Ratio and Proportion Mental Math

Ratios and Proportions

Ratio: Comparison of two quantities (3:4, written 3/4) Proportion: Equality of two ratios (3/4 = 6/8)

Cross Multiplication

For a/b = c/d: a × d = b × c

Finding Missing Terms

If 3/4 = x/12, find x:

• Cross multiply: 3 × 12 = 4 × x
• 36 = 4x
• x = 9

Scaling Up/Down

Recipe for 4 serves 2 cups flour, how much for 6?

• Ratio: 4:2
• For 6: 6 × (2÷4) = 6 × 0.5 = 3 cups

Or:

• 4 servings needs 2 cups
• 1 serving needs 2÷4 = 0.5 cups
• 6 servings needs 6 × 0.5 = 3 cups

Unit Rate Method

If 5 items cost $20, what do 8 items cost?

1. Find unit rate: $20 ÷ 5 = $4 per item
2. Multiply: 8 × $4 = $32

Percentage as Ratio

25% = 1/4 = 1:4 50% = 1/2 = 1:2 75% = 3/4 = 3:4

Splitting by Ratio

Divide $100 in ratio 2:3

• Total parts: 2+3 = 5
• Each part: $100 ÷ 5 = $20
• First share: 2 × $20 = $40
• Second share: 3 × $20 = $60

Map Scales

Scale 1:50,000 means 1 cm = 50,000 cm = 500 m = 0.5 km

3 cm on map at 1:50,000:

• 3 × 0.5 km = 1.5 km actual

Common Ratios to Remember

• 1:2 (half)
• 1:3 (third)
• 1:4 (quarter)
• 2:3 (two-thirds)
• 3:4 (three-quarters)
• 1:10 (tenth, 10%)