Multiplying and Dividing 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 two fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ .

A mixed number is a whole number combined with a fraction, such as 2 1/4.

Multiply the whole number by the denominator and add the numerator. For example, 2 1/4 becomes $$\frac{(2 \times 4) + 1}{4} = \frac{9}{4}$$ .

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

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

Divide both the numerator and denominator by their greatest common divisor (GCD), which is 2: $$\frac{2 \div 2}{10 \div 2} = \frac{1}{5}$$ .

The result is $$\frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = 1 \frac{1}{4}$$ .

Convert to an improper fraction: $$7 = \frac{7}{1}$$ , then multiply by the reciprocal: $$\frac{7}{1} \times \frac{7}{6} = \frac{49}{6} = 8 \frac{1}{6}$$ .

Convert the mixed number to an improper fraction before multiplying.