Mathematical: Ratios and Proportional Relationships Flashcards

A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 8 cups of flour, how many cups of sugar are needed?

Answer: 12 cups

The ratio is 2:3, so 8 ÷ 2 × 3 = 12 cups of sugar.

A car travels 150 miles in 3 hours. What is the unit rate in miles per hour?

Answer: 50 mph

150 miles ÷ 3 hours = 50 miles per hour.

Which equation represents a proportional relationship between x and y?

Answer: y = 3x

A proportional relationship has the form y = kx passing through the origin; y = 3x satisfies this.

On a map, 1 inch represents 25 miles. If two cities are 3.5 inches apart on the map, what is the actual distance?

Answer: 87.5 miles

3.5 inches × 25 miles per inch = 87.5 miles.

If 4 notebooks cost $12.00, how much would 7 notebooks cost at the same rate?

Answer: $21.00

The unit rate is $12 ÷ 4 = $3 per notebook; 7 × $3 = $21.

A store is offering 30% off all items. If a jacket originally costs $80, what is the sale price?

Answer: $56.00

30% of $80 = $24 discount; $80 minus $24 = $56.

The ratio of boys to girls in a class is 3:5. If there are 24 boys, how many girls are there?

Answer: 40

24 boys ÷ 3 parts × 5 parts = 40 girls.