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FRACTION AS A PART OF A COLLECTION
5 Fractions

Consider the following figures:

FRACTIONS AND FRACTIONAL NUMBERS

Look at the given figure.
In this figure, a strip has been divided into 7 equal parts.
Out of these 7 equal parts, 4 parts have been shaded.
Clearly, the shaded portion represents four-sevenths. 4
7 Fig. (i) Fig. (ii) Fig. (iii)

4 Fig. (i) contains a collection 3 of 8 circles, of which 3 circles are shaded.
In numeral, we denote it by (read as Four by seven’).
7 3
4 Shaded circles represent of the collection.
Here is a fraction and four-sevenths is a fractional number 8
7

FRACTIONS ON NUMBER LINE Fig. (ii) contains a collection of 12 triangles, of which 7 triangles are shaded.

4
Suppose we want to denote the fraction on the number line. Shaded triangles represent 7 of the collection.
7 P 12
Take a line segment OA of unit length. O 4 A Fig. (iii) contains a collection of 15 squares of which 8 squares are shaded.
7 Shaded squares represent 8 of the collection.
Divide OA into 7 equal parts and take 4 parts out of it to reach the point P. 15

Then, the point P represents the number
In general, we define a fraction as given below.

Some more examples are given below.
FRACTIONS The numbers of the form a , where a and b are natural numbers, are called fraction.
b
Fraction Fractional number Number line a
Here, a is called the numerator and b the denominator of the fraction ·
1 one - half 1 O 1 A b
2 2 2 5
1 1 O 1 A EXAMPLE 1: (i) 9 is a fraction with numerator= 5 and denominator= 9.
4 one - quarter 4 4

2 two - thirds 2 O 2 A EXAMPLE 2: (ii) 8 is a fraction with numerator = 8 and denominator = 1
3 3 3 17
3 three - fifths 3 O 3 A FRACTIONAL PART OF A COLLECTION
5 5 5 3
5 five - eighths 5 O 5 A EXAMPLE 3: Find 4 of 12.
8 8 8
SOLUTION: Consider a collection of 12 balls.
Divide this collection into 4 equal parts and take
Thus, the fractions shown above are 1 1 2 , 3 and 5 . 3 parts out of it.
,
,
2 4 3 5 8 CLearly, 3 parts out of 4 parts contain 9 balls.
The corresponding fractional numbers are one-half, one-quarter, two-thirds, three:ffjths and five-eighths z 8 of 12 balls = 9 balls.
respectively. 17