Page 71 - ICSE Math 6

5 Fractions

Key Concepts

• Fraction as Division • Conversion of Fractions (Mixed to Improper and vice
• Types of Fractions (Proper, Improper, Mixed and versa, Unlike to Like)
Equivalent) • Fractions on the Number Line
• Like and Unlike Fractions • Comparison of Fractions
• Simplest Form of Fractions • Operations on Fractions and Word Problems

A fraction represents part of a whole. The whole may be a single
object or a group of objects.
Consider a cardboard sheet. If it is divided into six equal parts, then
1 1
each part is (read as one-sixth) of the whole sheet. 6
6
If we use four parts of the sheet to make invitation cards, then we
2 4
are left with of the sheet. We can also say that of the sheet is
6 12 4 6 2
used. The numbers , and are known as fractions.
6 6 6 6
a
In a fraction , a is called the numerator and b is called the Maths Info
b
denominator. Numerator and denominator are also known as the The line separating the numerator
terms of the fraction. and the denominator is known as
the fraction bar.

Fraction as Division
In figure A, two wholes are divided into 6 equal parts and thus each part
represents 2 ÷ 6. Similarly, in figure B, a whole is divided into 6 equal
parts. We also observe that one part of a whole in figure A is equal to
the two parts of the whole in figure B. Since two parts of whole in figure Fig. A
2 2
B represent , we can say that 2 ÷ 6 = .
6 6
Thus, every fraction can be written as a division and every division can
be written as a fraction.
Fig. B
Example 1: What fraction of the natural numbers from 1 to 11 are prime numbers?

Solution: Natural numbers from 1 to 11 are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
Prime numbers from 1 to 11 are 2, 3, 5, 7, 11.
Total number of natural numbers from 1 to 11 = 11

Total number of prime numbers from 1 to 11 = 5
5
∴ The required fraction of prime numbers =
11

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