NCERT Solutions for Class 8 maths Chapter 1 Rational Numbers Exercise 1.1

NCERT Solutions for Class 8 maths Chapter 1 Exercise 1.1

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. 1 is the multiplicative identity
2. Commutatively
3. 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:

1. 0
2. 1 and -1
3. 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:

1. No
2. 1 and -1
3. -1/5
4. X
5. Rational Number
6. Positive rational number

Summary

1. NCERT Solutions for Class 8 maths Chapter 1 Rational Numbers Exercise 1.1 has been prepared by Expert with utmost care. If you find any mistake.Please do provide feedback on mail. You can download the solutions as PDF in the below Link also
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2. This chapter 1 has total 2 Exercise 1.1 and 1.2. This is the first exercise in the chapter.You can explore previous exercise of this chapter by clicking the link below

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