Question
Divide 120 in the ratio 3:5.
Solution — Step by Step
Add the two numbers in the ratio: parts total. Think of it this way — we’re splitting 120 into 8 equal chunks, then giving 3 chunks to the first share and 5 chunks to the second.
So each “chunk” is worth 15. Every ratio problem reduces to this — find the unit value first, then scale up.
First share
Second share
Always check: ✓
Also verify the ratio: (divide both by 15) ✓
The two parts are 45 and 75.
Why This Works
A ratio like tells us about relative sizes, not absolute amounts. We don’t know the actual values until we’re given the total. The ratio just tells us the second share is times as large as the first.
When we add the ratio terms (), we get the total number of equal parts the whole is divided into. Dividing the total (120) by this number (8) gives us what one part equals. After that, multiplying by 3 or 5 scales up to the actual shares.
This same logic works for any ratio division — two-part, three-part, or even four-part ratios. The method never changes.
Alternative Method
We can use fractions directly instead of finding one part.
First share
Second share
The fraction method is slightly faster once you’re comfortable with it. Write the share as a fraction of the total — numerator is the ratio term, denominator is the sum of all ratio terms — then multiply by the whole amount.
Common Mistake
The most common error: students divide 120 by 3 to get the first share and 120 by 5 to get the second. That gives 40 and 24, which add up to 64 — not 120. The total must always equal the original amount. You divide by the sum of ratio terms (8), not by each term separately.