Question

Jesse spends 1/2

of his pocket money on Monday.
On Tuesday, he spends 2/3

of what is left.
On Wednesday, he spends 1/4

of what remains.

What fraction of the pocket money does he have left? Choose the most reasonable answer.
answers: 1/3, 4/3, 6/6, 1/8

Answer 1

Let's denote Jesse's total pocket money as \( P \).

1. On **Monday**, he spends \( \frac{1}{2}P \).
- Remaining pocket money after Monday:
\[
P - \frac{1}{2}P = \frac{1}{2}P
\]

2. On **Tuesday**, he spends \( \frac{2}{3} \) of what is left, which is \( \frac{2}{3} \times \frac{1}{2}P = \frac{1}{3}P \).
- Remaining pocket money after Tuesday:
\[
\frac{1}{2}P - \frac{1}{3}P
\]
To subtract these fractions, we need a common denominator, which is 6:
\[
\frac{1}{2}P = \frac{3}{6}P \quad \text{and} \quad \frac{1}{3}P = \frac{2}{6}P
\]
So:
\[
\frac{3}{6}P - \frac{2}{6}P = \frac{1}{6}P
\]

3. On **Wednesday**, he spends \( \frac{1}{4} \) of what remains:
\[
\frac{1}{4} \times \frac{1}{6}P = \frac{1}{24}P
\]
- Remaining pocket money after Wednesday:
\[
\frac{1}{6}P - \frac{1}{24}P
\]
Again, we need a common denominator to subtract, which is 24:
\[
\frac{1}{6}P = \frac{4}{24}P \quad \text{and} \quad \frac{1}{24}P = \frac{1}{24}P
\]
So:
\[
\frac{4}{24}P - \frac{1}{24}P = \frac{3}{24}P = \frac{1}{8}P
\]

Finally, Jesse has \( \frac{1}{8} \) of his pocket money left.

The most reasonable answer is \( \frac{1}{8} \).