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Write the fractions. Are all these fractions equivalent?
$Write the fractions. Are all these fractions equivalent?$

Solution:

We use the concepts of fractions and equivalent fractions to write the fractions based on the shaded portions in the images and determine if the fractions are equivalent.

Fractions that have the same value irrespective of their numerator and denominator are called equivalent fractions.

$Write the fractions. Are all these fractions equivalent?$
(a) In the above images,
(i) the fraction represented by the shaded portion is 1 / 2
(ii) the fraction represented by the shaded portion is 2 / 4 = 1 / 2
(iii) the fraction represented by the shaded portion is 3 / 6 = 1 / 2
(iv) the fraction represented by the shaded portion is 4 / 8 = 1 / 2
The simplest form of all the fractions represented by the shaded portions is equal since they are all equal to 1 / 2.
∴ They all are equivalent fractions.

$Write the fractions. Are all these fractions equivalent?$
(b) In the above images,
(i) the fraction represented by the shaded portion is 4 / 12 = 1 / 3
(ii) the fraction represented by the shaded portion is 3 / 9 = 1 / 3
(iii) the fraction represented by the shaded portion is 2 / 6 = 1 / 3
(iv) the fraction represented by the shaded portion is 1 / 3 = 1 / 3
(v) the fraction represented by the shaded portion is 6 / 15 = 2 / 5
The simplest form of all the fractions represented by the shaded portions is not equal since 1/3 is not equal to 2/5.
∴ They all are not equivalent fractions.

NCERT Solutions for Class 6 Maths Chapter 7 Exercise 7.3 Question 1

Write the fractions. Are all these fractions equivalent?

Summary:

Based on the shaded portions in the given images, it can be concluded that for a) the fractions are equivalent fractions and for b) the fractions are not equivalent fractions.

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