Finding Equivalent Ratios

Learn to scale ratios and find missing values

1. Scaling Ratios Up and Down

The Key Rule

To find an equivalent ratio, multiply or divide EVERY term by the same number.

Example 1: Lemonade Recipe

Mrs Lim mixes 1 glass of lemon juice with 5 glasses of sparkling water to make lemonade.

Lemon juice	1	2	3	4
Sparkling water	5	10	15	?

If she uses 4 glasses of lemon juice, how many glasses of sparkling water does she need?

Since 1 × 4 = 4, multiply both by 4:

$1 : 5 = 4 : 20$

Mrs Lim needs 20 glasses of sparkling water.

1 : 5 → ×4 → 4 : 20

Example 2: Scaling Down

Find the missing value: $5 : 20 = 1 : ?$

Since 5 ÷ 5 = 1, divide both by 5:

20 ÷ 5 = 4

$5 : 20 = 1 : 4$

5 : 20 → ÷5 → 1 : 4

2. Finding Missing Values

Strategy

Look at the known values to find the scaling factor
Apply the same factor to find the missing value

Example 3: Find the missing number in $3 : 7 = ? : 28$

3 : 7 drawn as 3 units and 7 units. The 7 units stand for 28.

Step 1: Find the factor: 7 → 28 means ×4

Step 2: Apply to first term: 3 × 4 = 12

$3 : 7 = 12 : 28$

Example 4: Find the missing number in $? : 5 = 12 : 30$

Step 1: Find the factor: 30 → 5 means ÷6

Step 2: Apply to first term: 12 ÷ 6 = 2

$2 : 5 = 12 : 30$

12 : 30 → ÷6 → 2 : 5

Example 5: Three-Term Ratio

Find the missing numbers: $5 : 3 : 4 = ? : 18 : ?$

Step 1: Find the factor from 3 → 18: that's ×6

Step 2: Apply ×6 to all terms:

5 × 6 = 30
3 × 6 = 18 ✓
4 × 6 = 24

$5 : 3 : 4 = 30 : 18 : 24$

5 : 3 : 4 → ×6 → 30 : 18 : 24

3. Real-World Applications

Example 6: Bakery Tarts

A bakery sells boxes of tarts. Each box contains 6 strawberry tarts and 4 lemon tarts. Find the two missing numbers in the table.

Boxes	1	2	3	4	5
Strawberry	6	12	18	24	?
Lemon	4	8	?	16	20

The ratio stays constant: 3 : 2

5 boxes: Strawberry = 6 × 5 = 30 tarts

3 boxes: Lemon = 4 × 3 = 12 tarts

Key Points to Remember

✓ To scale up: multiply every term by the same number
✓ To scale down: divide every term by the same number
✓ Find the factor from known values first
✓ Apply the same factor to find missing values
✓ Ratio tables help track equivalent ratios