Question

Kiley had a piece of bamboo skewer that measured 14Three-fifths inches long. She wanted to cut it into toothpicks that were each 3One-fifth inches long. How many toothpicks can she make?
4 toothpicks
5 toothpicks
46 toothpicks
47 toothpicks

Answer 1

To determine how many toothpicks Kiley can make, we need to divide the total length of the bamboo skewer by the length of each toothpick.

1. **Convert the mixed numbers to improper fractions:**
- For \( 14\frac{3}{5} \):
\[
14\frac{3}{5} = \frac{14 \times 5 + 3}{5} = \frac{70 + 3}{5} = \frac{73}{5}
\]
- For \( 3\frac{1}{5} \):
\[
3\frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{15 + 1}{5} = \frac{16}{5}
\]

2. **Divide the total length by the length of each toothpick:**
\[
\text{Number of toothpicks} = \frac{14\frac{3}{5}}{3\frac{1}{5}} = \frac{\frac{73}{5}}{\frac{16}{5}}
\]

3. **Dividing fractions (multiply by the reciprocal):**
\[
= \frac{73}{5} \times \frac{5}{16} = \frac{73 \times 5}{5 \times 16} = \frac{73}{16}
\]

4. **Calculate \( 73 \div 16 \):**
- To find how many whole toothpicks she can make, divide 73 by 16.
\[
73 \div 16 = 4.5625
\]
This means Kiley can make 4 whole toothpicks since we only take the whole part.

Thus, Kiley can make **4 toothpicks**.