1. To obtain a equivalent rational number of the given rational number we have to multiply the numerator and denominator of a given rational number by the same nonzero number.
2. To obtain a rational number equivalent to the given rational number we have to divide the numerator and denominator of a given rational number by a common divisor.
Equivalent Rational Numbers Examples
Example 1
Are 6/8 and 9/12 equivalent Rational Numbers?
Explanation
If two Rational Numbers are equivalent, the product obtained by Cross Multiplying them would also be equal
On Cross Multiplying the given Rational numbers
6/8 and 9/12
we get,
6 x 12 = 72
and 9 x 8 = 72
Since, 6 x 12 = 9 x 8
So, 6/8 = 9/12
Hence, 6/8 and 9/12 are equivalent Rational Number.
Example 2
Are 14/21 and 12/15 are equivalent Rational Numbers?
Explanation
If two Rational Numbers are equivalent, the product obtained by Cross Multiplying them would also be equal
On Cross Multiplying the given Rational numbers
14/21 and 12/15
we get,
14 x 15 = 210
and 12 x 21 = 252
Since, 14 x 15 ≠12 x 21
So, 14/21 ≠12/15
Hence, 14/21 and 12/15 are not equivalent Rational Number.
Equivalent Rational Number with given Numerator Examples
Example 3
Express 7/5 as a Rational Number with Numerator 56.
Explanation
Numerator of 7/5 = 7
We need to change the Numerator of 7/5 to 56
We need to find a number, with which we should multiply 7 so it is equal to 56
To obtain that number, we would need to divide 56 by 7 i.e,
56/7 = 8
So, we have to multiply both the Numerator and Denominator of given Rational Number by 8
Hence, 7/5 can be expressed as 56/40
Example 4
Express (-9)/8 as a Rational Number with Numerator 54.
Explanation
Numerator of (-9)/8 = -9
We need to change the Numerator of (-9)/8 to 54
We need to find a number, with which we should multiply -9 so it is equal to 54
To obtain that number, we would need to divide 54 by -9 i.e,
54/(-9) = -6
So, we have to multiply both the Numerator and Denominator of given Rational Number by -6
Hence, (-9)/8 can be expressed as 54/(-48)
Equivalent Rational Number with given Denominator Examples
Example 5
Express 6/7 as a Rational Number with Denominator 49.
Explanation
Denominator of 6/7 = 7
We need to change the Denominator of 6/7 to 49
We need to find a number, with which we should multiply 7 so it is equal to 49
To obtain that number, we would need to divide 49 by 7 i.e,
49/7 = 7
So, we have to multiply both the Numerator and Denominator of given Rational Number by 7
Hence, 6/7 can be expressed as 42/49
Example 6
Express 12/6 as a Rational Number with Denominator -18.
ExplanationÂ
Denominator of 12/6 = 6
We need to change the Denominator of 12/6 to -18
We need to find a number, with which we should multiply 6 so it is equal to -18
To obtain that number, we would need to divide -18 by 6 i.e,
(-18)/6 = -3
So, we have to multiply both the Numerator and Denominator of given Rational Number by -3
Hence, 12/6 can be expressed as (-36)/(-18)