Share 120 books in the ratio 3:1

A school shares 120 books between the sixth grade and the fifth grade in the ratio 3:1, so the sixth grade gets 3 times as many books as the fifth grade. How many books does each grade get?

Step-by-step

1. 3 + 1 = 4
   Total parts = sum of all ratio terms
2. 120 ÷ 4 = 30
   Value of one part
3. 30 × 3 = 90
   Share for ratio term 1
4. 30 × 1 = 30
   Share for ratio term 2

Why it works

Sharing in a ratio means splitting the total into 3 + 1 = 4 equal parts; one part is the total divided by 4, and each share is that part multiplied by its number of parts.

Common mistakes

• Dividing 120 by 3 instead of by the 4 parts in total.
• Giving the 30-book share to the sixth grade and the larger share to the fifth grade.

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