Are the rational numbers -8/28 and 32/-112 equivalent? Give reason.
Solution:
Given, the rational numbers are -8/28 and 32/-112
We have to determine if the given rational numbers are equivalent.
We know that, to reduce the rational number to its standard form, we divide its numerator and denominator by their HCF.
Taking -8/28,
8 = 2 × 2 × 2
28 = 2 × 2 × 7
HCF of 8 and 28 = 2 × 2 = 4
Now, -8/4 = -2
28/4 = 7
So, -8/28 = -2/7 ---------------------------- (1)
Taking 32/-112,
32 = 2 × 2 × 2 × 2 × 2
112 = 2 × 2 × 2 × 2 × 7
HCF of 32 and 112 = 2 × 2 × 2 × 2 = 16
Now, 32/16 = 2
-112/16 = -7
So, 32/-112 = -2/7 ---------------------------- (2)
From (1) and (2),
-8/28 = 32/-112
The standard form of the given rational numbers are equal.
Therefore, the given rational numbers are equivalent.
✦ Try This: Are the rational numbers 299/161 and 13/7 equivalent? Give a reason.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 9
NCERT Exemplar Class 7 Maths Chapter 8 Problem 71
Are the rational numbers -8/28 and 32/-112 equivalent? Give reason.
Summary:
The rational numbers -8/28 and 32/-112 are equivalent, since their standard forms are equal
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