Multiplying Fractions and Mixed Numbers

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 a fraction by a whole number, multiply the numerator by the whole number and keep the denominator the same. For example, $$\frac{2}{3} \times 4 = \frac{2 \times 4}{3} = \frac{8}{3}$$ .

A mixed number is a whole number combined with a fraction, such as 1 $$\frac{3}{4}$$ .

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 over the original denominator.

The first step is to multiply the numerators together and the denominators together. For example, $$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$$ .

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

To simplify $$\frac{8}{12}$$ , divide both the numerator and denominator by their greatest common divisor, which is 4. So, $$\frac{8 \div 4}{12 \div 4} = \frac{2}{3}$$ .

The result is $$\frac{6}{7}$$ .

Divide 35 by 9. The quotient is 3 and the remainder is 8, so $$\frac{35}{9} = 3 \frac{8}{9}$$ .

The product is $$\frac{8}{3}$$ .