What is a fraction?

A fraction is a way of expressing a part of a whole or a ratio between two quantities. It consists of two parts: the top number (the numerator) indicating the part of a quantity, and the bottom number (the denominator) indicating the total or whole. Fractions can be used to represent values less than one (a part of a number) and can be added, subtracted, multiplied, and divided like any other numbers. Fractions divide numbers into equal parts, so the fraction 1/4 represents 1 part out of 4 total parts.

Adding and subtracting fractions

When adding or subtracting fractions, you must ensure that the denominator (bottom number) is the same for both fractions. If this is already the case, combine the top numbers. The denominator should not change during these operations. If you add 1/5 and 2/5, it gives you 3/5.

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

As you get used to fractions, you will start to learn to add/subtract fractions that have different denominators. As said above, you cannot add or subtract them if they have different denominators, so you first need to change them so the denominators match. The easiest method for doing this is to take the denominator of the opposite number and multiply the top and bottom of the fraction by that number. Once the denominators are the same, you can combine the fractions.

\frac{1}{5}+\frac{1}{4}

(\frac{4}{4})\frac{1}{5}+\frac{1}{4}(\frac{5}{5})

\frac{4}{20}+\frac{5}{20}=\frac{9}{20}

Multiplying fractions

Multiplying fractions is possibly the easiest operation to do with fractions. You don’t need to check to make sure the denominators are equal or anything special. Simply multiply straight across: top times top; bottom times bottom.

\frac{2}{7}\times \frac{3}{5}=\frac{6}{35}

Dividing fractions

Dividing fractions is similar to multiplying fractions but with one extra step. Keep in mind the phrase “Keep Change Flip.” Keep the first fraction as it is, change the division sign to multiplication, and flip the last fraction. Then multiply as usual.

\frac{1}{3}\div \frac{4}{5}

\frac{1}{3}\times \frac{5}{4}=\frac{5}{12}

Simplifying fractions

When doing operations with fractions, you will sometimes get really large numbers or fractions with numbers larger than they need to be. If you need to do multiple operations, this could make the problem more challenging, so it becomes necessary to simplify fractions whenever possible. To simplify a fraction, find the greatest common factor (GCF) for the top and bottom and divide both numbers by the GCF.

\frac{8}{12}\div \frac{4}{4}=\frac{2}{3}

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