Question

Joe give 2/5 of his stickers to Kelvin and half of the remainder to Larry.What fraction of the stickers was he left with ?

Answer 1

Let's denote the total number of stickers Joe originally had as \( S \).

1. **Giving stickers to Kelvin**: Joe gives \( \frac{2}{5} \) of his stickers to Kelvin. The number of stickers he gives to Kelvin is:
\[
\frac{2}{5} S
\]
After giving these stickers, the number of stickers Joe has left is:
\[
S - \frac{2}{5} S = \frac{3}{5} S
\]

2. **Giving stickers to Larry**: Now, Joe gives half of the remaining stickers to Larry. The number of stickers he gives to Larry is:
\[
\frac{1}{2} \times \frac{3}{5} S = \frac{3}{10} S
\]
After giving these stickers to Larry, the number of stickers Joe is left with is:
\[
\frac{3}{5} S - \frac{3}{10} S
\]

To subtract these fractions, we need a common denominator. The least common denominator between 5 and 10 is 10, so we can convert:
\[
\frac{3}{5} S = \frac{6}{10} S
\]
Thus, now we can rewrite the expression:
\[
\frac{6}{10} S - \frac{3}{10} S = \frac{3}{10} S
\]

So, Joe is left with \( \frac{3}{10} \) of his original stickers.

Thus, the fraction of the stickers Joe was left with is \( \frac{3}{10} \).