create a simple Grade 4 example about Sharing contexts using the numbers 2 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 Sharing contexts.

Practice Exercise

Create and solve one new example of Sharing contexts. 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.

25.9 Grouping contexts

Grouping contexts is an important Grade 4 mathematics idea in Three-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 Grouping contexts using the numbers 12 and 20.

  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 Grouping contexts.

Worked Example 2

Problem: Create a simple Grade 4 example about Grouping contexts using the numbers 4 and 15.

  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 Grouping contexts.

Worked Example 3

Problem: Create a simple Grade 4 example about Grouping contexts using the numbers 9 and 2.

  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 Grouping contexts.

Worked Example 4

Problem: Create a simple Grade 4 example about Grouping contexts using the numbers 19 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 Grouping contexts.

Worked Example 5

Problem: Create a simple Grade 4 example about Grouping contexts using the numbers 9 and 3.

  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 Grouping contexts.

Worked Example 6

Problem: Create a simple Grade 4 example about Grouping contexts using the numbers 13 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 Grouping contexts.

Worked Example 7

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

  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 Grouping contexts.

Worked Example 8

Problem: Create a simple Grade 4 example about Grouping contexts using the numbers 16 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 Grouping contexts.

Worked Example 9

Problem: Create a simple Grade 4 example about Grouping contexts using the numbers 15 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 Grouping contexts.

Worked Example 10

Problem: Create a simple Grade 4 example about Grouping contexts using the numbers 19 and 7.

  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 Grouping contexts.

Practice Exercise

Create and solve one new example of Grouping contexts. 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.

25.10 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 5 × 2.

  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: 10

Worked Example 2

Problem: Calculate 9 × 5.

  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: 45

Worked Example 3

Problem: Calculate 10 × 4.

  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: 40

Worked Example 4

Problem: Calculate 12 × 9.

  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: 108

Worked Example 5

Problem: Calculate 2 × 2.

  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: 4

Worked Example 6

Problem: Calculate 6 × 8.

  1. Break 6 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: 48

Worked Example 7

Problem: Calculate 6 × 6.

  1. Break 6 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 8

Problem: Calculate 8 × 2.

  1. Break 8 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 9

Problem: Calculate 3 × 2.

  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: 6

Worked Example 10

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

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.

25.11 Interpreting the 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 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 2

Problem: Calculate 44 ÷ 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 remainder 4

Worked Example 3

Problem: Calculate 45 ÷ 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 5

Worked Example 4

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 5

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 6

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 7

Problem: Calculate 59 ÷ 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: 9 remainder 5

Worked Example 8

Problem: Calculate 143 ÷ 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: 20 remainder 3

Worked Example 9

Problem: Calculate 31 ÷ 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 remainder 1

Worked Example 10

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

Practice Exercise

Create and solve one new example of Interpreting the 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.

25.12 Mixed three-digit division practice

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 34 ÷ 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 6

Worked Example 2

Problem: Calculate 117 ÷ 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 3

Worked Example 3

Problem: Calculate 12 ÷ 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

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 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 6

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

Worked Example 7

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 8

Problem: Calculate 28 ÷ 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

Worked Example 9

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 10

Problem: Calculate 36 ÷ 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: 18

Practice Exercise

Create and solve one new example of Mixed three-digit division practice. 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.

Advertisement area — AdSense / Auto Ads

30 Review Questions and Answers

Q1. What is important to understand about Breaking apart hundreds tens and ones?

Answer: Breaking apart hundreds tens and ones is an important Grade 4 mathematics idea in Three-Digit by One-Digit Division. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q2. What is important to understand about Using place value to divide?

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

Q3. 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.

Q4. What is important to understand about Long-division structure for beginners?

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

Q5. What is important to understand about Division with zero in the quotient?

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

Q6. 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.

Q7. What is important to understand about Estimating quotients?

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

Q8. What is important to understand about Sharing contexts?

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

Q9. What is important to understand about Grouping contexts?

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

Q10. 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.

Q11. What is important to understand about Interpreting the quotient?

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 three-digit division practice?

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

Q13. How would you explain Breaking apart hundreds tens and ones?

Answer: Breaking apart hundreds tens and ones is an important Grade 4 mathematics idea in Three-Digit by One-Digit Division. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q14. How would you explain Using place value to divide?

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

Q15. How would you explain Partial quotients?

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

Q16. How would you explain Long-division structure for beginners?

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

Q17. How would you explain Division with zero in the quotient?

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

Q18. 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.

Q19. How would you explain Estimating quotients?

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

Q20. How would you explain Sharing contexts?

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

Q21. How would you explain Grouping contexts?

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

Q22. How would you explain Checking with multiplication?

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

Q23. How would you explain Interpreting the quotient?

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

Q24. How would you explain Mixed three-digit division practice?

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 Breaking apart hundreds tens and ones?

Answer: Breaking apart hundreds tens and ones is an important Grade 4 mathematics idea in Three-Digit by One-Digit Division. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q26. What should a beginner check when working with Using place value to divide?

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 Partial quotients?

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 Long-division structure for beginners?

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 Division with zero in the quotient?

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 Division with a remainder?

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