Questions: 3 1/2 × 5 3/4 =

Solution Steps

To multiply mixed numbers, first convert each mixed number into an improper fraction. Then, multiply the numerators together and the denominators together to get the product. Finally, simplify the resulting fraction and, if necessary, convert it back to a mixed number.

To multiply mixed numbers, we first convert them to improper fractions. The mixed number \(3 \frac{1}{2}\) is converted to the improper fraction \(\frac{7}{2}\), and the mixed number \(5 \frac{3}{4}\) is converted to \(\frac{23}{4}\).

Next, we multiply the two improper fractions: \[ \frac{7}{2} \times \frac{23}{4} = \frac{7 \times 23}{2 \times 4} = \frac{161}{8} \]

The fraction \(\frac{161}{8}\) is already in its simplest form, so no further simplification is needed.

Convert the improper fraction \(\frac{161}{8}\) back to a mixed number. Divide the numerator by the denominator: \[ 161 \div 8 = 20 \quad \text{remainder} \quad 1 \] Thus, \(\frac{161}{8}\) can be expressed as the mixed number \(20 \frac{1}{8}\).

Final Answer