Question

complete the conversion.
1 pound = 16 ounces
3\frac{1}{2} pounds = \boxed{} ounces

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \( 3\frac{1}{2} \) can be converted to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). For \( 3\frac{1}{2} \), \( a = 3 \), \( b = 1 \), \( c = 2 \), so we have \( \frac{3\times2 + 1}{2}=\frac{6 + 1}{2}=\frac{7}{2} \).

Step2: Multiply by conversion factor

We know that 1 pound = 16 ounces. To find the number of ounces in \( 3\frac{1}{2} \) pounds (which is \( \frac{7}{2} \) pounds), we multiply the number of pounds by the conversion factor (16 ounces per pound). So the calculation is \( \frac{7}{2}\times16 \).
Simplify the multiplication: \( \frac{7\times16}{2}=7\times8 = 56 \).

Answer:

56