Question

1. $3\frac{1}{2} \times 2\frac{6}{7} =$

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \( 3\frac{1}{2} \) to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So for \( 3\frac{1}{2} \), we have \( \frac{3\times2 + 1}{2}=\frac{6 + 1}{2}=\frac{7}{2} \).

For \( 2\frac{6}{7} \), using the same formula, we get \( \frac{2\times7+6}{7}=\frac{14 + 6}{7}=\frac{20}{7} \).

Step2: Multiply the improper fractions

Now we multiply \( \frac{7}{2} \times \frac{20}{7} \). When multiplying fractions, we multiply the numerators together and the denominators together: \( \frac{7\times20}{2\times7} \).

We can simplify before multiplying. The 7 in the numerator and the 7 in the denominator cancel out, and we have \( \frac{20}{2} \) (because \( \frac{7\times20}{2\times7}=\frac{20}{2} \) after canceling the 7s).

Step3: Simplify the result

Simplifying \( \frac{20}{2} \) gives us 10.

Answer:

\( 10 \)