Ratios and Proportional Reasoning Flashcards

In a proportion, if a/b = c/d, which of the following must also be true?

Answer: a × d = b × c

In any proportion a/b = c/d, the cross-products are equal: a × d = b × c.

A store sells 3 apples for $1.20. At this rate, how much do 10 apples cost?

Answer: $4.00

Unit price = $1.20 ÷ 3 = $0.40 per apple; 10 × $0.40 = $4.00.

The ratio of red marbles to blue marbles is 2:7. If there are 63 blue marbles, how many red marbles are there?

Answer: 18

If 7 parts = 63, then 1 part = 9, so 2 parts (red) = 18.

Which table of values shows a proportional relationship?

Answer: x: 1,2,3 | y: 2,4,6

In x: 1,2,3 | y: 2,4,6, the ratio y/x = 2 for all pairs, confirming proportionality.

If 12 workers can complete a job in 8 days, how many days will 6 workers need to complete the same job?

Answer: 16 days

This is inverse proportion: 12 × 8 = 6 × d, so d = 96 ÷ 6 = 16 days.

A photograph is enlarged so that the new width is 15 inches. The original photo was 5 inches wide and 8 inches tall. What is the height of the enlarged photo?

Answer: 24 inches

Scale factor = 15 ÷ 5 = 3; new height = 8 × 3 = 24 inches.

The ratio 8:12 is the same as:

Answer: 2:3

Dividing both 8 and 12 by their GCF of 4 gives 2:3.