Page 194 - Ganit Kaushal

Let us see them again in the figures below. Observe the figures (i), (ii), (iii), (iv) and answer the following
questions:
(i) (ii)

1 1
2
(iii) (iv)

2 4
4 8
2
1
2
4
Are the lengths and equal? Are the lengths and equal?
2 4 4 8
1 2 4
Can we say = = ?
2 4 8
The answer to all these questions is “Yes”, as we observe that the blue part of all the paper strips is
equal. So, all the fractions represent the same part of a whole.
| Now, let us look at the following four fractions.
1 2 3 4
Observe that the fractions , , , and
8
2 4 6
are equivalent fractions since each represent
the same part of a whole.
1 2 3 4 1 2 3 4
∴ We can write: = = = . 2 4 6 8
2 4 6 8
Let us consider one more example.
3 6
In the adjoining figure, observe that the fractions , , and 9 , all
4 8 12
represent the same part of a whole. So they are equivalent fractions.
3 6 9 3 6 9
∴ We can write: = = .
4 8 12 4 8 12
Now, let’s make a wall of unit fractions using 0 1 UNIT 1
the number lines, as shown in the adjoining 1 2
picture. With the help of this fraction wall, 2 2
we can easily identify which unit fractions are 1 2 3
equivalent fractions. We will ask you some 1 3 2 3 3 3 4
questions based on this wall of fractions in 4 4 4 4
the upcoming exercise. For now, observe it 1 2 3 4 5
carefully. 5 5 5 5 5
1 2 3 4 5 6
To Find Equivalent Fractions 6 6 6 6 6 6
1 2 3 4 5 6 7
To find an equivalent fraction of a given 1 7 2 7 3 7 4 7 5 7 6 7 7 8 7
fraction, we can use the following two methods:
8 8 8 8 8 8 8 8
Method 1: Multiply both the numerator and 1 2 3 4 5 6 7 8 9
9
denominator of the given fraction by the same 1 9 2 9 3 9 4 9 5 9 6 9 7 9 8 9 9 10
natural number. 10 10 10 10 10 10 10 10 10 10
Wall of unit fractions

192 Mathematics-6