three equivalent rational numbers of 130/150
Answers
Answer:
Equivalent rational numbers by multiplication:
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
Equivalent rational numbers by division:
If
a
b
is a rational number and m is a common divisor of a and b, then
a÷m
b÷m
is a rational number equivalent to
a
b
.
For example, rational numbers
−48
−60
,
−28
−35
,
20
25
,
12
15
are equivalent to the rational number
4
5
We know that if we divide the numerator and denominator of a fraction by a common divisor, then the value of the fraction does not change.
For example,
48
64
=
48÷16
64÷16
=
3
4
Similarly, we have
−75
100
=
(−75)÷5
100÷5
=
−15
20
=
(−15)÷5
20÷5
=
−3
4
, and
42
−56
=
42÷2
(−56)÷2
=
21
−28
=
21÷(−7)
(−28)÷(−7)
=
−3
4
Solved examples:
1. Find the two rational numbers equivalent to
3
7
.
Solution:
3
7
=
3×4
7×4
=
12
28
and
3
7
=
3×11
7×11
=
33
77
Therefore, the two rational numbers equivalent to
3
7
are
12
28
and
33
77