A fraction is defined as a portion of the whole. It is made up of two numbers: one on the top which is called numerator and other at the bottom which is known as denominator. Fraction is a small amount of whole quantity.**Examples:**

- If a piece of sweet is divided into two parts, then each part is one-half ($\frac{1}{2}$) of the piece.
- Let us assume that a pizza is divided into 6 parts and 2 parts are consumed, then the fraction that is consumed will be $\frac{2}{6}$ which is equivalent to $\frac{1}{3}$.

Let us have a look on few fraction word problems with their solutions.

Peter ate two-thirds of a pie and John ate three-fifths of the pie. What fraction of the pie did they eat together?

Fraction of pie eaten by Peter = $\frac{2}{3}$

Fraction of pie eaten by John = $\frac{3}{5}$

Total amount of pie eaten = $\frac{2}{3}+\frac{3}{5}$

= $\frac{10+9}{15}$

= $\frac{19}{15}$

Problem 2:

Barbara has 4 pencils, 3 pens, 1 eraser and 2 scales in her pencil box. What fraction of stationary are pens?

Solution:

Fraction of pen = $\frac{\text{Number of pens}}{\text{Total number of stationary}}$

= $\frac{3}{4+3+1+2}$

= $\frac{3}{10}$

Problem 3:

The age of a girl is one-third of the age of her father who is presently 63 years old. Determine the age of the girl.

Solution:

Age of girl = One-third of the age of father

= $\frac{1}{3}$ x 63

= 21

Hence, the girl is 21 years old.

Problem 4:

Samuel purchased $(\frac{3}{7})^{th}$ of a pound of candies. He gave $(\frac{1}{4})^{th}$ of a pound to his friends. What fraction does he left with?

Solution:

Fraction of a pound purchased by Samuel = $\frac{3}{7}$

Fraction of a pound given to friends = $\frac{1}{4}$

Fraction of a pound left = $\frac{3}{7}-\frac{1}{4}$

= $\frac{12-7}{28}$

= $\frac{5}{28}$

He is left with $\frac{5}{28}$ of a pound candies.

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