Chapter 9: Adding and Subtracting Fractions
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Adding and Subtracting Fractions 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)
- 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.
9.1 Adding like fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Adding like 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: Calculate 1/2 + 1/2.
- Denominators already match.
- Add numerators: 1+1.
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 Adding like fractions .
Answer: 2/2
Worked Example 2
Problem: Calculate 2/3 + 1/3.
- Denominators already match.
- Add numerators: 2+1.
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 Adding like fractions .
Answer: 3/3
Worked Example 3
Problem: Calculate 3/4 + 1/4.
- Denominators already match.
- Add numerators: 3+1.
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 Adding like fractions .
Answer: 4/4
Worked Example 4
Problem: Calculate 5/6 + 1/6.
- Denominators already match.
- Add numerators: 5+1.
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 Adding like fractions .
Answer: 6/6
Worked Example 5
Problem: Calculate 7/8 + 1/8.
- Denominators already match.
- Add numerators: 7+1.
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 Adding like fractions .
Answer: 8/8
Worked Example 6
Problem: Calculate 1/3 + 1/4.
- Use common denominator 12.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 7/12
Worked Example 7
Problem: Calculate 2/5 + 3/10.
- Use common denominator 50.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 7/10
Worked Example 8
Problem: Calculate 3/8 + 1/6.
- Use common denominator 48.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 13/24
Worked Example 9
Problem: Calculate 5/12 + 1/4.
- Use common denominator 48.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 2/3
Worked Example 10
Problem: Calculate 7/9 + 2/3.
- Use common denominator 27.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 13/9
Practice Exercise
Create one new question about Adding like fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.2 Subtracting like fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Subtracting like 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: Calculate 1/2 - 1/2.
- Denominators match.
- Subtract numerators: 1-1.
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 Subtracting like fractions .
Answer: 0/2
Worked Example 2
Problem: Calculate 2/3 - 1/3.
- Denominators match.
- Subtract numerators: 2-1.
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 Subtracting like fractions .
Answer: 1/3
Worked Example 3
Problem: Calculate 3/4 - 1/4.
- Denominators match.
- Subtract numerators: 3-1.
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 Subtracting like fractions .
Answer: 2/4
Worked Example 4
Problem: Calculate 5/6 - 1/6.
- Denominators match.
- Subtract numerators: 5-1.
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 Subtracting like fractions .
Answer: 4/6
Worked Example 5
Problem: Calculate 7/8 - 1/8.
- Denominators match.
- Subtract numerators: 7-1.
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 Subtracting like fractions .
Answer: 6/8
Worked Example 6
Problem: Calculate 1/3 - 1/4.
- Use common denominator 12.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/12
Worked Example 7
Problem: Calculate 2/5 - 3/10.
- Use common denominator 50.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/10
Worked Example 8
Problem: Calculate 3/8 - 1/6.
- Use common denominator 48.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 5/24
Worked Example 9
Problem: Calculate 5/12 - 1/4.
- Use common denominator 48.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/6
Worked Example 10
Problem: Calculate 7/9 - 2/3.
- Use common denominator 27.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/9
Practice Exercise
Create one new question about Subtracting like fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.3 Finding common denominators
The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Finding 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 Finding 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 Finding 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 Finding 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 Finding 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 Finding 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 Finding common denominators. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.4 Least common denominator
The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Least common 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 Least common 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 Least common 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 Least common 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 Least common 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 Least common 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 Least common denominator. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.5 Adding unlike fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Adding unlike 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: Calculate 1/2 + 1/2.
- Denominators already match.
- Add numerators: 1+1.
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 Adding unlike fractions .
Answer: 2/2
Worked Example 2
Problem: Calculate 2/3 + 1/3.
- Denominators already match.
- Add numerators: 2+1.
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 Adding unlike fractions .
Answer: 3/3
Worked Example 3
Problem: Calculate 3/4 + 1/4.
- Denominators already match.
- Add numerators: 3+1.
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 Adding unlike fractions .
Answer: 4/4
Worked Example 4
Problem: Calculate 5/6 + 1/6.
- Denominators already match.
- Add numerators: 5+1.
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 Adding unlike fractions .
Answer: 6/6
Worked Example 5
Problem: Calculate 7/8 + 1/8.
- Denominators already match.
- Add numerators: 7+1.
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 Adding unlike fractions .
Answer: 8/8
Worked Example 6
Problem: Calculate 1/3 + 1/4.
- Use common denominator 12.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 7/12
Worked Example 7
Problem: Calculate 2/5 + 3/10.
- Use common denominator 50.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 7/10
Worked Example 8
Problem: Calculate 3/8 + 1/6.
- Use common denominator 48.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 13/24
Worked Example 9
Problem: Calculate 5/12 + 1/4.
- Use common denominator 48.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 2/3
Worked Example 10
Problem: Calculate 7/9 + 2/3.
- Use common denominator 27.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 13/9
Practice Exercise
Create one new question about Adding unlike fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.6 Subtracting unlike fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Subtracting unlike 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: Calculate 1/2 - 1/2.
- Denominators match.
- Subtract numerators: 1-1.
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 Subtracting unlike fractions .
Answer: 0/2
Worked Example 2
Problem: Calculate 2/3 - 1/3.
- Denominators match.
- Subtract numerators: 2-1.
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 Subtracting unlike fractions .
Answer: 1/3
Worked Example 3
Problem: Calculate 3/4 - 1/4.
- Denominators match.
- Subtract numerators: 3-1.
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 Subtracting unlike fractions .
Answer: 2/4
Worked Example 4
Problem: Calculate 5/6 - 1/6.
- Denominators match.
- Subtract numerators: 5-1.
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 Subtracting unlike fractions .
Answer: 4/6
Worked Example 5
Problem: Calculate 7/8 - 1/8.
- Denominators match.
- Subtract numerators: 7-1.
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 Subtracting unlike fractions .
Answer: 6/8
Worked Example 6
Problem: Calculate 1/3 - 1/4.
- Use common denominator 12.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/12
Worked Example 7
Problem: Calculate 2/5 - 3/10.
- Use common denominator 50.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/10
Worked Example 8
Problem: Calculate 3/8 - 1/6.
- Use common denominator 48.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 5/24
Worked Example 9
Problem: Calculate 5/12 - 1/4.
- Use common denominator 48.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/6
Worked Example 10
Problem: Calculate 7/9 - 2/3.
- Use common denominator 27.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/9
Practice Exercise
Create one new question about Subtracting unlike fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.7 Adding mixed numbers
Adding mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. 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: Calculate 1/2 + 1/2.
- Denominators already match.
- Add numerators: 1+1.
Very beginner explanation: Adding mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2/2
Worked Example 2
Problem: Calculate 2/3 + 1/3.
- Denominators already match.
- Add numerators: 2+1.
Very beginner explanation: Adding mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3/3
Worked Example 3
Problem: Calculate 3/4 + 1/4.
- Denominators already match.
- Add numerators: 3+1.
Very beginner explanation: Adding mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 4/4
Worked Example 4
Problem: Calculate 5/6 + 1/6.
- Denominators already match.
- Add numerators: 5+1.
Very beginner explanation: Adding mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 6/6
Worked Example 5
Problem: Calculate 7/8 + 1/8.
- Denominators already match.
- Add numerators: 7+1.
Very beginner explanation: Adding mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 8/8
Worked Example 6
Problem: Calculate 1/3 + 1/4.
- Use common denominator 12.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 7/12
Worked Example 7
Problem: Calculate 2/5 + 3/10.
- Use common denominator 50.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 7/10
Worked Example 8
Problem: Calculate 3/8 + 1/6.
- Use common denominator 48.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 13/24
Worked Example 9
Problem: Calculate 5/12 + 1/4.
- Use common denominator 48.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 2/3
Worked Example 10
Problem: Calculate 7/9 + 2/3.
- Use common denominator 27.
- Rewrite both fractions.
- Add numerators and simplify.
Very beginner explanation: Fractions need equal-sized parts before their numerators can be added.
Answer: 13/9
Practice Exercise
Create one new question about Adding mixed numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.8 Subtracting mixed numbers
Subtracting mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. 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: Calculate 1/2 - 1/2.
- Denominators match.
- Subtract numerators: 1-1.
Very beginner explanation: Subtracting mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 0/2
Worked Example 2
Problem: Calculate 2/3 - 1/3.
- Denominators match.
- Subtract numerators: 2-1.
Very beginner explanation: Subtracting mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1/3
Worked Example 3
Problem: Calculate 3/4 - 1/4.
- Denominators match.
- Subtract numerators: 3-1.
Very beginner explanation: Subtracting mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2/4
Worked Example 4
Problem: Calculate 5/6 - 1/6.
- Denominators match.
- Subtract numerators: 5-1.
Very beginner explanation: Subtracting mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 4/6
Worked Example 5
Problem: Calculate 7/8 - 1/8.
- Denominators match.
- Subtract numerators: 7-1.
Very beginner explanation: Subtracting mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 6/8
Worked Example 6
Problem: Calculate 1/3 - 1/4.
- Use common denominator 12.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/12
Worked Example 7
Problem: Calculate 2/5 - 3/10.
- Use common denominator 50.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/10
Worked Example 8
Problem: Calculate 3/8 - 1/6.
- Use common denominator 48.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 5/24
Worked Example 9
Problem: Calculate 5/12 - 1/4.
- Use common denominator 48.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/6
Worked Example 10
Problem: Calculate 7/9 - 2/3.
- Use common denominator 27.
- Rewrite both fractions.
- Subtract numerators and simplify.
Very beginner explanation: A common denominator makes both fractions use the same-sized parts.
Answer: 1/9
Practice Exercise
Create one new question about Subtracting mixed numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.9 Regrouping mixed numbers
Regrouping mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. 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: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: Regrouping mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: Regrouping mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: Regrouping mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: Regrouping mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: Regrouping mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
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 Regrouping mixed numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.10 Negative fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Negative 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 Negative 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 Negative 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 Negative 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 Negative 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 Negative 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 Negative fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.11 Estimating fraction answers
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Estimating fraction answers .
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 Estimating fraction answers .
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 Estimating fraction answers .
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 Estimating fraction answers .
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 Estimating fraction answers .
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 Estimating fraction answers .
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 Estimating fraction answers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.12 Multi-step fraction problems
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Multi-step fraction problems .
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 Multi-step fraction problems .
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 Multi-step fraction problems .
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 Multi-step fraction problems .
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 Multi-step fraction problems .
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 Multi-step fraction problems .
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 Multi-step fraction problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
9.13 Real-life fraction problems
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Real-life fraction problems .
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 Real-life fraction problems .
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 Real-life fraction problems .
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 Real-life fraction problems .
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 Real-life fraction problems .
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 Real-life fraction problems .
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 Real-life fraction problems. 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 Adding like fractions . Show your reasoning and check your answer.
- Create and solve a new question about Subtracting like fractions . Show your reasoning and check your answer.
- Create and solve a new question about Finding common denominators . Show your reasoning and check your answer.
- Create and solve a new question about Least common denominator . Show your reasoning and check your answer.
- Create and solve a new question about Adding unlike fractions . Show your reasoning and check your answer.
- Create and solve a new question about Subtracting unlike fractions . Show your reasoning and check your answer.
- Create and solve a new question about Adding mixed numbers . Show your reasoning and check your answer.
- Create and solve a new question about Subtracting mixed numbers . Show your reasoning and check your answer.
- Create and solve a new question about Regrouping mixed numbers . Show your reasoning and check your answer.
- Create and solve a new question about Negative fractions . Show your reasoning and check your answer.
- Create and solve a new question about Estimating fraction answers . Show your reasoning and check your answer.
- Create and solve a new question about Multi-step fraction problems . 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 Adding like fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Adding like fractions.
Q2. What is important to remember about Subtracting like fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Subtracting like fractions.
Q3. What is important to remember about Finding common denominators?
Answer: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Finding common denominators.
Q4. What is important to remember about Least common denominator?
Answer: The denominator (bottom number of a fraction) tells how many equal parts make one whole. This topic focuses on Least common denominator.
Q5. What is important to remember about Adding unlike fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Adding unlike fractions.
Q6. What is important to remember about Subtracting unlike fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Subtracting unlike fractions.
Q7. What is important to remember about Adding mixed numbers?
Answer: Adding mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Subtracting mixed numbers?
Answer: Subtracting mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q9. What is important to remember about Regrouping mixed numbers?
Answer: Regrouping mixed numbers is an important Grade 7 idea in Adding and Subtracting Fractions. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Negative fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Negative fractions.
Q11. What is important to remember about Estimating fraction answers?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Estimating fraction answers.
Q12. What is important to remember about Multi-step fraction problems?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Multi-step fraction problems.
Q13. What is important to remember about Real-life fraction problems?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Real-life fraction problems.
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.