Macey wants to buy gifts for her mom and brother. She decides to spend 1/2

Question

of the money she has on her mom and 1/3
of the money she has on her brother. What fractional portion of her money does she have left after purchasing the two gifts?

Answer 1

Let \( x \) be the total amount of money Macey has.

1. She spends \( \frac{1}{2} \) of her money on her mom: \[ \text{Amount spent on mom} = \frac{1}{2} x \]

2. She spends \( \frac{1}{3} \) of her money on her brother: \[ \text{Amount spent on brother} = \frac{1}{3} x \]

3. To find the total amount spent, we sum both amounts: \[ \text{Total amount spent} = \frac{1}{2} x + \frac{1}{3} x \]

4. To add these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6. We convert the fractions: \[ \frac{1}{2} x = \frac{3}{6} x, \quad \frac{1}{3} x = \frac{2}{6} x \]

5. Now we can add the fractions: \[ \text{Total amount spent} = \frac{3}{6} x + \frac{2}{6} x = \frac{5}{6} x \]

6. Finally, we determine the amount of money Macey has left. This is found by subtracting the total amount spent from her original total: \[ \text{Amount left} = x - \frac{5}{6} x = \frac{1}{6} x \]

Therefore, the fractional portion of her money that Macey has left after purchasing the gifts is \( \frac{1}{6} \).