Equivalent ratios & ratio tables drills

Generate equivalent ratios and complete ratio tables.

Free, timed SHSAT practice sets on equivalent ratios & ratio tables— every question includes a full worked explanation, and there's no account required.

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How to solve equivalent ratio and ratio table problems

Two ratios are equivalent when you get one from the other by multiplying (or dividing) both terms by the same number. Adding the same number does not work.

Common traps: dividing the known amount by the wrong term (sugar must go with sugar), adding instead of multiplying (\(3:2\) is not equal to \(4:3\)), and on a "NOT equivalent" question, picking one that works.

Worked examples

Example 1.
The ratio of goals to shots is always 4:5. If there are 20 shots, how many goals are there?
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Answer:
D

Scale factor \(= 20 \div 5 = 4\), so goals \(= 4 \times 4 = 16\). (Using the wrong ratio term, \(20 \div 4 \times 5\), gives 25. Keeping the same difference as the ratio terms, \(20 - 1\), instead of scaling gives 19. Using a scale factor of 5 instead of 4 gives 20.)

Example 2.
The ratio of blue paint cans to white paint cans is 4:9. Which of the following ratios is NOT equivalent to this ratio?
Show answer and explanation
Answer:
A

An equivalent ratio multiplies both terms of 4:9 by the same number: 12:27 is \(4 \times 3 : 9 \times 3\); 24:54 is \(4 \times 6 : 9 \times 6\); 28:63 is \(4 \times 7 : 9 \times 7\). But 8:13 adds 4 to both terms, and adding does not keep the ratio the same, so it is NOT equivalent. (Choosing 12:27, 24:54 or 28:63 means the word NOT was missed.)