Question

Question 8 Divide: 5 2/3÷3 4/7 (1 point) Responses 1 44/75 −1 44/75 15 8/21 −15 8/21

Answer 1

To solve the division of mixed numbers \(5 \frac{2}{3} \div 3 \frac{4}{7}\), we first convert the mixed numbers into improper fractions.

1. Convert \(5 \frac{2}{3}\):
\[
5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{15 + 2}{3} = \frac{17}{3}
\]

2. Convert \(3 \frac{4}{7}\):
\[
3 \frac{4}{7} = \frac{3 \times 7 + 4}{7} = \frac{21 + 4}{7} = \frac{25}{7}
\]

Now we can perform the division of the two improper fractions:
\[
\frac{17}{3} \div \frac{25}{7}
\]

Dividing by a fraction is the same as multiplying by its reciprocal:
\[
\frac{17}{3} \times \frac{7}{25} = \frac{17 \times 7}{3 \times 25} = \frac{119}{75}
\]

Now, we can convert \(\frac{119}{75}\) to a mixed number:
1. Divide 119 by 75:
\[
119 \div 75 = 1 \quad \text{(remainder } 44\text{)}
\]

So, we have:
\[
\frac{119}{75} = 1 \frac{44}{75}
\]

The answer is \(1 \frac{44}{75}\).

Among the responses, the correct answer is:
**1 \( \frac{44}{75} \)**.