# NCERT  Solution for Class 8th Maths Chapter – 1 Rational Numbers

## Exercise – 1.1

Q1. Using appropriate properties find.

• -2/3 x 3/5 + 5/2 – 3/5 x 1/6

Solution:-

= -2/3 x 3/5 + 5/2 – 3/5 x 1/6

= -2/3 x 3/5 – 3/5 x 1/6 + 5/2  ( by commutativity)

= 3/5 ( -2/3 – 1/6 ) + 5/2

= 3/5 (( -4 -1 )/6) + 5/2

= 3/5 (( -5)/6) + 5/2 ( by distributivity)

=   -15/30 + 5/2

= -1/2 + 5/2

= 4/2

= 2

• 2/5 x (-3/7) – 1/6 x 3/2 + 1/14 x 2/5

Solution:-

= 2/5  x (-3/7 + 1/4 ) – 3/12

= 2/5 x ((

-6 + 1)/14) – 3/12

= 2/5 x (( -5 / 14)) – 1/4

= (-10/70) – 1/4

= -1/7 – 1/4

= (-4-7) / 28

= -11/28

Q2. Write the additive inverse of each of the following

• 2/8

= Additive inverse of 2/8 is -2/8.

• -5/9

Additive inverse of -5/9 is 5/9

• -6/-5 = 6/5

Solution:-

Additive inverse of 6/5 is -6/5

• 2/-9 = -2/9

Solution:-

Additive inverse of -2/9 is 2/9

• 19/-16 = -19/16

Solution:-

= Additive inverse of -19/16 is 19/16

Q3. Verify that (-x) = x for.

• X = 11/15
• X = -13/17

Solution:-

• X = 11/15

We have , x = 11/15

Then, the additive inverse of 11/15 is -11/15 ( as 11/15 + (-11/15) = 0)

The same equality 11/15 + (-11/15) = 0 , Show that the additive inverse of -11/15 is 11/15

Or, -(-11/15) = 11/15

1. e -(-x) = x

• -13/17

Solution:-

We have , x = -13/17

The additive inverse of x is -x ( as x + (-x) = 0)

Then, the additive inverse of -13/17 is 13/17 ( as 13/17 + (-13/17)= 0 )

The same equality (-13/17 + 13/17 ) = 0, shows that the additive inverse of 13/17 is -13/17.

Or, -(13/17) = -13/17

1. e -(-x) = x

Q4. Find the multiplicative inverse of the

• -13

Multiplicative inverse of -13/19 is -19/13.

• -13/19

Solution:-

= Multiplicative inverse of -13/19 is -19/13.

• 1/5

Solution:-

Multiplicative inverse of 1/5 is 5

• -5/8 x (-3/7) = 15/56

Solution:-

Multiplicative inverse of 15/56 is 56/15

• -1 x (-2/5) = 2/5

Solution:-

Multiplicative inverse of 2/5 is 5/2

• -1

Solution:-

Multiplicative inverse of -1 is -1.

Q5.Name the property under multiplication used in each of the following.

• -4/5 x 1 = 1 x (-4/5) = -4/5

Solution:-

Multiplicative identity

• -13/17 x (-2/7) = -2/7 x (-13/17)

Solution:-

Commutativity property

• -19/29 x 29/-19 = 1

Solution:-

Multiplicative inverse

Q6. Multiply 6/13 by the reciprocal of -7/16

Solution:-

Reciprocal of -7/16 = 16/-7 = -16/7

6/13 x ( Reciprocal of -7/16)

6/13 x (-16/7) = -96/91

Q7. Tell what property allows you to compute 1/3 x ( 6 x 4/3) as ( 1/3 x 6) x 4/3

Solution:-

1/3 x ( 6 x 4/3) = (1/3 x 6) x 4/3

Here, the way in which factors are grouped in a multiplication problem, supposedly does not change the product. Hence , the associativity property is used here.

Q8. Is 8/9 the multiplication inverseof -1 1/8 ? Why or why not?

Solution:-

8/9 is not the multiplicative inverse of 11/8

Q9. If 0.3 the multiplicative inverse of 31/3 ? Why or why not ?

Solution:-

31/3 = 10/3

0.3 = 3/10

3/10 x 10/3 = 1

Therefore, 0.3 is the multiplicative inverse of 31/3

Q10. Write

• The rational number that does not have a reciprocal

Solution:-

0 = 0/1

Reciprocal of 0 = 1/0 which is not defined.

• The rational numbers that are equal to their reciprocals.

Solution:-

1 = 1/1

Reciprocal of 1 = 1/1 = 1, Similarly , Reciprocal of -1 = -1

• The rational number that is equal to is negative.

Solution:-

= negative of 0 =-0=0

Q-11 Fill in the blanks :-

1. Zero has ______
2. The number _________ and ______ are their own reciprocals
• The reciprocal of -5 is _________
1. Reciprocal of 1/x where x, 0 is _______
2. The product of two rational is always a _________
3. The reciprocal of a positive rational number is _________.

Solution:-

• No
• -1
• -1/5
• X
• Rational numbers

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