Chapter 17: Ratios
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Ratios with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Ratio (a comparison of two quantities)
- 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.
17.1 Meaning of ratio
A ratio compares two quantities in a fixed order. This topic focuses on Meaning of ratio .
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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Meaning of ratio .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Meaning of ratio .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Meaning of ratio .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Meaning of ratio .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Meaning of ratio .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Meaning of ratio. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.2 Part-to-part ratios
A ratio compares two quantities in a fixed order. This topic focuses on Part-to-part ratios .
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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-part ratios .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-part ratios .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-part ratios .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-part ratios .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-part ratios .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Part-to-part ratios. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.3 Part-to-whole ratios
A ratio compares two quantities in a fixed order. This topic focuses on Part-to-whole ratios .
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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-whole ratios .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-whole ratios .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-whole ratios .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-whole ratios .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-whole ratios .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Part-to-whole ratios. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.4 Writing ratios three ways
A ratio compares two quantities in a fixed order. This topic focuses on Writing ratios three ways .
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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Writing ratios three ways .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Writing ratios three ways .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Writing ratios three ways .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Writing ratios three ways .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Writing ratios three ways .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Writing ratios three ways. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.5 Simplifying ratios
A ratio compares two quantities in a fixed order. This topic focuses on Simplifying ratios .
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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Simplifying ratios .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Simplifying ratios .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Simplifying ratios .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Simplifying ratios .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Simplifying ratios .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Simplifying ratios. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.6 Equivalent ratios
A ratio compares two quantities in a fixed order. This topic focuses on Equivalent ratios .
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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Equivalent ratios .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Equivalent ratios .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Equivalent ratios .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Equivalent ratios .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Equivalent ratios .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Equivalent ratios. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.7 Ratio tables
A ratio compares two quantities in a fixed order. This topic focuses on Ratio tables .
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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Ratio tables .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Ratio tables .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Ratio tables .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Ratio tables .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Ratio tables .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Ratio tables. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.8 Comparing ratios
A ratio compares two quantities in a fixed order. This topic focuses on Comparing ratios .
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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Comparing ratios .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Comparing ratios .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Comparing ratios .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Comparing ratios .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Comparing ratios .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Comparing ratios. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.9 Ratios with fractions
A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Ratios with 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 Ratios with 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 Ratios with 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 Ratios with 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 Ratios with 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 Ratios with 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 Ratios with fractions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.10 Ratios with decimals
A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Ratios with decimals .
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: Identify the tenths digit in 3.47.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Ratios with decimals .
Answer: 4
Worked Example 2
Problem: Identify the tenths digit in 8.205.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Ratios with decimals .
Answer: 2
Worked Example 3
Problem: Identify the tenths digit in 0.96.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Ratios with decimals .
Answer: 9
Worked Example 4
Problem: Identify the tenths digit in 12.375.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Ratios with decimals .
Answer: 3
Worked Example 5
Problem: Identify the tenths digit in 5.004.
- The tenths digit is the first digit to the right of the decimal point.
Very beginner explanation: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Ratios with decimals .
Answer: 0
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 3.8
Worked Example 7
Problem: Round 8.4 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 8.4
Worked Example 8
Problem: Round 12.05 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 12.1
Worked Example 9
Problem: Round 0.96 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 1
Worked Example 10
Problem: Round 5.125 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 5.1
Practice Exercise
Create one new question about Ratios with decimals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.11 Scaling recipes
Scaling recipes is an important Grade 7 idea in Ratios. 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: Scaling recipes: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Scaling recipes is an important Grade 7 idea in Ratios. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Scaling recipes: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Scaling recipes is an important Grade 7 idea in Ratios. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Scaling recipes: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Scaling recipes is an important Grade 7 idea in Ratios. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Scaling recipes: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Scaling recipes is an important Grade 7 idea in Ratios. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Scaling recipes: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Scaling recipes is an important Grade 7 idea in Ratios. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Scaling recipes in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Scaling recipes becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Scaling recipes and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Scaling recipes becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Scaling recipes using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Scaling recipes becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Scaling recipes problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Scaling recipes becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Scaling recipes could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Scaling recipes becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Scaling recipes. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.12 Classroom and sports ratios
A ratio compares two quantities in a fixed order. This topic focuses on Classroom and sports ratios .
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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Classroom and sports ratios .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Classroom and sports ratios .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Classroom and sports ratios .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Classroom and sports ratios .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Classroom and sports ratios .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Classroom and sports ratios. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
17.13 Real-life ratio problems
A ratio compares two quantities in a fixed order. This topic focuses on Real-life ratio 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: Simplify 4:6.
- GCF(4,6)=2.
- Divide both terms by 2.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Real-life ratio problems .
Answer: 2:3
Worked Example 2
Problem: Simplify 8:12.
- GCF(8,12)=4.
- Divide both terms by 4.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Real-life ratio problems .
Answer: 2:3
Worked Example 3
Problem: Simplify 15:25.
- GCF(15,25)=5.
- Divide both terms by 5.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Real-life ratio problems .
Answer: 3:5
Worked Example 4
Problem: Simplify 21:28.
- GCF(21,28)=7.
- Divide both terms by 7.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Real-life ratio problems .
Answer: 3:4
Worked Example 5
Problem: Simplify 18:30.
- GCF(18,30)=6.
- Divide both terms by 6.
Very beginner explanation: A ratio compares two quantities in a fixed order. This topic focuses on Real-life ratio problems .
Answer: 3:5
Worked Example 6
Problem: Simplify the ratio 4:6.
- Find the greatest common factor, 2.
- Divide both terms by 2.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 7
Problem: Simplify the ratio 8:12.
- Find the greatest common factor, 4.
- Divide both terms by 4.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 2:3
Worked Example 8
Problem: Simplify the ratio 15:25.
- Find the greatest common factor, 5.
- Divide both terms by 5.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 9
Problem: Simplify the ratio 18:30.
- Find the greatest common factor, 6.
- Divide both terms by 6.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:5
Worked Example 10
Problem: Simplify the ratio 21:28.
- Find the greatest common factor, 7.
- Divide both terms by 7.
Very beginner explanation: Simplifying a ratio is like simplifying a fraction: divide both quantities by the same common factor.
Answer: 3:4
Practice Exercise
Create one new question about Real-life ratio 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 Meaning of ratio . Show your reasoning and check your answer.
- Create and solve a new question about Part-to-part ratios . Show your reasoning and check your answer.
- Create and solve a new question about Part-to-whole ratios . Show your reasoning and check your answer.
- Create and solve a new question about Writing ratios three ways . Show your reasoning and check your answer.
- Create and solve a new question about Simplifying ratios . Show your reasoning and check your answer.
- Create and solve a new question about Equivalent ratios . Show your reasoning and check your answer.
- Create and solve a new question about Ratio tables . Show your reasoning and check your answer.
- Create and solve a new question about Comparing ratios . Show your reasoning and check your answer.
- Create and solve a new question about Ratios with fractions . Show your reasoning and check your answer.
- Create and solve a new question about Ratios with decimals . Show your reasoning and check your answer.
- Create and solve a new question about Scaling recipes . Show your reasoning and check your answer.
- Create and solve a new question about Classroom and sports ratios . 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 Meaning of ratio?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Meaning of ratio.
Q2. What is important to remember about Part-to-part ratios?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-part ratios.
Q3. What is important to remember about Part-to-whole ratios?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Part-to-whole ratios.
Q4. What is important to remember about Writing ratios three ways?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Writing ratios three ways.
Q5. What is important to remember about Simplifying ratios?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Simplifying ratios.
Q6. What is important to remember about Equivalent ratios?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Equivalent ratios.
Q7. What is important to remember about Ratio tables?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Ratio tables.
Q8. What is important to remember about Comparing ratios?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Comparing ratios.
Q9. What is important to remember about Ratios with fractions?
Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, or a ratio. This topic focuses on Ratios with fractions.
Q10. What is important to remember about Ratios with decimals?
Answer: A decimal uses place value to represent parts of one, such as tenths, hundredths, and thousandths. This topic focuses on Ratios with decimals.
Q11. What is important to remember about Scaling recipes?
Answer: Scaling recipes is an important Grade 7 idea in Ratios. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Classroom and sports ratios?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Classroom and sports ratios.
Q13. What is important to remember about Real-life ratio problems?
Answer: A ratio compares two quantities in a fixed order. This topic focuses on Real-life ratio 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.