Multiplication and division of fractions

Multiplying Fractions

Multiplying fractions is very easy. Simply multiply the numerators of the fractions to find the numerator of the answer. Then multiply the denominators of the fractions to find the denominator of the answer. In other words, it can be said “top times top equals top”, and “bottom times bottom equals bottom.” This rule is used to multiply both proper and improper fractions, and can be used to find the answer to more than two fractions in any given problem.

Example

Multiply ${\frac {1}{2}}\times {\frac {3}{4}}$

Step 1

Multiply the numerators to find the numerator of the answer. $1\times 3=3$

Step 2

Multiply the denominators to find the denominator of the answer. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2 \times 4 = 8 }

Answer

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \times \frac{3}{4} = \frac{3}{8}}

Make sure to reduce your answer if possible.

Whole and Mixed Numbers

When you need to multiply a fraction by a whole number, you must first convert the whole number into a fraction. This, fortunately, is not as difficult as it may sound; just put the whole number over the number one. Then proceed to multiply as you would with any two fractions. An example is given below.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3}{4} \times {5} = \frac{3}{4} \times \frac{5}{1} = \frac{15}{4} = 3\,\!\frac{3}{4}}

If a problem contains one or more mixed numbers, you must first convert all mixed numbers into improper fractions, and multiply as before. Finally, convert any improper fraction back to a mixed number.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1\,\!\frac{1}{2} \times 2\,\!\frac{1}{4} = \frac{3}{2} \times \frac{9}{4} = \frac{27}{8} = 3\,\!\frac{3}{8}}

Dividing Fractions

To divide fractions, simply exchange the numerator and the denominator of the second term in the problem, then multiply the two fractions.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \div \frac{3}{4}}

Invert the second fraction:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{2} \times \frac{4}{3}}

Multiply:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1 \times 4}{2 \times 3} = \frac{4}{6}}

Always check to see if simplifying the resulting fraction can be done:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4}{6} = \frac{2}{3}}

Licensing

Content obtained and/or adapted from:

• Fractions, Wikibooks under a CC BY-SA license