NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1, are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1.
NCERT Solutions for Class 8 Maths Chapter 1 Rational Numbers Ex 1.1
Question 1.
Using appropriate properties find:
(i) (-frac { 2 }{ 5 } times frac { 3 }{ 5 } +frac { 5 }{ 2 } -frac { 3 }{ 5 } times frac { 1 }{ 6 } )
(ii) (frac { 2 }{ 5 } times left( -frac { 3 }{ 7 } right) -frac { 1 }{ 6 } times frac { 3 }{ 2 } +frac { 1 }{ 14 } times frac { 2 }{ 5 } )
Solution.
Question 2.
Write the additive inverse of each of the following:
Solution.
(i) (frac { 2 }{ 8 } )
Additive inverse of (frac { 2 }{ 8 } ) is (frac { 2 }{ 8 } )
(ii) (-frac { 5 }{ 9 } )
(frac { -6 }{ -5 } =frac { 6 }{ 5 } )
Additive inverse of (frac { -6 }{ -5 } ) is (frac { -6 }{ 5 } )
(iii) (frac { -6 }{ -5 } )
(frac { -6 }{ -5 } )=(frac { 6 }{ 5 } )
Additive inverse of (frac { -6 }{ -5 } ) is (frac { -6 }{ 5 } )
(iv) (frac { 2 }{ -9 } )
Additive inverse of (frac { 2 }{ -9 } ) is (frac { 2 }{ 9 })
(v) (frac { 19 }{ -6 } )
Additive inverse of (frac { 19 }{ -6 } ) is (frac { 19 }{ 6 })
Question 3.
Verify that – (-x) = x for :
(i) (x=frac { 11 }{ 15 } )
(ii) (x=-frac { 13 }{ 17 } )
Solution.
Question 4.
Find the multiplicative inverse of the following:
Solution.
Question 5.
Name the property under multiplication used in each of the following:
(i) (frac { -4 }{ 5 } times left( 1 right) =1times frac { -4 }{ 5 } =-frac { 4 }{ 5 } )
(ii) (-frac { 13 }{ 17 } times frac { -2 }{ 7 } =frac { -2 }{ 7 } times frac { -13 }{ 17 } )
(iii) (frac { -19 }{ 29 } times frac { 29 }{ -19 } =1)
Solution.
(i) 1 is the multiplicative identity
(ii) Commutativity of multiplication
(iii) Multiplicative inverse.
Question 6.
Multiply (frac { 6 }{ 13 } ) by the reciprocal of (frac { -7 }{ 16 } )
Solution.
Reciprocal of (frac { -7 }{ 16 } ) is (frac { -16 }{ 7 } )
Now,
(frac { 6 }{ 13 } times frac { -16 }{ 7 } =frac { 6times left( -16 right) }{ 13times 7 } =frac { -96 }{ 91 } )
Question 7.
Tell what property allows you to compute : (frac { 1 }{ 3 } times left( 6times frac { 4 }{ 3 } right) ) as (left( frac { 1 }{ 3 } times 6 right) times frac { 4 }{ 3 } )
Solution.
Associativity.
Question 8.
Is the (frac { 8 }{ 9 } ) multiplicative inverse of (-1frac { 1 }{ 8 } ) ? Why or why not?
Solution.
(-1frac { 1 }{ 8 } =-frac { 9 }{ 8 } )
Now, (frac { 8 }{ 9 } times frac { -9 }{ 8 } =-1neq 1)
So, No ; (frac { 8 }{ 9 } ) is not the multiplicative inverse of (-1frac { 1 }{ 8 } left( =-frac { 9 }{ 8 } right) ) because the product of (frac { 8 }{ 9 } ) and -13(-) and (-1frac { 1 }{ 8 } left( =-frac { 9 }{ 8 } right) ) is not 1.
Question 9.
Is 0.3 the multiplicative inverse of (3frac { 1 }{ 3 }) ? Why or why not?
Solution.
Yes ; 0.3 is the multiplicative inverse of (frac { 10 }{ 3 } ) because
(frac { 3 }{ 10 } times frac { 10 }{ 3 } =frac { 3times 10 }{
10times 3 } =frac { 30 }{ 30 } =1)
Question 10.
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.
Solution.
(i) The rational number ‘0′ does not have a reciprocal.
(ii) The rational numbers 1 and (-1) are equal to their own reciprocals.
(iii) The rational number 0 is equal to its negative.
Question 11.
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 (frac { 1 }{ x } ), where (xneq 0)
(v) The product of two rational numbers is always a.………
(vi) The reciprocal of a positive rational number is……….
Solution.
(i) Zero has no reciprocal.
(ii) The numbers 1 and -1 are their own reciprocals.
(iii) The reciprocal of – 5 is (-frac { 1 }{ 5 } )
(iv) Reciprocal of (frac { 1 }{ x } ), where (xneq 0) is x.
(v) The product of two rational numbers is always a rational number.
(vi) The reciprocal of a positive rational number is positive.
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