There are several ways to calculate this.
1. The general method.
Multipy numerator (top) with numerator and denominator (bottom) with denominator.
$$\frac{4}{9} *\frac{1}{2} = \frac{4*1}{9*2}$$
Remember that the fraction retains it value if you multiply/divide the numerator and denominator with the same number:
$$\frac{4}{9}*\frac{1}{2} = \frac{4*1}{9*2} = \frac{2}{9}$$
2. This method requires a little experience with fractions. You simply ask yourself what the answer logically should be. Say you ate pizza with your friends. The pizza is divided into nine pieces. You and your brother shares four pieces equally between you. How big amount of the whole pizza do you alone get? Well there's just two pieces left for you, out of nine pieces. So it'll be 2/9, right?
Remember that:
$$\frac{a}{b}*\frac{1}{x}= \frac{a/x}{b}$$
Proof:
$$\frac{a}{b}*\frac{1}{x}= \frac{a}{bx}=\frac{a/x}{bx/x}=\frac{a/x}{b}$$
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