Split 240 books in the ratio 5 to 3

Distribute 240 books between Class A and Class B in the ratio of 5 to 3. How many books does Class A receive?

Step-by-step

1. 5 + 3 = 8
   Total parts = sum of all ratio terms
2. 240 ÷ 8 = 30
   Value of one part
3. 30 × 5 = 150
   Share for ratio term 1
4. 30 × 3 = 90
   Share for ratio term 2

Why it works

The key to ratio distribution is first finding the value of "one part", then multiplying by each class's share. The two parts are in the ratio 5 to 3, so the total number of parts is 8. Dividing the total amount by the total parts gives the value of one part. Reversing the order (multiplying by the parts first, then dividing by the total) yields the same result, but finding one part first is less error-prone because the intermediate quantity has a clear meaning.

Common mistakes

• Dividing the total amount by the larger single share instead of dividing by the total number of parts.
• Calculating Class B's share and treating it as the answer without noticing that the question asks for Class A.
• Misinterpreting "5 to 3" as three-fifths and directly multiplying by a fraction.

Related

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