Fraction Operations

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 add fractions with different denominators, find a common denominator, convert the fractions, and then add the numerators.

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

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

To subtract fractions, ensure they have a common denominator, then subtract the numerators and keep the denominator the same.

To multiply fractions, multiply the numerators together and the denominators together. For example, $$\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12} = \frac{1}{2}$$ .

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

To divide fractions, multiply by the reciprocal of the second fraction. For example, $$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}$$ .

A common denominator is a shared multiple of the denominators of two or more fractions, used to add or subtract them.

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