Multiplying and Dividing Fractions

A fraction represents a part of a whole and is written as 'a/b', where 'a' is the numerator and 'b' is the denominator.

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

Dividing fractions means multiplying by the reciprocal of the second fraction. For example, $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ .

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

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as $$\frac{5}{4}$$ .

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

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the new numerator.

The first step in multiplying fractions is to multiply the numerators together.

The first step in dividing fractions is to find the reciprocal of the second fraction.