Multiplying and Dividing Fractions

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: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ .

The reciprocal of a fraction $$\frac{a}{b}$$ is $$\frac{b}{a}$$ , obtained by swapping the numerator and denominator.

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

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

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 least common denominator is the smallest multiple that two or more denominators share, used to add or subtract fractions.

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

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

To add fractions with different denominators, first find the least common denominator (LCD), convert the fractions, and then add the numerators.