## 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
• Equivalent fractions is tqo different fractions that have equal value.

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

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

Fractions in the Simplest Form
• $\frac{3}{9}$ has the same value as $\frac{1}{3}$
• 3 and 9 can be divided by 3.
• So, $\frac{1}{3}$ is the simplest form of  $\frac{3}{9}$

Improper Fractions and Mixed Numbers

1                                  $\frac{3}{4}$

• There is one and three over four of the shaded area from the diagram above.
• One and three over four is written as $1\frac{3}{4}$.
 $1\frac{3}{4}$ is a mixed number. $1$ is a whole number. $\frac{3}{4}$ is a proper fraction.

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 $\frac{4}{8}$

$\frac{4÷2}{8÷2}=\frac{1}{2}$

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

## 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
• Equivalent fractions is tqo different fractions that have equal value.

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

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

Fractions in the Simplest Form
• $\frac{3}{9}$ has the same value as $\frac{1}{3}$
• 3 and 9 can be divided by 3.
• So, $\frac{1}{3}$ is the simplest form of  $\frac{3}{9}$

Improper Fractions and Mixed Numbers

1                                  $\frac{3}{4}$

• There is one and three over four of the shaded area from the diagram above.
• One and three over four is written as $1\frac{3}{4}$.
 $1\frac{3}{4}$ is a mixed number. $1$ is a whole number. $\frac{3}{4}$ is a proper fraction.

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 $\frac{4}{8}$

$\frac{4÷2}{8÷2}=\frac{1}{2}$

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