Multiplying and Dividing Fractions

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

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 $$\frac{b}{a}$$ . It is obtained by flipping 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 (where the numerator is greater than the denominator) 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 (LCD) is the smallest multiple that two or more denominators share. It is 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 (GCF) 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 each fraction to an equivalent fraction with the LCD, and then add the numerators.