8th Maths 1.1

Chapter 1

Rational Numbers

NCERT Class 10th solution of Exercise 1.2

Exercise 1.1

Q1. Using appropriate properties find.

i) `-2/3times3/5+5/2-3/5times1/6` 

Solution :

`=-2/3times3/5+5/2-3/5times1/6`

`=-2/5+5/2-1/10`

`=(-4+25-1)/10`

`=(-5+25)/10`

`=20/10`

`=2`

Answer :

`=2` 

ii) `2/5times(-3/7)-1/6times3/2+1/14times2/5`

Solution :

`=2/5times(-3/7)-1/6times3/2+1/14times2/5`

`=-6/35-1/4+1/35`

`=(-6+1)/35-1/4`

`=-5/35-1/4`

`=-1/7-1/4`

`=(-4-7)/28`

`=-11/28`

Answer :

`=-11/28`

Q2. Write the additive inverse of each of the following.

i) `2/3` ii) `-5/9` iii) `-6/-5` iv) `2/-9` v) `19/-6`

Solution :

i) The additive inverse of `2/3` is `-2/3`.

ii) The additive inverse of `-5/9` is `5/9`.

iii) The additive inverse of `-6/-5=6/5` is `-6/5`.

iv) The additive inverse of `2/-9` is `2/9`.

v) The additive inverse of `19/-6` is `19/6`.

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

i) `x=11/15`  ii) `x=-13/17`

Solution :

i) 

`-(-x)=x`

`-(-11/5)=11/5`      [`-(-a)=a`]

`11/5=11/5`

hence verified.

ii) 

`-(-x)=x`

`-{-(-13/17)}=-13/17`

`-13/17=-13/17`

hence verified.

Q4. Find the multiplicative inverse of the following.

i) `-13` ii) `-13/19` iii) `1/5` iv) `-5/8times-3/7` v) `-1times-2/5` vi) `-1`

Solution :

i) The multiplicative inverse of `-13` is `-1/13`.

ii) The multiplicative inverse of `-13/19` is `-19/13`.

iii) The multiplicative inverse of `1/5` is `5`.

iv) The multiplicative inverse of `-5/8times-3/7=15/56` is `56/15`.

v) The multiplicative inverse of `-1times-2/5=2/5` is `5/2`.

vi) The multiplicative inverse of `-1` is `1`.

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

i) `-4/5times1=1times-4/5=-4/5`

Answer :

`1` is the multiplicative identity

ii) `-13/17times-2/7=-2/7times-13/17`

Answer :

Multiplicative inverse.

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

Solution :

The reciprocal of `-7/16` is `-16/7`.

Then 

`=6/13times(-16/7)`

`=-96/91`

Answer :

`-96/91`

Q7. Tell what property allows you to compute `1/3times(6times4/3)as(1/3times6)times4/3`.

Answer :

Associativity.

Q8. Is `8/9` the multiplicative inverse of `-1(1)/8`? Why or why not?

Solution :

`=8/9times(-1(1)/8)`

`=8/9times(-(8times1+1)/8)`

`=8/9times(-9/8)`

`=-1`

Answer :

No, because the product is not `1`.

Q9. Is `0.3` the multiplicative inverse of `3(1)/3`? Why or why not?

Solution :

`=0.3times3(1)/3`

`=3/10times(3times3+1)/3`

`=3/10times10/3`

`=1`

Answer :

Yes, because the product is `1`.

Q10. Write.

i) The rational number that does not have a reciprocal.

ii) The rational numbers that are equal to their reciprocals.

iii) The rational number that is equal to its negative.

Answer :

i) `0`

ii) `1` and `(-1)`

iii) `0`

Q11. Fill in the blanks.

i) Zero has ___ reciprocal.

ii) The numbers ___ and ___ are their own reciprocals.

iii) The reciprocal of `-5` is ____.

iv) Reciprocal of `1/x`, where `xne0` is ___.

v) The product of two rational numbers is always a _____.

vi) The reciprocal of a positive rational number is _____.

Answer :

i) No, ii) `1, -1` iii) `-1/5`, iv) `x`, v) `x`, vi) Rational number, vii) positive.