Writing & simplifying ratios drills

Express and reduce ratios; distinguish part-to-part from part-to-whole.

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

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How to write and simplify ratios

A ratio compares two amounts in the order the question names them. "Red to blue" means red comes first.

  1. Write the two numbers in that order.
  2. Divide both numbers by their greatest common factor (GCF). With 24 red beads and 18 blue beads, the GCF is 6, so \(24:18 = 4:3\).
  3. Check if the question wants part-to-part or part-to-whole. If it says "to the total", add the parts first: red to total is \(24:42 = 4:7\).

Common traps:

Worked examples

Example 1.
A weather log has 90 sunny days and 27 rainy days. What is the ratio of sunny days to rainy days in simplest form?
Show answer and explanation
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.)

Example 2.
A sports bin has 14 basketballs and 12 soccer balls. What is the ratio of basketballs to the total number of balls?
Show answer and explanation
Answer:
A

Total balls \(= 14 + 12 = 26\). Ratio of basketballs to total \(= 14:26\), which reduces to 7:13. (Using soccer balls instead of basketballs against the total gives the wrong answer 6:13. Writing the total first gives 13:7. Leaving it as a part-to-part ratio gives 7:6.)