Question

Find the quotient and write it in simplest form: 1 and two-thirds divided by 2 and one-half equals
(1 point)
Responses


Image with alt text:

The fraction shows 2 over 3.
Image with alt text: The fraction shows 2 over 3.


Image with alt text:


Image with alt text:

Answer 1

To find the quotient of \(1 \frac{2}{3}\) divided by \(2 \frac{1}{2}\), we first convert the mixed numbers into improper fractions.

1. **Convert \(1 \frac{2}{3}\) to an improper fraction:**
\[
1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}
\]

2. **Convert \(2 \frac{1}{2}\) to an improper fraction:**
\[
2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}
\]

3. **Now we divide the fractions:**
\[
\frac{5}{3} \div \frac{5}{2}
\]
When dividing fractions, we multiply by the reciprocal of the divisor:
\[
= \frac{5}{3} \times \frac{2}{5}
\]

4. **Multiplying the fractions:**
\[
= \frac{5 \times 2}{3 \times 5} = \frac{10}{15}
\]

5. **Simplifying \(\frac{10}{15}\):**
\[
= \frac{2}{3}
\]

Thus, the quotient of \(1 \frac{2}{3}\) divided by \(2 \frac{1}{2}\) is \(\frac{2}{3}\).

So the answer is \(\frac{2}{3}\).