NCERT Solutions for Class 8 maths Chapter 1 Exercise 1.1
In this page we have NCERT Solutions for Class 8 maths Chapter 1 : rational Numbers for
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Question 1:
Using appropriate properties find:
Answer
(i)Using commutativity property of rational number
Now using Distributivity property
(ii) Using commutativity property of rational numbers
Now using Distributivity property
Question 2
Write the additive inverse of each of the following:
(a) $\frac {2}{8}$
(b) $ \frac {-5}{9}$
(c) $\frac {-6}{-5}$
(d) $\frac {2}{-9}$
(e) $\frac {19}{-6}$
Answer:
(i) $\frac {2}{8}$
Additive inverse of $\frac {2}{8}$= $\frac {-2}{8}$
(ii) $ \frac {-5}{9}$
Additive inverse of $ \frac {-5}{9}$ = $ \frac {5}{9}$
(iii) $\frac {-6}{-5} =\frac {6}{5}$
Additive inverse of $\frac {-6}{-5}$= $\frac {-6}{5}$
(iv)$\frac {2}{-9}=\frac {-2}{9}$
Additive inverse of $\frac {2}{-9}$ =$\frac {2}{9}$
(v) $\frac {19}{-6}= \frac {-19}{6}$
Additive inverse of $\frac {19}{-6}$ =$\frac {19}{6}$
Question 3
Verify that - ( -
x) =
x for.
(i) x =11/15 (ii) x=-13/17
Answer:
(i) x=11/15
Additive inverse
-x=-11/15
As (11/15) + (-11/15) =0
The above also represent that additive inverse of (-11/15) is (11/15) or we can say that
-(-11/15)=11/15
Or x=-(-x)
(ii)
x=-13/17
Additive inverse
-x=-13/17
As (-13/17) + (13/17) =0
The above also represent that additive inverse of (13/17) is (-13/17)) or we can say that
-(13/17) = -13/17
Or x=-(-x)
Question 4
Find the multiplicative inverse of the following.
(a)$-13$
(b)$ \frac {-13}{19}$
(c) $\frac {1}{5}$
(d) $\frac {-5}{8} \times \frac {-3}{7}$
(e) $-1 \times \frac {-2}{5}$
(f) $-1$
Answer
(a) $-13$
Multiplicative inverse of $-13$=$\frac {-1}{13}$
(b)$ \frac {-13}{19}$
Multiplicative inverse of $ \frac {-13}{19}$ =$ \frac {-19}{13}$
(c)$\frac {1}{5}$
Multiplicative inverse of $\frac {1}{5}$=$5$
(d) $\frac {-5}{8} \times \frac {-3}{7}=\frac {15}{56}$
Multiplicative inverse of $\frac {-5}{8} \times \frac {-3}{7}$ =$\frac {56}{15}$
(e) $-1 \times \frac {-2}{5}= \frac {2}{5}$
Multiplicative inverse of $-1 \times \frac {-2}{5}$ =$ \frac {5}{2}$
(f) $-1$<
Multiplicative inverse of $-1$=-1
Question 5 :
Name the property under multiplication used in each of the following:
Answer:
- 1 is the multiplicative identity
- Commutatively
- Multiplicative inverse
Question 6:
Multiply 6/13 by the reciprocal of -7/16
Answer
Reciprocal of -7/16= -16/7
So $ \frac {6}{13} \times (- \frac {16}{7}) =- \frac {96}{91}$
Question 7
Tell what property allows you to compute
Answer:
Associativity
Question 8
Is 8/9 the multiplicative inverse of $-1 \frac {1}{8}$
Why or why not?
Answer:
$-1 \frac {1}{8}$
$=\frac {-9}{8}$
Now
$ \frac {8}{9} \times (-\frac {9}{8}) = -1$
So it is not the multiplicative inverse
Question 9
Is 0.3 the multiplicative inverse of $3 \frac {1}{3}$
Why or why not?
Answer:
$3 \frac {1}{3}$
=10/3
Now
$ \frac {3}{10} \times \frac {10}{3} =1$
So it is the multiplicative inverse
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.
Answer:
- 0
- 1 and -1
- 0
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 (1/x) where is x ≠ 0 __________.
(v) The product of two rational numbers is always a __________.
(vi) The reciprocal of a positive rational number is __________.
Answer:
- No
- 1 and -1
- -1/5
- X
- Rational Number
- Positive rational number
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