Jesse spends 1/2

Question

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 \( \frac{1}{8} \).