Fraction operations

Fractions are numbers, actually known as rational numbers For any fraction x/y where x and y are integers and y ≠ 0, you can perform the four basic arithmetic operations: addition, subtraction, multiplication, and division However, since a fraction involves two numbers, it does require some operational manipulation depending on the nature of the digits involved in the operation – whether the numbers are the same or different, as well as the type of operation You’ll need to follow specific rules for handling the numerators and denominators.

Addition and subtraction of fractions

Class 1: Same denominators

In this case, the numerators are added together and the same denominator remains:

Example with sum:

$\frac{5}{7}+\frac{1}{7}=\frac{\mathrm{5+1}}{7}=\frac{6}{7}$

Example with subtraction:

$\frac{5}{7}–\frac{1}{7}=\frac{\mathrm{5-1}}{7}=\frac{4}{7}$

Class 2: Different Denominators

The numerator of the result is the sum of the cross-multiplication of the fractions and the denominator of the result is the multiplication of the denominators of the fractions:

Example with sum:

$\frac{4}{7}+\frac{6}{\mathrm{11}}=\frac{\mathrm{4*11+7*6}}{\mathrm{7*11}}=\frac{\mathrm{44+42}}{\mathrm{77}}=\frac{86}{\mathrm{77}}$

Example with subtraction:

$\frac{4}{7}–\frac{6}{\mathrm{11}}=\frac{\mathrm{4*11-7*6}}{\mathrm{7*11}}=\frac{\mathrm{44-42}}{\mathrm{77}}=\frac{2}{\mathrm{77}}$

General form of addition and subtraction operations of fractions:

$\frac{\mathrm{x}}{y}\pm \frac{\mathrm{a}}{b}=\frac{\mathrm{x*b\; \pm \; y*a}}{\mathrm{y*b}}$

Multiplication of Fractions

The multiplication of fractions is a very simple process, and it consists of multiplying all the numerators directly to obtain the numerator of the result, as well as multiplying all the denominators and that will be the denominator of the final result:

In its general form:

Example:

$\frac{4}{5}*\frac{9}{2}*\frac{7}{2}=\frac{\mathrm{4*9*7}}{\mathrm{5*2*2}}=\frac{252}{\mathrm{20}}$

Division of Fractions

Fraction division may seem a bit strange, but it is basically a cross-multiplication of the first numerator by the second denominator and the following denominators in case there are more fractions to get the numerator of the result, as well as with the denominator of the result but with the other set of numerators and denominators.

En su forma general:

For Example:

$\frac{1}{4}÷\frac{1}{5}÷\frac{1}{6}=\frac{\mathrm{1\; *\; 5\; *\; 6}}{\mathrm{4\; *\; 1\; *\; 1}}$