_find the value of ‘a’ if the following pairs are equivalent rational no. 1, 5/11 and a/-13
Answers
Answer:
If
a
b
is a rational number and m is a non-zero integer then
a×m
b×m
is a rational number equivalent to
a
b
.
For example, rational numbers
12
15
,
20
25
,
−28
−35
,
−48
−60
are equivalent to the rational number
4
5
.
We know that if we multiply the numerator and denominator of a fraction by the same positive integer, the value of the fraction does not change.
For example, the fractions
3
7
and
21
49
are equal because the numerator and the denominator of
21
49
can be obtained by multiplying each of the numerator and denominator of
3
7
by 7.
Also,
−3
4
=
−3×(−1)
4×(−1)
=
3
−4
,
−3
4
=
−3×2
4×2
=
−6
8
,
−3
4
=
−3×(−2)
4×(−2)
=
6
−8
and so on …….
Therefore,
−3
4
=
−3×(−1)
4×(−1)
=
−3×2
4×2
=
(−3)×(−2)
4×(−2)
and so on …….
Note: If the denominator of a rational number is a negative integer, then by using the above property, we can make it positive by multiplying its numerator and denominator by -1.
For example,
5
−7
=
5×(−1)
(−7)×(−1)
=
−5
7