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Ratios and Proportional Reasoning Flashcards

7 cards from real IAAT practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. The ratio 8:12 is the same as:

    Answer: 2:3

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