Question

Divide. Write your answer as a fraction or a mixed number in simplest form.
2 1/2 divided by 1 3/4

Answer 1

To divide the mixed numbers \(2 \frac{1}{2}\) and \(1 \frac{3}{4}\), first convert them to improper fractions.

1. Convert \(2 \frac{1}{2}\):
\[
2 \frac{1}{2} = 2 \times 2 + 1 = 5 \implies \frac{5}{2}
\]

2. Convert \(1 \frac{3}{4}\):
\[
1 \frac{3}{4} = 1 \times 4 + 3 = 7 \implies \frac{7}{4}
\]

Now, divide the fractions:
\[
\frac{5}{2} \div \frac{7}{4}
\]

When dividing by a fraction, multiply by its reciprocal:
\[
\frac{5}{2} \times \frac{4}{7} = \frac{5 \times 4}{2 \times 7} = \frac{20}{14}
\]

Next, simplify \(\frac{20}{14}\):
\[
\frac{20 \div 2}{14 \div 2} = \frac{10}{7}
\]

Now, convert \(\frac{10}{7}\) to a mixed number:
\[
10 \div 7 = 1 \quad \text{remainder} \ 3 \implies 1 \frac{3}{7}
\]

Thus, the final answer is:
\[
\boxed{1 \frac{3}{7}}
\]