### How to read fractions ?

$$\displaystyle \frac{1}{2}$$ "one half" or "a half"

$$\displaystyle \frac{1}{3}$$ "one third" or "a third"

$$\displaystyle \frac{1}{4}$$ "one quarter" or "a quarter"

$$\displaystyle \frac{2}{3}$$ "two thirds" not "two third" ( 2 is plural so we add "s" ) .

$$\displaystyle \frac{2}{5}$$  "two fifths"

$$\displaystyle \frac{3}{7}$$ " three sevenths"

$$\displaystyle \frac{5}{6}$$ " five sixths"

$$\displaystyle \frac{3}{4}$$ " three quarters"

$$\displaystyle \frac{11}{10}$$  "eleven tenths"

$$\displaystyle 2\frac{9}{10}$$ " two and nine tenths"  is like $$\displaystyle \text 2 whole$$ and  $$\displaystyle \text nine$$ $$\displaystyle \frac{1}{10}$$

Why do we read fractions in this way ?

## How to Read Fractions ?

We read fractions based on unit fractions. Unit fraction is shortly the smallest part of
fractions and all fractions are made of unit fractions.

Reading fraction is telling “the fraction consist of how many unit fraction”.

$$\displaystyle \frac{1}{2}$$  "a half" or "one half"

$$\displaystyle \frac{1}{3}$$  "one third"

$$\displaystyle \frac{2}{3}$$  "two thirds"

We add “s” to the end couse 2 is plural . Not one !

$$\displaystyle \frac{1}{4}$$ "a quarter" , or "one quarter
You may also read as “one fourth” but it is not preferred

$$\displaystyle \frac{3}{4}$$  "three quarters"
Or “three fourths” but not preferred.

$$\displaystyle \frac{1}{6}$$  " a sixth" or "one sixth"

$$\displaystyle \frac{5}{6}$$ "five sixths"

This fraction consist of 5 , $$\displaystyle \frac{1}{6}$$ th.

$$\displaystyle \frac{11}{10}$$  "eleven tenths"

$$\displaystyle 2\frac{4}{5}$$  " two and four fifths"

it is like “ two whole and four $$\displaystyle \frac{1}{5}$$ ths.

## Misconceptions in Reading Fractions

$$\displaystyle \frac{3}{5}$$

"3 divided by 5 " or "3 over 5"

This is one of the most common misconceptions in reading fractions .

a ) $$\displaystyle \frac{3}{5}$$  "3 divided by 5"

This reading style is valid for rational numbers, not fractions. There is a difference between
fractions and rational numbers.

b) $$\displaystyle \frac{3}{5}$$  "3 over 5"

It just describes its fractional form. it is like telling “there is a cat on the table”.

If you read fractions as above , students may understand what you are talking about, they may get the fraction form but they will fall  in misconception as fractions are made up two numbers , numerator and dominator .They cannot get the concept of Fraction.

Best to avoid this kind of misconceptions by reading fractions based on unit fractions.