Question

2
$4\frac{1}{2} \div \frac{3}{4}$
work for problems 1 - 9.

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \(4\frac{1}{2}\) can be converted to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(4\frac{1}{2}\), we have \(a = 4\), \(b = 1\), \(c = 2\). Then \(\frac{4\times2+1}{2}=\frac{9}{2}\).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction \(\frac{3}{4}\) is the same as multiplying by its reciprocal \(\frac{4}{3}\). So we have \(\frac{9}{2}\div\frac{3}{4}=\frac{9}{2}\times\frac{4}{3}\).

Step3: Simplify the multiplication

Multiply the numerators and denominators: \(\frac{9\times4}{2\times3}=\frac{36}{6}\). Then simplify \(\frac{36}{6}=6\).

Answer:

\(6\)