Ratios & Proportions • Topic 2 of 3

Solving Equivalent Ratio Problems

What are Equivalent Ratios?

Equivalent ratios are ratios that name the same comparison. They are like equivalent fractions!

Example: 1:2 = 2:4 = 3:6 = 4:8

Finding Equivalent Ratios:

Multiply or divide both terms by the same number
Just like finding equivalent fractions!

The Proportion Method:

When two ratios are equal, they form a proportion:

3/5 = ?/20

Cross-multiply: 3 × 20 = 5 × ?
             60 = 5 × ?
             ? = 60 ÷ 5 = 12

So 3/5 = 12/20

EQUIVALENT RATIOS - TAPE DIAGRAM:

    Ratio 1:2
    
    │■│  :  │■■│
    
    Ratio 2:4 (multiply both by 2)
    
    │■■│  :  │■■■■│
    
    Ratio 3:6 (multiply both by 3)
    
    │■■■│  :  │■■■■■■│


CROSS-MULTIPLICATION METHOD:

    3   =   ?
    5       20
    
    Step 1: Cross-multiply
    3 × 20 = 5 × ?
    60 = 5 × ?
    
    Step 2: Divide to find ?
    ? = 60 ÷ 5 = 12
    
    Check: 3/5 = 12/20 ✓


FINDING MISSING TERM:

    ?   =   8
    7       28
    
    Cross-multiply: ? × 28 = 7 × 8
                  ? × 28 = 56
                  ? = 56 ÷ 28 = 2
    
    Check: 2/7 = 8/28 ✓ (both simplify to ~0.2857)

Solved Examples

Worked Example

Find the missing term: (2)/(3) = ?/15

Solution

Cross-multiply: 2 × 15 = 3 × ?
30 = 3 × ?
? = 30 ÷ 3 = 10
Answer: 10 ((2)/(3) = 10/15)

Worked Example

Find the missing term: (5)/(8) = 20/?

Solution

Cross-multiply: 5 × ? = 8 × 20
5 × ? = 160
? = 160 ÷ 5 = 32
Answer: 32 ((5)/(8) = 20/32)

Worked Example

A recipe uses 3 cups of flour for every 2 cups of sugar. How much sugar for 9 cups of flour?

Solution

Ratio: flour : sugar = 3 : 2
Set up proportion: (3)/(2) = 9/x
Cross-multiply: 3x = 18
x = 6
Answer: 6 cups of sugar

Worked Example

Are the ratios 4:6 and 8:12 equivalent?

Solution

Simplify 4:6 = divide by 2 = 2:3
Simplify 8:12 = divide by 4 = 2:3
Both simplify to 2:3, so YES they are equivalent
Answer: Yes

Key Points

Equivalent ratios = same value when simplified
Multiply or divide both terms by same number
Use cross-multiplication to find missing terms
Proportion: two equal ratios
Check equivalence by simplifying or cross-multiplying

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.Equivalent ratios have the same:

Explanation: Same value.

Q2.$1:2$ is equivalent to:

Explanation: Multiply both by $2$.

Q3.To find an equivalent ratio, multiply or divide both parts by the:

Explanation: Same number.

Q4.Complete: $3:4=9:?$

Explanation: $\times3$.

Practice more MCQs → 📝 Assignment · 35 marks