Find the missing term

The idea

To complete a : b :: c : ?, find the factor of change from a to c by dividing c by a, and multiply b by the same factor, which may be a fraction.

Kesang's lemonade, again

Kesang puts 10 spoons of sugar in 6 glasses of lemonade. Her father needs 18 glasses with the same sweetness.

How many spoons of sugar for 18 glasses?

• 22 spoons
• 28 spoons
• 30 spoons

Complete the proportion

The ratios must change by the same factor. First find the factor from a to c. Then use it on b. Follow the hints.

Factor of change

To complete a : b :: c : ?, find the factor of change from a to c by dividing c by a, and multiply b by the same factor, which may be a fraction.

6 : 10 :: 18 : ?. The factor is 18 ÷ 6 = 3. So 10 × 3 = 30.

The factor can be a fraction. 120 : 15 :: 80 : ?. The factor is 80 ÷ 120 = 2/3. So 15 × 2/3 = 10.

Notes

To complete a : b :: c : ?, find the factor of change from a to c by dividing c by a, and multiply b by the same factor, which may be a fraction.

Check yourself

Complete the proportion: 4 : 7 :: 12 : ?

Answer: 21

12 ÷ 4 = 3, so 7 × 3 = 21. 4 : 7 :: 12 : 21.

Complete the proportion: 9 : 6 :: 12 : ?

Answer: 8

12 ÷ 9 = 4/3, so 6 × 4/3 = 8. 9 : 6 :: 12 : 8.

To complete 8 : 12 :: 20 : ?, what is the factor of change from the first terms?

A bus uses 14 litres of diesel for 98 km. Complete 98 : 14 :: 49 : ? How many litres for 49 km?

Answer: 7 litres

49 ÷ 98 = 1/2, so 14 × 1/2 = 7 litres.

• 20 − 8 = 12. That is the difference. A factor is what we multiply by.
• 12 ÷ 8 = 3/2. That compares the two terms of the first ratio. The factor is from 8 to 20.
• 20 ÷ 8 = 5/2 — correct. Yes! 8 × 5/2 = 20. Then 12 × 5/2 = 30.
• 8 ÷ 20 = 2/5. That is the factor from 20 back to 8. We want from 8 up to 20.