Chapter 8: Fraction Foundations and Equivalence
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Fraction Foundations and Equivalence with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Rational Number (a number that can be written as a fraction of integers with a nonzero denominator)
- Prime Number (a whole number greater than 1 with exactly two positive factors)
- Numerator (the top number of a fraction)
- Denominator (the bottom number of a fraction)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
8.1 Numerator
The numerator (top number of a fraction) tells how many equal parts are being considered. This topic focuses on Numerator .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: The numerator (top number of a fraction) tells how many equal parts are being considered. This topic focuses on Numerator .
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: The numerator (top number of a fraction) tells how many equal parts are being considered. This topic focuses on Numerator .
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: The numerator (top number of a fraction) tells how many equal parts are being considered. This topic focuses on Numerator .
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: The numerator (top number of a fraction) tells how many equal parts are being considered. This topic focuses on Numerator .
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: The numerator (top number of a fraction) tells how many equal parts are being considered. This topic focuses on Numerator .
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Numerator. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.2 Denominator
The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Denominator .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Denominator .
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Denominator .
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Denominator .
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Denominator .
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Denominator .
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Denominator. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.3 Proper fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Proper fractions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Proper fractions .
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Proper fractions .
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Proper fractions .
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Proper fractions .
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Proper fractions .
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Proper fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.4 Improper fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Improper fractions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Improper fractions .
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Improper fractions .
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Improper fractions .
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Improper fractions .
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Improper fractions .
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Improper fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.5 Mixed numbers
Mixed numbers is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: Mixed numbers is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: Mixed numbers is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: Mixed numbers is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: Mixed numbers is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: Mixed numbers is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Mixed numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.6 Equivalent fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Equivalent fractions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write an equivalent fraction for 1/2.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Equivalent fractions .
Answer: 2/4
Worked Example 2
Problem: Write an equivalent fraction for 2/3.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Equivalent fractions .
Answer: 4/6
Worked Example 3
Problem: Write an equivalent fraction for 3/4.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Equivalent fractions .
Answer: 6/8
Worked Example 4
Problem: Write an equivalent fraction for 5/6.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Equivalent fractions .
Answer: 10/12
Worked Example 5
Problem: Write an equivalent fraction for 7/8.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Equivalent fractions .
Answer: 14/16
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Equivalent fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.7 Simplifying fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Simplifying fractions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write an equivalent fraction for 1/2.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Simplifying fractions .
Answer: 2/4
Worked Example 2
Problem: Write an equivalent fraction for 2/3.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Simplifying fractions .
Answer: 4/6
Worked Example 3
Problem: Write an equivalent fraction for 3/4.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Simplifying fractions .
Answer: 6/8
Worked Example 4
Problem: Write an equivalent fraction for 5/6.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Simplifying fractions .
Answer: 10/12
Worked Example 5
Problem: Write an equivalent fraction for 7/8.
- Multiply numerator and denominator by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Simplifying fractions .
Answer: 14/16
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Simplifying fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.8 Common denominators
The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Common denominators .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Common denominators .
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Common denominators .
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Common denominators .
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Common denominators .
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Common denominators .
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Common denominators. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.9 Fractions on number lines
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions on number lines .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions on number lines .
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions on number lines .
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions on number lines .
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions on number lines .
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Fractions on number lines .
Answer: 0.875
Worked Example 6
Problem: Which is farther right on a number line: 3,000 or 3,750?
- Numbers get larger as you move right.
- 3,750 is greater than 3,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 3,750
Worked Example 7
Problem: Which is farther right on a number line: 4,000 or 4,750?
- Numbers get larger as you move right.
- 4,750 is greater than 4,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 4,750
Worked Example 8
Problem: Which is farther right on a number line: 5,000 or 5,750?
- Numbers get larger as you move right.
- 5,750 is greater than 5,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 5,750
Worked Example 9
Problem: Which is farther right on a number line: 6,000 or 6,750?
- Numbers get larger as you move right.
- 6,750 is greater than 6,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 6,750
Worked Example 10
Problem: Which is farther right on a number line: 7,000 or 7,750?
- Numbers get larger as you move right.
- 7,750 is greater than 7,000.
Very beginner explanation: On a standard number line, the greater number is farther to the right.
Answer: 7,750
Practice Exercise
Create one new question about Fractions on number lines. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.10 Comparing fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Comparing fractions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 1/2 and 2/3.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Comparing fractions .
Answer: 1/2 < 2/3
Worked Example 2
Problem: Compare 2/3 and 3/4.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Comparing fractions .
Answer: 2/3 < 3/4
Worked Example 3
Problem: Compare 3/4 and 4/5.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Comparing fractions .
Answer: 3/4 < 4/5
Worked Example 4
Problem: Compare 5/6 and 6/7.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Comparing fractions .
Answer: 5/6 < 6/7
Worked Example 5
Problem: Compare 7/8 and 8/9.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Comparing fractions .
Answer: 7/8 < 8/9
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Comparing fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.11 Ordering fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Ordering fractions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 1/2 and 2/3.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Ordering fractions .
Answer: 1/2 < 2/3
Worked Example 2
Problem: Compare 2/3 and 3/4.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Ordering fractions .
Answer: 2/3 < 3/4
Worked Example 3
Problem: Compare 3/4 and 4/5.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Ordering fractions .
Answer: 3/4 < 4/5
Worked Example 4
Problem: Compare 5/6 and 6/7.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Ordering fractions .
Answer: 5/6 < 6/7
Worked Example 5
Problem: Compare 7/8 and 8/9.
- Convert to decimals or use common denominators.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Ordering fractions .
Answer: 7/8 < 8/9
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Ordering fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.12 Benchmark fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Benchmark fractions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Benchmark fractions .
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Benchmark fractions .
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Benchmark fractions .
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Benchmark fractions .
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Benchmark fractions .
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Benchmark fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
8.13 Converting mixed and improper forms
Converting mixed and improper forms is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: Converting mixed and improper forms is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: Converting mixed and improper forms is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.6667
Worked Example 3
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: Converting mixed and improper forms is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.75
Worked Example 4
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: Converting mixed and improper forms is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.8333
Worked Example 5
Problem: Write 7/8 as a decimal.
- Divide 7 by 8.
Very beginner explanation: Converting mixed and improper forms is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0.875
Worked Example 6
Problem: Write 1/3 as a decimal.
- A fraction bar means division.
- Divide 1 by 3.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.3333
Worked Example 7
Problem: Write 2/5 as a decimal.
- A fraction bar means division.
- Divide 2 by 5.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4
Worked Example 8
Problem: Write 3/8 as a decimal.
- A fraction bar means division.
- Divide 3 by 8.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.375
Worked Example 9
Problem: Write 5/12 as a decimal.
- A fraction bar means division.
- Divide 5 by 12.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.4167
Worked Example 10
Problem: Write 7/9 as a decimal.
- A fraction bar means division.
- Divide 7 by 9.
Very beginner explanation: Fractions and decimals can represent the same rational number.
Answer: 0.7778
Practice Exercise
Create one new question about Converting mixed and improper forms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Numerator . Show your reasoning and check your answer.
- Create and solve a new question about Denominator . Show your reasoning and check your answer.
- Create and solve a new question about Proper fractions . Show your reasoning and check your answer.
- Create and solve a new question about Improper fractions . Show your reasoning and check your answer.
- Create and solve a new question about Mixed numbers . Show your reasoning and check your answer.
- Create and solve a new question about Equivalent fractions . Show your reasoning and check your answer.
- Create and solve a new question about Simplifying fractions . Show your reasoning and check your answer.
- Create and solve a new question about Common denominators . Show your reasoning and check your answer.
- Create and solve a new question about Fractions on number lines . Show your reasoning and check your answer.
- Create and solve a new question about Comparing fractions . Show your reasoning and check your answer.
- Create and solve a new question about Ordering fractions . Show your reasoning and check your answer.
- Create and solve a new question about Benchmark fractions . Show your reasoning and check your answer.
Common Mistakes
- Changing only one part of an equivalent fraction or ratio.
- Moving a decimal point without a mathematical reason.
- Using the new amount instead of the original amount for percent change.
- Mixing units when comparing rates or scale.
30 Review Questions and Answers
Q1. What is important to remember about Numerator?
Answer: The numerator (top number of a fraction) tells how many equal parts are being considered. This topic focuses on Numerator.
Q2. What is important to remember about Denominator?
Answer: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Denominator.
Q3. What is important to remember about Proper fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Proper fractions.
Q4. What is important to remember about Improper fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Improper fractions.
Q5. What is important to remember about Mixed numbers?
Answer: Mixed numbers is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Equivalent fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Equivalent fractions.
Q7. What is important to remember about Simplifying fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Simplifying fractions.
Q8. What is important to remember about Common denominators?
Answer: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Common denominators.
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, or a ratio. This topic focuses on Fractions on number lines.
Q10. What is important to remember about Comparing fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Comparing fractions.
Q11. What is important to remember about Ordering fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Ordering fractions.
Q12. What is important to remember about Benchmark fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Benchmark fractions.
Q13. What is important to remember about Converting mixed and improper forms?
Answer: Converting mixed and improper forms is an important Grade 7 idea in Fraction Foundations and Equivalence. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
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 final answer is reasonable before accepting it.
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 of a calculation 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 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, check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q26. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q27. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q28. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q29. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q30. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.