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Chapter 8: Rational Numbers and Fraction Review

Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.

Grade 8Beginner Friendly5+ Examples Per TopicPractice30 Q&A
Estimated reading time0% read
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What this chapter covers

This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.

8.1 Rational numbers

A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Rational numbers.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Simplify the ratio 4:6.

  1. Find the GCF: 2.
  2. Divide both terms by 2.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 2

Problem: Simplify the ratio 8:12.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 3

Problem: Simplify the ratio 15:25.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 4

Problem: Simplify the ratio 21:28.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:4

Worked Example 5

Problem: Simplify the ratio 18:30.

  1. Find the GCF: 6.
  2. Divide both terms by 6.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 6

Problem: Simplify the ratio 12:20.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 7

Problem: Simplify the ratio 9:15.

  1. Find the GCF: 3.
  2. Divide both terms by 3.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 8

Problem: Simplify the ratio 16:24.

  1. Find the GCF: 8.
  2. Divide both terms by 8.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 9

Problem: Simplify the ratio 25:35.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 5:7

Worked Example 10

Problem: Simplify the ratio 14:49.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:7

Practice exercise

Create one new Grade 8 problem involving Rational numbers. Show the important steps, include units when needed, and explain how you checked the answer.

8.2 Positive rational numbers

A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Positive rational numbers.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Simplify the ratio 4:6.

  1. Find the GCF: 2.
  2. Divide both terms by 2.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 2

Problem: Simplify the ratio 8:12.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 3

Problem: Simplify the ratio 15:25.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 4

Problem: Simplify the ratio 21:28.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:4

Worked Example 5

Problem: Simplify the ratio 18:30.

  1. Find the GCF: 6.
  2. Divide both terms by 6.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 6

Problem: Simplify the ratio 12:20.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 7

Problem: Simplify the ratio 9:15.

  1. Find the GCF: 3.
  2. Divide both terms by 3.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 8

Problem: Simplify the ratio 16:24.

  1. Find the GCF: 8.
  2. Divide both terms by 8.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 9

Problem: Simplify the ratio 25:35.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 5:7

Worked Example 10

Problem: Simplify the ratio 14:49.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:7

Practice exercise

Create one new Grade 8 problem involving Positive rational numbers. Show the important steps, include units when needed, and explain how you checked the answer.

8.3 Negative rational numbers

A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Negative rational numbers.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Simplify the ratio 4:6.

  1. Find the GCF: 2.
  2. Divide both terms by 2.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 2

Problem: Simplify the ratio 8:12.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 3

Problem: Simplify the ratio 15:25.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 4

Problem: Simplify the ratio 21:28.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:4

Worked Example 5

Problem: Simplify the ratio 18:30.

  1. Find the GCF: 6.
  2. Divide both terms by 6.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 6

Problem: Simplify the ratio 12:20.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 7

Problem: Simplify the ratio 9:15.

  1. Find the GCF: 3.
  2. Divide both terms by 3.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 8

Problem: Simplify the ratio 16:24.

  1. Find the GCF: 8.
  2. Divide both terms by 8.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 9

Problem: Simplify the ratio 25:35.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 5:7

Worked Example 10

Problem: Simplify the ratio 14:49.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:7

Practice exercise

Create one new Grade 8 problem involving Negative rational numbers. Show the important steps, include units when needed, and explain how you checked the answer.

8.4 Proper fractions

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Proper fractions.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Proper fractions. Show the important steps, include units when needed, and explain how you checked the answer.

8.5 Improper fractions

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Improper fractions.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Improper fractions. Show the important steps, include units when needed, and explain how you checked the answer.

8.6 Mixed numbers

Mixed numbers is an important Grade 8 concept in Rational Numbers and Fraction Review. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Mixed numbers. Show the important steps, include units when needed, and explain how you checked the answer.

8.7 Equivalent fractions

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Equivalent fractions.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Equivalent fractions. Show the important steps, include units when needed, and explain how you checked the answer.

8.8 Simplifying fractions

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Simplifying fractions.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Simplifying fractions. Show the important steps, include units when needed, and explain how you checked the answer.

8.9 Fractions on number lines

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Fractions on number lines.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Fractions on number lines. Show the important steps, include units when needed, and explain how you checked the answer.

8.10 Comparing rational numbers

A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Comparing rational numbers.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Simplify the ratio 4:6.

  1. Find the GCF: 2.
  2. Divide both terms by 2.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 2

Problem: Simplify the ratio 8:12.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 3

Problem: Simplify the ratio 15:25.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 4

Problem: Simplify the ratio 21:28.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:4

Worked Example 5

Problem: Simplify the ratio 18:30.

  1. Find the GCF: 6.
  2. Divide both terms by 6.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 6

Problem: Simplify the ratio 12:20.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 7

Problem: Simplify the ratio 9:15.

  1. Find the GCF: 3.
  2. Divide both terms by 3.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 8

Problem: Simplify the ratio 16:24.

  1. Find the GCF: 8.
  2. Divide both terms by 8.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 9

Problem: Simplify the ratio 25:35.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 5:7

Worked Example 10

Problem: Simplify the ratio 14:49.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:7

Practice exercise

Create one new Grade 8 problem involving Comparing rational numbers. Show the important steps, include units when needed, and explain how you checked the answer.

8.11 Ordering rational numbers

A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Ordering rational numbers.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Simplify the ratio 4:6.

  1. Find the GCF: 2.
  2. Divide both terms by 2.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 2

Problem: Simplify the ratio 8:12.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 3

Problem: Simplify the ratio 15:25.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 4

Problem: Simplify the ratio 21:28.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:4

Worked Example 5

Problem: Simplify the ratio 18:30.

  1. Find the GCF: 6.
  2. Divide both terms by 6.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 6

Problem: Simplify the ratio 12:20.

  1. Find the GCF: 4.
  2. Divide both terms by 4.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 7

Problem: Simplify the ratio 9:15.

  1. Find the GCF: 3.
  2. Divide both terms by 3.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 3:5

Worked Example 8

Problem: Simplify the ratio 16:24.

  1. Find the GCF: 8.
  2. Divide both terms by 8.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:3

Worked Example 9

Problem: Simplify the ratio 25:35.

  1. Find the GCF: 5.
  2. Divide both terms by 5.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 5:7

Worked Example 10

Problem: Simplify the ratio 14:49.

  1. Find the GCF: 7.
  2. Divide both terms by 7.

Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both parts by the same common factor.

Answer: 2:7

Practice exercise

Create one new Grade 8 problem involving Ordering rational numbers. Show the important steps, include units when needed, and explain how you checked the answer.

8.12 Terminating decimals

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Terminating decimals.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Which is greater: 3.6 or 0.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 3.6

Worked Example 2

Problem: Which is greater: 8.25 or 1.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 8.25

Worked Example 3

Problem: Which is greater: 12.75 or 2.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 12.75

Worked Example 4

Problem: Which is greater: 0.96 or 0.3?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 0.96

Worked Example 5

Problem: Which is greater: 5.04 or 1.2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 5.04

Worked Example 6

Problem: Which is greater: 14.8 or 2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 14.8

Worked Example 7

Problem: Which is greater: 7.125 or 0.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 7.125

Worked Example 8

Problem: Which is greater: 20.05 or 3.75?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 20.05

Worked Example 9

Problem: Which is greater: 2.4 or 0.06?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 2.4

Worked Example 10

Problem: Which is greater: 100.5 or 4.02?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 100.5

Practice exercise

Create one new Grade 8 problem involving Terminating decimals. Show the important steps, include units when needed, and explain how you checked the answer.

8.13 Repeating decimals

A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Repeating decimals.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Which is greater: 3.6 or 0.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 3.6

Worked Example 2

Problem: Which is greater: 8.25 or 1.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 8.25

Worked Example 3

Problem: Which is greater: 12.75 or 2.4?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 12.75

Worked Example 4

Problem: Which is greater: 0.96 or 0.3?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 0.96

Worked Example 5

Problem: Which is greater: 5.04 or 1.2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 5.04

Worked Example 6

Problem: Which is greater: 14.8 or 2?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 14.8

Worked Example 7

Problem: Which is greater: 7.125 or 0.5?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 7.125

Worked Example 8

Problem: Which is greater: 20.05 or 3.75?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 20.05

Worked Example 9

Problem: Which is greater: 2.4 or 0.06?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 2.4

Worked Example 10

Problem: Which is greater: 100.5 or 4.02?

  1. Compare whole-number parts first.
  2. Then compare tenths, hundredths, and later decimal places.

Very beginner explanation: Decimal comparison is place-value comparison.

Answer: 100.5

Practice exercise

Create one new Grade 8 problem involving Repeating decimals. Show the important steps, include units when needed, and explain how you checked the answer.

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Chapter 8 Review Questions and Answers

Q1. What is important to remember about Rational numbers?

Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Rational numbers.

Q2. What is important to remember about Positive rational numbers?

Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Positive rational numbers.

Q3. What is important to remember about Negative rational numbers?

Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Negative rational numbers.

Q4. What is important to remember about Proper fractions?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Proper fractions.

Q5. What is important to remember about Improper fractions?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Improper fractions.

Q6. What is important to remember about Mixed numbers?

Answer: Mixed numbers is an important Grade 8 concept in Rational Numbers and Fraction Review. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q7. What is important to remember about Equivalent fractions?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Equivalent fractions.

Q8. What is important to remember about Simplifying fractions?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Simplifying fractions.

Q9. What is important to remember about Fractions on number lines?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Fractions on number lines.

Q10. What is important to remember about Comparing rational numbers?

Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Comparing rational numbers.

Q11. What is important to remember about Ordering rational numbers?

Answer: A rational number (a number that can be written as a fraction of integers with a nonzero denominator) includes integers, fractions, terminating decimals, and repeating decimals. In this section, the focus is Ordering rational numbers.

Q12. What is important to remember about Terminating decimals?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Terminating decimals.

Q13. What is important to remember about Repeating decimals?

Answer: A decimal uses place value to represent parts of one, including tenths, hundredths, thousandths, and smaller values. In this section, the focus is Repeating decimals.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a calculated answer is reasonable.

Q16. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q17. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.

Q23. Why are tables useful?

Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.

Q24. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer was obtained.

Q25. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.

Q26. When is a calculator useful?

Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.

Q27. Why compare more than one strategy?

Answer: Different strategies may make a problem easier and provide a way to verify the result.

Q28. What is mathematical communication?

Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.

Q29. What is mathematical modelling?

Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.

Q30. Why should assumptions be stated?

Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.