Multiplication and Division of Fractions Mixed Review

A fraction represents a part of a whole and is written as $$\frac{a}{b}$$ , where 'a' is the numerator and 'b' is the denominator.

To multiply two fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ .

A mixed number is a whole number combined with a fraction, such as 2 $$\frac{1}{3}$$ .

Multiply the whole number by the denominator, add the numerator, and place that over the original denominator: For example, 2 $$\frac{1}{3}$$ becomes $$\frac{2 \times 3 + 1}{3} = \frac{7}{3}$$ .

The reciprocal of a fraction $$\frac{a}{b}$$ is $$\frac{b}{a}$$ .

To divide fractions, multiply by the reciprocal of the second fraction: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ .

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.

The GCF is the largest number that divides two or more numbers without leaving a remainder.

List the factors of each number and identify the largest factor they have in common.

A proper fraction is a fraction where the numerator is less than the denominator, such as $$\frac{2}{3}$$ .