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) -23×35+52-35×16
Solution :
=-23×35+52-35×16
=-25+52-110
=-4+25-110
=-5+2510
=2010
=2
Answer :
=2
ii) 25×(-37)-16×32+114×25
Solution :
=25×(-37)-16×32+114×25
=-635-14+135
=-6+135-14
=-535-14
=-17-14
=-4-728
=-1128
Answer :
=-1128
Q2. Write the additive inverse of each of the following.
i) 23 ii) -59 iii) -6-5 iv) 2-9 v) 19-6
Solution :
i) The additive inverse of 23 is -23.
ii) The additive inverse of -59 is 59.
iii) The additive inverse of -6-5=65 is -65.
iv) The additive inverse of 2-9 is 29.
v) The additive inverse of 19-6 is 196.
Q3. Verify that -(-x)=x for.
i) x=1115 ii) x=-1317
Solution :
i)
-(-x)=x
-(-115)=115 [-(-a)=a]
115=115
hence verified.
ii)
-(-x)=x
-{-(-1317)}=-1317
-1317=-1317
hence verified.
Q4. Find the multiplicative inverse of the following.
i) -13 ii) -1319 iii) 15 iv) -58×-37 v) -1×-25 vi) -1
Solution :
i) The multiplicative inverse of -13 is -113.
ii) The multiplicative inverse of -1319 is -1913.
iii) The multiplicative inverse of 15 is 5.
iv) The multiplicative inverse of -58×-37=1556 is 5615.
v) The multiplicative inverse of -1×-25=25 is 52.
vi) The multiplicative inverse of -1 is 1.
Q5. Name the property under multiplication used in each of the following.
i) -45×1=1×-45=-45
Answer :
1 is the multiplicative identity
ii) -1317×-27=-27×-1317
Answer :
Multiplicative inverse.
Q6. Multiply 613 by the reciprocal of -716
Solution :
The reciprocal of -716 is -167.
Then
=613×(-167)
=-9691
Answer :
-9691
Q7. Tell what property allows you to compute 13×(6×43)as(13×6)×43.
Answer :
Associativity.
Q8. Is 89 the multiplicative inverse of -118? Why or why not?
Solution :
=89×(-118)
=89×(-8×1+18)
=89×(-98)
=-1
Answer :
No, because the product is not 1.
Q9. Is 0.3 the multiplicative inverse of 313? Why or why not?
Solution :
=0.3×313
=310×3×3+13
=310×103
=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 1x, where x≠0 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) -15, iv) x, v) x, vi) Rational number, vii) positive.
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