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Chapter 12: Rounding Decimals and Fraction-Decimal Connections

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

12.1 Rounding tenths to the nearest whole number

A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10. 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: Write 0/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.0

Worked Example 2

Problem: Write 4/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.4

Worked Example 3

Problem: Write 6/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.6

Worked Example 4

Problem: Write 3/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.3

Worked Example 5

Problem: Write 8/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.8

Worked Example 6

Problem: Write 3/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.3

Worked Example 7

Problem: Write 7/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.7

Worked Example 8

Problem: Write 3/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.3

Worked Example 9

Problem: Write 9/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.9

Worked Example 10

Problem: Write 0/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.0

Practice Exercise

Create and solve one new example of Rounding tenths to the nearest whole number. 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.

12.2 Using a number line to round decimals

A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10. 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: Write 2/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.2

Worked Example 2

Problem: Write 2/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.2

Worked Example 3

Problem: Write 4/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.4

Worked Example 4

Problem: Write 3/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.3

Worked Example 5

Problem: Write 0/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.0

Worked Example 6

Problem: Write 4/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.4

Worked Example 7

Problem: Write 4/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.4

Worked Example 8

Problem: Write 1/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.1

Worked Example 9

Problem: Write 6/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.6

Worked Example 10

Problem: Write 7/10 as a decimal.

  1. The denominator 10 means tenths.
  2. Put the numerator in the tenths place.

Very beginner explanation: Tenths can be written as either fractions or decimals.

Answer: 0.7

Practice Exercise

Create and solve one new example of Using a number line to round decimals. 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.

12.3 Midpoints between whole numbers

Midpoints between whole numbers is an important Grade 4 mathematics idea in Rounding Decimals and Fraction-Decimal Connections. 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 Midpoints between whole numbers using the numbers 5 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 Midpoints between whole numbers.

Worked Example 2

Problem: Create a simple Grade 4 example about Midpoints between whole numbers using the numbers 17 and 10.

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

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

Answer: A correct example that demonstrates Midpoints between whole numbers.

Worked Example 3

Problem: Create a simple Grade 4 example about Midpoints between whole numbers 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 Midpoints between whole numbers.

Worked Example 4

Problem: Create a simple Grade 4 example about Midpoints between whole numbers using the numbers 3 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 Midpoints between whole numbers.

Worked Example 5

Problem: Create a simple Grade 4 example about Midpoints between whole numbers using the numbers 2 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 Midpoints between whole numbers.

Worked Example 6

Problem: Create a simple Grade 4 example about Midpoints between whole numbers 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 Midpoints between whole numbers.

Worked Example 7

Problem: Create a simple Grade 4 example about Midpoints between whole numbers 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 Midpoints between whole numbers.

Worked Example 8

Problem: Create a simple Grade 4 example about Midpoints between whole numbers using the numbers 9 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 Midpoints between whole numbers.

Worked Example 9

Problem: Create a simple Grade 4 example about Midpoints between whole numbers using the numbers 6 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 Midpoints between whole numbers.

Worked Example 10

Problem: Create a simple Grade 4 example about Midpoints between whole numbers using the numbers 4 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 Midpoints between whole numbers.

Practice Exercise

Create and solve one new example of Midpoints between whole numbers. 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.

12.4 One tenth as fraction and decimal

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 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 3

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 4

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 5

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 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 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 8

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 9

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 10

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

Practice Exercise

Create and solve one new example of One tenth as fraction and decimal. 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.

12.5 Two tenths as fraction and decimal

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 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 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 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 5

Problem: A model has 6 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: 4/6

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 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 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 9

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 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 Two tenths as fraction and decimal. 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.

12.6 Five tenths and one half

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 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 3

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

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

Very beginner explanation: Fractions describe equal-sized parts.

Answer: 1/2

Worked Example 4

Problem: A model has 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 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 6 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: 4/6

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 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 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 10

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

Practice Exercise

Create and solve one new example of Five tenths and one half. 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.

12.7 Equivalent fraction and decimal tenths

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 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: 6/10

Worked Example 2

Problem: A model has 10 equal parts and 9 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: 9/10

Worked Example 3

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 4

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 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 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 7

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 8

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 9

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 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 Equivalent fraction and decimal tenths. 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.

12.8 Matching fractions to decimals

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 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

Worked Example 2

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 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 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 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 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 7

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 8

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

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 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

Practice Exercise

Create and solve one new example of Matching fractions to decimals. 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.

12.9 Ordering fractions and decimal tenths

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 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 2

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 3

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 4

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 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 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

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 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 9

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 10

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

Practice Exercise

Create and solve one new example of Ordering fractions and decimal tenths. 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.

12.10 Using equivalence in measurement

Using equivalence in measurement is an important Grade 4 mathematics idea in Rounding Decimals and Fraction-Decimal Connections. 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 equivalence in measurement using the numbers 9 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 Using equivalence in measurement.

Worked Example 2

Problem: Create a simple Grade 4 example about Using equivalence in measurement 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 Using equivalence in measurement.

Worked Example 3

Problem: Create a simple Grade 4 example about Using equivalence in measurement using the numbers 20 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 equivalence in measurement.

Worked Example 4

Problem: Create a simple Grade 4 example about Using equivalence in measurement using the numbers 17 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 equivalence in measurement.

Worked Example 5

Problem: Create a simple Grade 4 example about Using equivalence in measurement using the numbers 8 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 equivalence in measurement.

Worked Example 6

Problem: Create a simple Grade 4 example about Using equivalence in measurement using the numbers 9 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 Using equivalence in measurement.

Worked Example 7

Problem: Create a simple Grade 4 example about Using equivalence in measurement using the numbers 9 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 equivalence in measurement.

Worked Example 8

Problem: Create a simple Grade 4 example about Using equivalence in measurement using the numbers 17 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 Using equivalence in measurement.

Worked Example 9

Problem: Create a simple Grade 4 example about Using equivalence in measurement using the numbers 2 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 Using equivalence in measurement.

Worked Example 10

Problem: Create a simple Grade 4 example about Using equivalence in measurement using the numbers 6 and 16.

  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 equivalence in measurement.

Practice Exercise

Create and solve one new example of Using equivalence in measurement. 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.

12.11 Using equivalence in money contexts

Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value. 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: Option A costs $9 for 5 items. Option B costs $10 for 1 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 2

Problem: Option A costs $12 for 3 items. Option B costs $5 for 4 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 3

Problem: Option A costs $9 for 2 items. Option B costs $2 for 1 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 4

Problem: Option A costs $7 for 4 items. Option B costs $7 for 3 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 5

Problem: Option A costs $9 for 1 items. Option B costs $6 for 3 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 6

Problem: Option A costs $6 for 5 items. Option B costs $9 for 2 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 7

Problem: Option A costs $10 for 3 items. Option B costs $6 for 2 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 8

Problem: Option A costs $8 for 2 items. Option B costs $4 for 1 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Same value

Worked Example 9

Problem: Option A costs $5 for 4 items. Option B costs $4 for 3 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 10

Problem: Option A costs $8 for 1 items. Option B costs $2 for 1 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Practice Exercise

Create and solve one new example of Using equivalence in money 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.

12.12 Checking fraction-decimal equivalence

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 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 2

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 3

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 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 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 6

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 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 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 9

Problem: A model has 6 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: 4/6

Worked Example 10

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

Practice Exercise

Create and solve one new example of Checking fraction-decimal equivalence. 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 Rounding tenths to the nearest whole number?

Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.

Q2. What is important to understand about Using a number line to round decimals?

Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.

Q3. What is important to understand about Midpoints between whole numbers?

Answer: Midpoints between whole numbers is an important Grade 4 mathematics idea in Rounding Decimals and Fraction-Decimal Connections. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q4. What is important to understand about One tenth as fraction and decimal?

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

Q5. What is important to understand about Two tenths as fraction and decimal?

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 Five tenths and one half?

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 Equivalent fraction and decimal tenths?

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 Matching fractions to decimals?

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 Ordering fractions and decimal tenths?

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 Using equivalence in measurement?

Answer: Using equivalence in measurement is an important Grade 4 mathematics idea in Rounding Decimals and Fraction-Decimal Connections. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q11. What is important to understand about Using equivalence in money contexts?

Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.

Q12. What is important to understand about Checking fraction-decimal equivalence?

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 Rounding tenths to the nearest whole number?

Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.

Q14. How would you explain Using a number line to round decimals?

Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.

Q15. How would you explain Midpoints between whole numbers?

Answer: Midpoints between whole numbers is an important Grade 4 mathematics idea in Rounding Decimals and Fraction-Decimal Connections. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q16. How would you explain One tenth as fraction and decimal?

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

Q17. How would you explain Two tenths as fraction and decimal?

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 Five tenths and one half?

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 Equivalent fraction and decimal tenths?

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 Matching fractions to decimals?

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 Ordering fractions and decimal tenths?

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 Using equivalence in measurement?

Answer: Using equivalence in measurement is an important Grade 4 mathematics idea in Rounding Decimals and Fraction-Decimal Connections. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q23. How would you explain Using equivalence in money contexts?

Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.

Q24. How would you explain Checking fraction-decimal equivalence?

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 Rounding tenths to the nearest whole number?

Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.

Q26. What should a beginner check when working with Using a number line to round decimals?

Answer: A decimal with one digit after the decimal point represents tenths. Tenths can also be written as fractions with denominator 10.

Q27. What should a beginner check when working with Midpoints between whole numbers?

Answer: Midpoints between whole numbers is an important Grade 4 mathematics idea in Rounding Decimals and Fraction-Decimal Connections. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q28. What should a beginner check when working with One tenth as fraction and decimal?

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

Q29. What should a beginner check when working with Two tenths as fraction and decimal?

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 Five tenths and one half?

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.