Multiplying Mixed Fractions

Home > Pre-Algebra > Fractions > Multiplying Mixed Fractions

Multiplying Mixed Fractions

Introduction

In order to multiply mixed fractions, the fractions must first be expressed as improper fractions.

Terms

Fraction - Fractions are used when using numbers to express parts of whole.

Improper Fraction - A fraction where the numerator is greater than the denominator.

Mixed Fraction - A fraction where a whole number is combined with a fraction.

Numerator - The top part of the fraction, referring to the parts taken from the whole.

Denominator - The bottom part of the fraction, referring to the number of parts that make up the whole.

Lesson

Since we know that multiplying fractions and improper fractions require us to multiply the numerators and denominators of both fractions, if we are given mixed fractions to multiply, we must first express the mixed fraction as an improper fraction. So if we are given $1 rac{2}{3} * rac{4}{5}$ , we first express $1 rac{2}{3}$ as an improper fraction, giving us $rac{5}{3}$ . We then multiply the numerators ( $5 * 4 = 20$ ) and denominators ( $3 * 5 = 15$ ), giving us $rac{20}{15}$ as the answer. This can then be expressed as a mixed fraction – we reduce the improper fraction to $rac{4}{3}$ , and the convert it to a mixed fraction – $1 rac{1}{3}$

Examples

Multiplying Mixed Numbers (Example #1)

1\dfrac{1}{4} * 1\dfrac{1}{2}

Convert the mixed numbers to improper fractions

1\dfrac{1}{4} = \dfrac{\text{1 * 4 + 1}}{\text{4}} = \dfrac{5}{4}

1\dfrac{1}{2} = \dfrac{\text{1 * 2 + 1}}{\text{2}} = \dfrac{3}{2}

\dfrac{5}{4} * \dfrac{3}{2}

\dfrac{(5 * 3)}{(4 * 2)}

1\dfrac{7}{8}

Multiplying Mixed Numbers (Example #2)

1\dfrac{1}{3} * 1\dfrac{1}{5}

Convert the mixed numbers to improper fractions

1\dfrac{1}{3} = \dfrac{\text{1 * 3 + 1}}{\text{3}} = \dfrac{4}{3}

1\dfrac{1}{5} = \dfrac{\text{1 * 5 + 1}}{\text{5}} = \dfrac{6}{5}

\dfrac{4}{3} * \dfrac{6}{5}

\dfrac{(4 * 6)}{(3 * 5)}

\dfrac{(4 * 6^2)}{(3^1 * 5)}

1\dfrac{3}{5}

Multiplying Mixed Numbers (Example #3)

2\dfrac{1}{2} * 1\dfrac{2}{3}

Convert the mixed numbers to improper fractions

2\dfrac{1}{2} = \dfrac{\text{2 * 2 + 1}}{\text{2}} = \dfrac{5}{2}

1\dfrac{2}{3} = \dfrac{\text{1 * 3 + 2}}{\text{3}} = \dfrac{5}{3}

\dfrac{5}{2} * \dfrac{5}{3}

\dfrac{(5 * 5)}{(2 * 3)}

4\dfrac{1}{6}

Multiplying Mixed Numbers (Example #4)

1\dfrac{1}{4} * 1\dfrac{1}{4}

Convert the mixed numbers to improper fractions

1\dfrac{1}{4} = \dfrac{\text{1 * 4 + 1}}{\text{4}} = \dfrac{5}{4}

1\dfrac{1}{4} = \dfrac{\text{1 * 4 + 1}}{\text{4}} = \dfrac{5}{4}

\dfrac{5}{4} * \dfrac{5}{4}

\dfrac{(5 * 5)}{(4 * 4)}

1\dfrac{9}{16}