Ratio direction flip sprint

Invert a ratio or set up a proportion with numerator and denominator swapped.

An error-pattern drill: practice spotting and avoiding this specific SHSAT trap.

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How to avoid flipping a ratio

A recipe uses 2 cups of sugar for every 3 cups of flour. How much sugar goes with 12 cups of flour? If you flip the ratio, you get \(12 \times \tfrac{3}{2} = 18\) cups. The right setup is \(\tfrac{\text{sugar}}{\text{flour}} = \tfrac{2}{3} = \tfrac{x}{12}\), so \(x = 8\) cups.

The trap is easy to fall into because both setups use the same numbers, and both give a clean answer. Only the order is wrong.

Check habits:

Worked examples

Example 1.
A cyclist rides at a constant rate. It is known that 8 hours correspond to 70.4 miles ridden, and \(y = kx\). What is \(k\)?
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Answer:
A

\(k = y \div x = 70.4 \div 8 = 8.8\). (Dividing \(x\) by \(y\) gives about 0.114. Stopping at \(y\) without dividing gives 70.4. Multiplying \(8 \times 70.4\) instead of dividing gives 563.2.)

Example 2.
Two figures are similar. A side of 22 cm in the smaller figure corresponds to a side of 33 cm in the larger figure. If a different side of the smaller figure is 6 cm, what is the length of the corresponding side in the larger figure?
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Answer:
D

Scale factor \(= 33 \div 22 = 3/2\). Corresponding side \(= 6 \times 3/2 = 9\) cm. (Dividing by the scale factor instead of multiplying gives 4 cm. Adding the difference \(33 - 22 = 11\) instead of multiplying gives 17 cm. Matching the wrong sides, \(22 \times 33 \div 6\), gives 121 cm.)

Example 3.
A weather log has 90 sunny days and 27 rainy days. What is the ratio of sunny days to rainy days in simplest form?
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Answer:
D

\(\gcd(90,27) = 9\), so 90:27 reduces to 10:3 by dividing both terms by 9. (Reversing the order gives 3:10. Leaving the ratio unreduced gives 90:27. Dividing only the first term by 9 gives 10:27.)