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Chapter 9: Comparing and Ordering Fractions

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

9.1 Comparing fractions with the same denominator

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 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 2

Problem: A model has 5 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: 2/5

Worked Example 3

Problem: A model has 8 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: 1/8

Worked Example 4

Problem: A model has 5 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: 5/5

Worked Example 5

Problem: A model has 10 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: 7/10

Worked Example 6

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 7

Problem: A model has 10 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: 1/10

Worked Example 8

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 9

Problem: A model has 8 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: 1/8

Worked Example 10

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

Practice Exercise

Create and solve one new example of Comparing fractions with the same denominator. 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.

9.2 Comparing fractions with the same numerator

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 5 equal parts and 4 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: 4/5

Worked Example 2

Problem: A model has 4 equal parts and 4 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: 4/4

Worked Example 3

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

Worked Example 4

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 5

Problem: A model has 4 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: 2/4

Worked Example 6

Problem: A model has 5 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: 3/5

Worked Example 7

Problem: A model has 3 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: 3/3

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 5 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: 3/5

Worked Example 10

Problem: A model has 8 equal parts and 6 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: 6/8

Practice Exercise

Create and solve one new example of Comparing fractions with the same numerator. 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.

9.3 Using fraction strips to compare

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 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: 3/4

Worked Example 2

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 3

Problem: A model has 5 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: 5/5

Worked Example 4

Problem: A model has 4 equal parts and 4 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: 4/4

Worked Example 5

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 6

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 7

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 8

Problem: A model has 5 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: 1/5

Worked Example 9

Problem: A model has 5 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: 3/5

Worked Example 10

Problem: A model has 4 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: 3/4

Practice Exercise

Create and solve one new example of Using fraction strips to compare. 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.

9.4 Using number lines to compare

Using number lines to compare is an important Grade 4 mathematics idea in Comparing and Ordering Fractions. 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 Using number lines to compare using the numbers 6 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 Using number lines to compare.

Worked Example 2

Problem: Create a simple Grade 4 example about Using number lines to compare using the numbers 10 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 Using number lines to compare.

Worked Example 3

Problem: Create a simple Grade 4 example about Using number lines to compare using the numbers 2 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 Using number lines to compare.

Worked Example 4

Problem: Create a simple Grade 4 example about Using number lines to compare using the numbers 15 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 Using number lines to compare.

Worked Example 5

Problem: Create a simple Grade 4 example about Using number lines to compare using the numbers 10 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 Using number lines to compare.

Worked Example 6

Problem: Create a simple Grade 4 example about Using number lines to compare using the numbers 19 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 Using number lines to compare.

Worked Example 7

Problem: Create a simple Grade 4 example about Using number lines to compare using the numbers 8 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 Using number lines to compare.

Worked Example 8

Problem: Create a simple Grade 4 example about Using number lines to compare using the numbers 2 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 Using number lines to compare.

Worked Example 9

Problem: Create a simple Grade 4 example about Using number lines to compare using the numbers 8 and 12.

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

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

Answer: A correct example that demonstrates Using number lines to compare.

Worked Example 10

Problem: Create a simple Grade 4 example about Using number lines to compare using the numbers 6 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 Using number lines to compare.

Practice Exercise

Create and solve one new example of Using number lines to compare. 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.

9.5 Using one-half as a benchmark

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 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 2

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 3

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 4

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 5

Problem: A model has 8 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: 5/8

Worked Example 6

Problem: A model has 10 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: 5/10

Worked Example 7

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 8

Problem: A model has 8 equal parts and 6 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: 6/8

Worked Example 9

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 10

Problem: A model has 4 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: 3/4

Practice Exercise

Create and solve one new example of Using one-half as a benchmark. 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.

9.6 Ordering fractions least to greatest

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 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: 2/4

Worked Example 2

Problem: A model has 8 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: 1/8

Worked Example 3

Problem: A model has 8 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: 1/8

Worked Example 4

Problem: A model has 5 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: 5/5

Worked Example 5

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 6

Problem: A model has 8 equal parts and 8 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: 8/8

Worked Example 7

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 8

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 9

Problem: A model has 4 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: 2/4

Worked Example 10

Problem: A model has 4 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: 3/4

Practice Exercise

Create and solve one new example of Ordering fractions least to greatest. 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.

9.7 Ordering fractions greatest to least

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 8 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: 1/8

Worked Example 2

Problem: A model has 5 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: 5/5

Worked Example 3

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 4

Problem: A model has 5 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: 3/5

Worked Example 5

Problem: A model has 3 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: 3/3

Worked Example 6

Problem: A model has 3 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: 3/3

Worked Example 7

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 8

Problem: A model has 10 equal parts and 8 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: 8/10

Worked Example 9

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 10

Problem: A model has 8 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: 2/8

Practice Exercise

Create and solve one new example of Ordering fractions greatest to least. 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.

9.8 Finding a fraction between two fractions

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 10 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: 5/10

Worked Example 2

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 3

Problem: A model has 5 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: 5/5

Worked Example 4

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 5

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 6

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

Worked Example 7

Problem: A model has 3 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: 3/3

Worked Example 8

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 9

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 10

Problem: A model has 8 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: 3/8

Practice Exercise

Create and solve one new example of Finding a fraction between two fractions. 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.

9.9 Explaining a fraction comparison

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 10 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: 2/10

Worked Example 2

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 3

Problem: A model has 6 equal parts and 6 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: 6/6

Worked Example 4

Problem: A model has 5 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: 5/5

Worked Example 5

Problem: A model has 10 equal parts and 8 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: 8/10

Worked Example 6

Problem: A model has 3 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: 3/3

Worked Example 7

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

Worked Example 8

Problem: A model has 10 equal parts and 4 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: 4/10

Worked Example 9

Problem: A model has 8 equal parts and 4 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: 4/8

Worked Example 10

Problem: A model has 8 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: 2/8

Practice Exercise

Create and solve one new example of Explaining a fraction comparison. 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.

9.10 Checking with a model

Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows. 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 data set is [8, 12, 15, 3, 6]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 15

Worked Example 2

Problem: A data set is [3, 6, 7, 3, 14]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 14

Worked Example 3

Problem: A data set is [2, 5, 10, 15, 3]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 15

Worked Example 4

Problem: A data set is [3, 6, 5, 7, 14]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 14

Worked Example 5

Problem: A data set is [9, 11, 13, 7, 6]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 13

Worked Example 6

Problem: A data set is [15, 3, 5, 10, 2]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 15

Worked Example 7

Problem: A data set is [8, 2, 2, 10, 2]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 10

Worked Example 8

Problem: A data set is [8, 6, 11, 11, 4]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 11

Worked Example 9

Problem: A data set is [4, 10, 14, 3, 12]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 14

Worked Example 10

Problem: A data set is [4, 11, 3, 8, 3]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 11

Practice Exercise

Create and solve one new example of Checking with a model. 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.

9.11 Comparing fair-share fractions

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 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 2

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 3

Problem: A model has 5 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: 5/5

Worked Example 4

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 5

Problem: A model has 5 equal parts and 4 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: 4/5

Worked Example 6

Problem: A model has 10 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: 7/10

Worked Example 7

Problem: A model has 10 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: 1/10

Worked Example 8

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 9

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 10

Problem: A model has 6 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: 2/6

Practice Exercise

Create and solve one new example of Comparing fair-share fractions. 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.

9.12 Mixed fraction comparison practice

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 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 2

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 3

Problem: A model has 3 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: 3/3

Worked Example 4

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 5

Problem: A model has 3 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: 3/3

Worked Example 6

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 7

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 8

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 9

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 10

Problem: A model has 5 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: 5/5

Practice Exercise

Create and solve one new example of Mixed fraction comparison 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.

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30 Review Questions and Answers

Q1. What is important to understand about Comparing fractions with the same denominator?

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.

Q2. What is important to understand about Comparing fractions with the same numerator?

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.

Q3. What is important to understand about Using fraction strips to compare?

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.

Q4. What is important to understand about Using number lines to compare?

Answer: Using number lines to compare is an important Grade 4 mathematics idea in Comparing and Ordering Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q5. What is important to understand about Using one-half as a benchmark?

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 Ordering fractions least to greatest?

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 Ordering fractions greatest to least?

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.

Q8. What is important to understand about Finding a fraction between two fractions?

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.

Q9. What is important to understand about Explaining a fraction comparison?

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.

Q10. What is important to understand about Checking with a model?

Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.

Q11. What is important to understand about Comparing fair-share fractions?

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.

Q12. What is important to understand about Mixed fraction comparison practice?

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.

Q13. How would you explain Comparing fractions with the same denominator?

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.

Q14. How would you explain Comparing fractions with the same numerator?

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.

Q15. How would you explain Using fraction strips to compare?

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.

Q16. How would you explain Using number lines to compare?

Answer: Using number lines to compare is an important Grade 4 mathematics idea in Comparing and Ordering Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q17. How would you explain Using one-half as a benchmark?

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 Ordering fractions least to greatest?

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 Ordering fractions greatest to least?

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.

Q20. How would you explain Finding a fraction between two fractions?

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.

Q21. How would you explain Explaining a fraction comparison?

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.

Q22. How would you explain Checking with a model?

Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.

Q23. How would you explain Comparing fair-share fractions?

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.

Q24. How would you explain Mixed fraction comparison practice?

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.

Q25. What should a beginner check when working with Comparing fractions with the same denominator?

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.

Q26. What should a beginner check when working with Comparing fractions with the same numerator?

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.

Q27. What should a beginner check when working with Using fraction strips to compare?

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.

Q28. What should a beginner check when working with Using number lines to compare?

Answer: Using number lines to compare is an important Grade 4 mathematics idea in Comparing and Ordering Fractions. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q29. What should a beginner check when working with Using one-half as a benchmark?

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 Ordering fractions least to greatest?

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.