**Download NCERT Solutions for Class 7 Maths Chapter 9 – Rational Numbers**

[Read more…] about NCERT Solutions for Class 7 Maths Chapter 9 – Rational Numbers

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**Download NCERT Solutions for Class 7 Maths Chapter 9 – Rational Numbers**

[Read more…] about NCERT Solutions for Class 7 Maths Chapter 9 – Rational Numbers

Rational Numbers Class 7 Questions, deals with various concepts which are as under:-

**Additive Inverse of a Rational Number****Equivalent Rational Numbers****Addition of Rational Numbers****Subtracting Rational Numbers****Multiplication of Rational Numbers****Dividing Rational Numbers**

- To obtain a rational number equivalent to the given rational number we have to multiply the numerator and denominator of a given rational number by the same nonzero number.
- 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.

**Example 1**

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,

3 x 15 = 45

and 9 x 5 = 45

Since, 3 x 15 = 9 x 5

So, =

Hence, and are equivalent Rational Number.

**Equivalent Rational Number with given Numerator**

**Example 2**

Express as a Rational Number with Numerator 24.

**Explanation:**

Numerator of = -8

We need to change the Numerator of to 24

We need to find a number, with which we should multiply -8 so it is equal to 24

To obtain that number, we would need to divide 24 by -8 i.e,

= -3

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

=

Hence, can be expressed as

**Equivalent Rational Number with given Denominator**

**Example 3**

Express as a Rational Number with Denominator -75.

**Explanation:**

Denominator of = 25

We need to change the Denominator of to -75

We need to find a number, with which we should multiply 25 so it is equal to -75

To obtain that number, we would need to divide -75 by 25 i.e,

= -3

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

=

Hence, can be expressed as

Additive inverse of any rational number is that number with minus (negative) sign before it.

i.e, Additive inverse of

**Example 4**

Additive inverse of is?

**Explanation:**

Additive inverse of any number is that number with minus (negative) sign before it.

Additive inverse of = =

Alternative Method:

We can also find the additive inverse of a Number by multipying it with -1

x (-1) =

When we have to add two rational numbers, First we should convert each of them into a rational number with a positive denominator.

**Addition of Rational Numbers When Denominator Are Equal**

**Question 5**

Find the sum of

**Explanation**

=

=

=

Hence, the sum of of

**Question 6**

Find the sum of

**Explanation**

To add two Rational Numbers, first their Denominators should be positive

So, we would first express as a Rational Number with a positive Denominator.

Multiplying both the Numerator and Denominator by (-1)

i.e, =

=

=

=

Hence, the sum of

**Addition of Rational Numbers When Denominators Are Unequal**

**Question 7**

Find the sum of ?

**Explanation**

To add two Rational Numbers with different Denominator, we will first find the LCM of both the Denominators.

LCM of 6 and 9 is 18

Now we would divide such LCM by Denominator of first number and the result would be multiplied with both the numerator and denominator of such number

Dividing LCM by the Denominator of first number

18 ÷ 6 = 3

Multiplying both the Numerator and Denominator of by the quotient i.e, 3

=

Dividing LCM by the Denominator of Second number

18 ÷ 9 = 2

Multiplying both the Numerator and Denominator of by 2

=

Now + =

Hence, the sum of =

**Question 8**

Find the sum of ?

**Explanation**

To add two Rational Numbers,

first

their Denominators should be positive

So, we would first express as a Rational Number with positive Denominator.

Multiplying both the Numerator and Denominator by (-1)

i.e, =

To add two Rational Numbers with different Denominator first we will find the LCM of both the Denominators.

LCM of 8 and 6 is 24

Divide LCM by the Denominator of first number

24 ÷ 8 = 3

We have to multiply , both the Numerator and Denominator of by the quotient i.e, 3

=

Divide LCM by the Denominator of second number

24 ÷ 6 = 4

We have to multiply , both the Numerator and Denominator of by 4

=

Now + =

Hence, the sum of and =

**Subtracting Rational Numbers When Denominators are Equal**

**Question 9**

Subtract:

–

**Explanation**

Difference of Rational Numbers when Denominators are equal =

=

=

So, the difference of

**Question 10**

Subtract:

–

**Explanation**

Difference of Rational Numbers when Denominators are equal =

=

=

So, the difference of

**Subtracting Rational Numbers When Denominators are Unequal**

**Question 11**

Subtract:

–

**Explanation**

To subtract two Rational Numbers with different Denominators, first we will find the LCM of both the Denominators.

LCM of 4 and 7 is 28

Now we would divide such LCM by Denominator of first number and the result would be multiplied with both the numerator and denominator of such number

Divide LCM by the Denominator of first number

28 ÷ 4 = 7

We have to multiply , both the Numerator and Denominator of by the quotient i.e, 7

=

Divide LCM by the Denominator of second number

28 ÷ 7 = 4

We have to multiply , both the Numerator and Denominator of by the quotient i.e, 4

=

Now – =

Hence, – =

**Question 12**

Subtract:

–

**Explanation**

To subtract two Rational Numbers with different Denominators, first we will find the LCM of both the Denominators.

LCM of 4 and 5 is 20

Now we would divide such LCM by Denominator of first number and the result would be multiplied with both the numerator and denominator of such number

Divide LCM by the Denominator of first number

20 ÷ 4 = 5

We have to multiply , both the Numerator and Denominator of by the quotient i.e, 5

=

Divide LCM by the Denominator of second number

20 ÷ 5 = 4

We have to multiply , both the Numerator and Denominator of by the quotient i.e, 4

=

Now – =

Hence, – =

If and are two Rational Numbers,

then, x =

**Question 13**

Find the product of ?

**Explanation**

x = =

To further simplify the given numbers into their lowest form, we would divide both the Numerator and Denominator by their HCF

HCF of 45 and 35 is 5

Dividing both the Numerator and Denominator by their HCF

=

Hence, the product of and =

**Question 14**

Find the product of and ?

**Explanation**

x

=

( Product of one negative and one positive integer is always negative)

=

To further simplify the given numbers into their lowest form, we would divide both the Numerator and Denominator by their HCF

HCF of 108 and 56 is 4

Dividing both the Numerator and Denominator by their HCF

=

Hence, product of and =

**Question 15**

Find the product of and ?

**Explanation**

x

=

( Product of one negative and one positive integer is always negative )

=

To further simplify the given numbers into their lowest form, we would divide both the Numerator and Denominator by their HCF

HCF of 32 and 84 is 4

Dividing both the Numerator and Denominator by their HCF

=

Hence, product of x =

**Question 16**

Find the product of x ?

**Explanation**

x

=

( Product of two negative integers is always positive )

=

HCF of 66 and 40 is 2

Dividing both the Numerator and Denominator by their HCF

=

Hence, product of x =

In order to divide a Rational Number by another Rational Number

We have to multiply first Rational Number with Reciprocal of the second Rational Number.

If and are two Rational Numbers,

then, ÷ = x

**Question 17**

Divide:

÷

**Explanation**

We have, ÷

In order to divide a Rational Number by another Rational Number

We have to multiply first Rational Number with Reciprocal of the second Rational Number.

We have ÷

(Reciprocal of is )

So we can say that,

÷

= x

=

HCF of 36 and 21 is 3

= =

**Question 18**

Divide:

÷

**Explanation**

We have, ÷

In order to divide a Rational Number by another Rational Number

We have to multiply first Rational Number with Reciprocal of the second Rational Number

Since, Reciprocal of is

We can write the given equation as ÷

= x

To make the Denominator positive, we would multiply 12 and -6 by -1

Given equation would now be x

=

HCF of 168 and 30 is 6

= =

Hence, ÷ is

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