How to add fractions

What are the fractions

A fraction is a number that consists of one or more equal parts of a unit. In simple terms, this number denotes a part of something, for example, one piece of cake, or a whole with several additional parts, for example, one whole cake and three more pieces of another.

Common fractions consist of a numerator (top) and a denominator (bottom), separated by a horizontal or slash. The denominator reflects how many parts our conditional cake can be divided into, and the numerator - how many of them are available: ¹/₂, ³/₄, ⁹/₁₀.

Ordinary fractions are both right and wrong. The correct numerator is less than the denominator (⁵/₈, ⁷/₁₅), while the wrong ones, on the contrary, have more (⁸/₅, ¹⁵/₇). The whole and fractional parts can be distinguished from an incorrect fraction: 1³/₅, 2¹/₇… The resulting number will be called a mixed fraction.

There are also decimal fractions. They have a power of 10 in the denominator, and they are written differently - separated by commas: 0, 5, 0, 98. Although decimal fractions can also be represented in the form of ordinary ones: ⁵/₁₀, ⁹⁸/₁₀₀.

Ordinary with the same denominators

To add fractions with the same denominator, simply add the numerators and leave the denominators unchanged. For example: ¹/₅ + ²/₅ = ³/_5; ⁹/₆ + ¹⁰/₆ = ¹⁹/₆ = 3¹/₆.

Ordinary with different denominators

First you need to bring the fractions to a common denominator. To do this, find the smallest number that is evenly divisible by both of your denominators. For example, for fractions ⁵/₆ and ⁴/₉ this number is 18.

Then divide it by your denominators - and you get the so-called additional factor (18: 6 = 3, 18: 9 = 2). This is the number by which both sides of the fraction must be multiplied to bring it to the new denominator. That is: ^{5 x 3}/_{6 x 3} + ^{4 x 2}/_{9 x 2} = ¹⁵/₁₈ + ⁸/₁₈.

It remains only to repeat the process from the previous paragraph, adding the numerators. In our example, we get ²³/_18, or 1⁵/₁₈if you select the whole part.

Mixed fractions

There are several ways to add such fractions. The easiest is to sum the whole and fractional parts separately. For example, you need to calculate how much 3 is¹/₅ + 4²/₃… First, add 3 + 4 and get 7. Then we move on to the fractional parts: ¹/₅ + ²/₃ = ^{1 x 3}/_{5 x 3} + ^{2 x 5}/_{3 x 5} = ³/₁₅ + ¹⁰/₁₅ = ¹³/₁₅… And together - 7¹³/₁₅.

If, when adding the fractional parts, an incorrect fraction is obtained, it is also necessary to select the whole from it and add it to the previously obtained whole part.

Decimal fractions

The first step is to equalize the number of digits after the decimal point. For example, you want to add the numbers 33, 142 and 5, 6. Add two zeros to the second fraction - 5, 600. Now add up the numbers before the decimal point (33 + 5) and after (142 + 600). It turns out 38, 742.

If you are not yet very good at working with decimal fractions, add them in a column, like ordinary numbers. Be sure to place the comma below the comma. This method of addition will make the calculations easier for you in the case when an "extra" digit appears after the decimal point.

For example, you need to find the sum of the numbers 1, 742 and 5, 6. You already know that 1 + 5 = 6, and 742 + 600 = 1 342, but in the column you will immediately see that the unit of 1 342 needs to be transferred, added to whole part. The result is 7, 342.