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.
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