Fractions

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Fractions

Fractions have two pieces, the numerator, and the denominator. The numerator is the number on top of the fraction and the denominator is the number on the bottom. In the following example, the number 3 is the numerator, and the number 4 is the denominator.

Fractions can also be illustrated using the denominator value as the number of segments, and the numerator shows the amount needed. The following picture shows 3 out of 4 segments highlighted.

Equivalent fractions

Equivalent fractions use different numbers in the numerator and denominator but have the same value. Typically these are simplified to the smallest number in the numerator.

\frac{3}{9} = \frac{2}{6} = \frac{1}{3}

Improper fractions

Improper fractions are fractions where the numerator is greater than the denominator.

\frac{7}{3}

How to add fractions

Adding fractions requires having a common denominator.

\frac{5}{3} + \frac{1}{3} = \frac{{5 + 1}}{3} = \frac{6}{3} = \frac{2}{1} = 2

When the denominators do not match, multiply them by the smallest multiple of both denominators. Typically, this is simply multiplying the denominators together.

The following example shows how to do this with two different denominators.

\frac{1}{2} + \frac{3}{7} = \frac{7}{{14}} + \frac{6}{{14}} = \frac{{7 + 6}}{{14}} = \frac{{13}}{{14}}

How to multiply fractions

Multiplying fractions involves multiplying the numerator by the numerator, and the denominator by the denominator.

\frac{1}{4}*\frac{3}{5} = \frac{{1*3}}{{4*5}} = \frac{3}{{20}}

How to divide fractions

Dividing fractions involves flipping the fraction on the bottom of the division, and subsequentially multiplying the fractions.

\frac{7}{2}/\frac{3}{4} = \frac{{\left( {\frac{7}{2}} \right)}}{{\left( {\frac{3}{4}} \right)}} = \frac{7}{2}*\frac{4}{3} = \frac{{7*4}}{{2*3}} = \frac{{28}}{6} = \frac{{14}}{3}

Addition, subtraction, multiplication, and division can be easier when using improper fractions if integers are also in the expression. Turn the integer into an improper fraction to simplify.

The following example converts the integer 5, into a fraction 20/4 to complete the expression. As previously discussed, these are equivalent fractions with the same value.

5 + \frac{3}{4} = \frac{5}{1} + \frac{3}{4} = \frac{{20}}{4} + \frac{3}{4} = \frac{{20 + 3}}{4} = \frac{{23}}{4}
3\frac{1}{6}*\frac{5}{8} = \frac{{19}}{6}*\frac{5}{8} = \frac{{19*5}}{{6*8}} = \frac{{95}}{{48}}

Frequently Asked Questions

What is .375 as a fraction?

Converting a decimal to a fraction is not always simple. Some are understood from memory, others will look at tables for conversion, and lastly, some will use a calculator with decimal to fraction conversion. .375 is 3/8 as a fraction.

More Information

Check out the Algebra Index for more Algebra topics!

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