Ratios and Proportional Reasoning Flashcards

A recipe calls for 3 cups of flour for every 2 cups of sugar. If you use 9 cups of flour, how many cups of sugar do you need?

Answer: 6 cups

The ratio 3:2 scales by a factor of 3 when flour becomes 9, so sugar = 2 × 3 = 6 cups.

The ratio of boys to girls in a class is 4:5. If there are 20 boys, how many girls are there?

Answer: 25

If 4 parts = 20 boys, then 1 part = 5, so 5 parts (girls) = 25.

Which of the following ratios is equivalent to 6:9?

Answer: 2:3

Dividing both 6 and 9 by 3 gives 2:3, which is the simplified form.

A car travels 150 miles in 3 hours. At the same rate, how many miles will it travel in 5 hours?

Answer: 250 miles

The rate is 150 ÷ 3 = 50 miles per hour; 50 × 5 = 250 miles.

If 5 notebooks cost $7.50, what is the cost of 8 notebooks at the same rate?

Answer: $12.00

Unit cost = $7.50 ÷ 5 = $1.50 per notebook; 8 × $1.50 = $12.00.

Two quantities x and y are proportional. When x = 4, y = 10. What is y when x = 6?

Answer: 15

The constant of proportionality is 10 ÷ 4 = 2.5, so when x = 6, y = 6 × 2.5 = 15.

A map has a scale of 1 inch : 50 miles. Two cities are 3.5 inches apart on the map. What is the actual distance?

Answer: 175 miles

3.5 inches × 50 miles per inch = 175 miles.