Key Points

To multiply a fraction by a whole number, multiply the whole number with the numerator and keep the denominator the same. For example, $5 imes \frac{2}{3} = \frac{5 \times 2}{3} = \frac{10}{3}$.

To multiply a fraction by a whole number, multiply the whole number with the numerator of the fraction, keeping the denominator the same. The formula is $a \times \frac{b}{c} = \frac{a \times b}{c}$.

To multiply two fractions, multiply their numerators together and their denominators together. The general formula is $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$.

The product of two fractions is found by multiplying their numerators together and their denominators together. This general rule is given by the formula $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$.

The word 'of' represents multiplication when used with fractions. For example, finding $\frac{1}{4}$ of 20 means calculating $\frac{1}{4} \times 20 = 5$.

To multiply mixed fractions, you must first convert each mixed fraction into an improper fraction. After converting, multiply the resulting improper fractions using the standard rule.

Before multiplying fractions, you can simplify by dividing any numerator and any denominator by their common factors. This process is called cancellation and makes calculations easier.

Before multiplying fractions, you can simplify by dividing any numerator and any denominator by their common factors. This process, called cancelling, makes the final multiplication easier.

In word problems, the term 'of' signifies multiplication. For example, finding $\frac{2}{5}$ of 20 is the same as calculating $\frac{2}{5} \times 20$.

The reciprocal of a fraction is found by inverting it, which means swapping the numerator and the denominator. The reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$, provided $a \neq 0$ and $b \neq 0$.

The product of any non-zero fraction and its reciprocal is always 1. For example, $\frac{2}{3} \times \frac{3}{2} = \frac{6}{6} = 1$.

When you multiply two proper fractions (values between 0 and 1), the product is smaller than both of the original fractions. If you multiply a number greater than 1 by a proper fraction, the product will be smaller than the original number.

The reciprocal of a fraction is obtained by swapping its numerator and denominator. The reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$, where $a \neq 0$ and $b \neq 0$. The product of any fraction and its reciprocal is always 1.

To divide one fraction by another, you multiply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor). This is often called the 'invert and multiply' rule.

The formula for dividing fractions is $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$. Remember to only invert the fraction you are dividing by.

To divide one fraction by another, you multiply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor). The rule is $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$.

Before multiplying or dividing mixed fractions, you must first convert them into improper fractions. For example, to calculate $2\frac{1}{2} \times \frac{3}{4}$, first convert $2\frac{1}{2}$ to $\frac{5}{2}$.

To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. For example, $\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c} = \frac{a}{b \times c}$.

When you multiply two proper fractions (values between 0 and 1), the product is always smaller than both of the original fractions. For example, $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$, and $\frac{1}{6}$ is smaller than both $\frac{1}{2}$ and $\frac{1}{3}$.

To divide a whole number by a fraction, multiply the whole number by the reciprocal of the fraction. For example, $a \div \frac{b}{c} = a \times \frac{c}{b} = \frac{a \times c}{b}$.

When the divisor is a proper fraction (between 0 and 1), the quotient will be greater than the dividend. When the divisor is greater than 1, the quotient will be less than the dividend.

When you divide by a proper fraction (a number between 0 and 1), the quotient is greater than the dividend. For example, $5 \div \frac{1}{2} = 10$, and the result $10$ is greater than the dividend $5$.

The order of multiplication for fractions does not affect the final product. This means that $\frac{a}{b} \times \frac{c}{d}$ is equal to $\frac{c}{d} \times \frac{a}{b}$.

The order in which you multiply fractions does not change the result, which is the commutative property: $\frac{a}{b} \times \frac{c}{d} = \frac{c}{d} \times \frac{a}{b}$. Division, however, is not commutative.