Fractions

Fraction

This topic explains the basics of fractions in mathematics.

3.1

Fraction

State the quantity by comparison.

Types of Fractions

Proper Fraction

Based on the diagram above, 3 out of 4 circles are shaded. 3 out of 4 is three over four.
Three over four is written as

$\underline{3}\;\;\;\text{numerator} \\4\;\;\;\text{denominator}$

$\frac{3}{4}$ is a proper fraction. The numerator is smaller than the denominator.

Equivalent Fractions

For example: $\underline{\;1\;}\\\;2\;$ is equivalent to $\underline{\;2\;}\\\;4\;$

$\underline{1\times2}=\underline{\;2\;} \\2\times2\;\;\;\;\;\;4$

$\Rightarrow$ $\underline{\;1\;}=\underline{\;2\;} \\\;2\;\;\;\;\;\;\;4$

Fractions in the Simplest Form

\frac{3 \div 3}{9 \div 3} = \frac{1}{3} \frac{3}{9} = \frac{1}{3}

Improper Fractions and Mixed Numbers

1 $\frac{3}{4}$

$1 \frac{3}{4}$ is a mixed number.

$1$ is a whole number.

$\frac{3}{4}$ is a proper fraction.

Addition of Fractions

Tips: If the denominator is the same, just add the numenator.

Example, $\frac{1}{5} + \frac{2}{5} = \frac{3}{5}$

Substraction of Fractions

Tips: If the denominator is the same, just substract the numenator.

Example, $\frac{7}{8} - \frac{3}{8} = \frac{4}{8}$

Tips: Simplify $\frac{4}{8}$

$\frac{4 \div 2}{8 \div 2} = \frac{1}{2}$

So, $\frac{7}{8} - \frac{3}{8} = \frac{4}{8} = \frac{1}{2}$