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 and 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

we get,

6 x 12 = 72

and 9 x 8 = 72

Since, 6 x 12 = 9 x 8

So, =

Hence, are equivalent Rational Number.

**Example 2**

Are and 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

and

we get,

14 x 15 = 210

and 12 x 21 = 252

Since, 14 x 15 ≠ 12 x 21

So, ≠

Hence, are not equivalent Rational Number.

### Equivalent Rational Number with given Numerator Examples

**Example 3**

Express as a Rational Number with Numerator 56.

**Explanation**

Numerator of = 7

We need to change the Numerator of 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,

= 8

So, we have to multiply both the Numerator and Denominator of given Rational Number by 8

=

Hence, can be expressed as

**Example 4**

Express as a Rational Number with Numerator 54.

**Explanation**

Numerator of = -9

We need to change the Numerator of 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,

= -6

So, we have to multiply both the Numerator and Denominator of given Rational Number by -6

=

Hence, can be expressed as

### Equivalent Rational Number with given Denominator Examples

**Example 5**

Express as a Rational Number with Denominator 49.

**Explanation**

Denominator of = 7

We need to change the Denominator of 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,

= 7

So, we have to multiply both the Numerator and Denominator of given Rational Number by 7

=

Hence, can be expressed as

**Example 6**

Express as a Rational Number with Denominator -18.

**Explanation **

Denominator of = 6

We need to change the Denominator of 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,

= -3

So, we have to multiply both the Numerator and Denominator of given Rational Number by -3

=

Hence, can be expressed as