Page 30 - Start Up Mathematics_7

2 Fractions

Fractions are a part of a whole. This whole can be either one unit or a combination of many units.
Fraction can also be considered as the ratio of two entities, like ratio of the number of boys to the
number of girls in the class.

1 3
6 4
In fractions we have studied about proper, improper and mixed fractions, their addition, subtraction,

comparison of fractions, equivalent fractions and their representation on the number line, etc. In
this chapter, we will learn multiplication and division of fractions. Before we proceed further, let’s

recall what we have learnt earlier.

Fraction
a
A fraction is a number which can be written in the form , where a and b are natural numbers.
b
The number a is known as the numerator and b is called the denominator.

Proper fractions

If the numerator of a fraction is less than the denominator, then it is called a proper fraction.
1 2 6 3 , etc. are examples of proper fractions.
, , ,
2 5 7 13

Improper fractions

If the numerator of a fraction is greater than or equal to the denominator, then it is called an
improper fraction. In other words, a fraction which is not proper is called an improper fraction.
7 11 5 15 , etc. are examples of improper fractions.
,
, ,
4 6 5 8
Mixed fractions

Mixed fractions are a combination of a whole number and a proper fraction. For example,
1 2 3 1 1
7 , 5 , 3 , etc. In fact 7 is equal to the sum of 7 and .
2 3 4 2 2