CBSE 8 maths Chapter-1: Rational Numbers

Chapter-1: Rational Numbers

1. Using appropriate properties find the value of −23×35+52−35×16

Sol.   −23×35+52−35×16 – −23×35−35×16+52

=−35(23+16)+52

=−35(4+16)+52

=−35(56)+52

=−1530+52

₌−12+52

=42

=2

 therefore−23×35+52−35×16 =2

2. Using appropriate properties find the value of 25×−37−16×32+114×25

Sol. 25×−37−16×32+114×25

= −25×37−12×12+17×15

=−635−14+135

=−535−14

=−17−14

=−1128

=25×−37−16×32+114×25

=−1128

3. Solving the additive inverse of 28

Sol.  Additive inverse of 28is−28

4. Solving the additive inverse of −59

Sol.  Additive inverse of −59is59

5. Solving the additive inverse of −6−5

Sol. −6−5−6−5

Additive inverse of 65is−65

Additive inverse of −6−5−65

6. Solving the additive inverse of 2−9

Sol.  Additive inverse of 2−9is29

7. Verify that –(-x )=x for x=1115

Sol. x=1115

–x=−1115 −(−x)=−(−1115)

=1115=x

 therefore−(−x)=x

8. Verify that –(-x )=x for x=−1317

Sol. x=−1317

–x=(−−1317)=1317 −(−x)=−(−1317)

=−1317=x

 therefore−(−x)=x

9. Solve that multiplicative inverse of -13

Sol. Given multiplicative inverse -13 is−113

10. Solve that multiplicative inverse of −1319

Sol. Given multiplicative inverse −1319is−1913

11. Solve that multiplicative inverse of −58×−37

Sol. Given multiplicative inverse −58×−37is 85×73 or −85×−73

12. What is the multiplicative inverse of -1.

Sol.  The multiplicative inverse of -1 is -1.

13. Name the property under multiplicative used in each of the following.

 (i) −45×1=1×−45=−45

(ii) −1317×−27=−27×−1317

(iii) −1929×29−19=1

Sol. (i) ROLE OF 1

(ii) COMMUTATIVITY

(iii) MULTIPLICATIVE  INVERSE

14. Multiply 613 by the reciprocal of −76

Sol. Reciprocal of −76 is 6−7

 therefore613×6−7

=−3691

15. what property allows you to compute 13×(6×43)(13×6)×45

Sol.  Associativity

16. Is 89 the multiplicative inverse of −118 ? why or why not.

Sol.

−118=−98

=89×−98

=−1≠1

 therefore89 is  not the multiplicative inverse of −118

17. Is 0.3 the multiplicative inverse of 313 ? why or why not.

Sol.        313=103=3.3

                          3.3×0.3=0.99≠1

 therefore0.3isnotthemultiplicativeinverseof313

Exercise 1.1:

Question 1:

Solve the following using appropriate properties:

1. ii)25∗−37–16∗32+114∗25

Answers:

1. ii) Use commutativity of rational numbers

25∗−37–16∗32+114∗25

Using distributive property

25∗[−37+114]–14

= 25∗−3∗2+114–14

=25∗−514–14

=−4−728=−1128

Question 2:

(i) −5−7

(ii) −4−7

(iii)2−5

(iv)5−9

Solution:

(i) −5−7

additive inverse = 5−7

(ii)  −4−7 = 47

Additive inverse = −47

(iii)  2−5

Additive inverse = 25

(iv)  5−9

Additive inverse = 59
Question 3:

(i)  x = 1115

(ii) x= −1317

Solution:

x = 1115

The additive inverse of  is   x = −1115

This equality

x = 1115+frac−1115=0

=−(−x)=x

x= −1317

The additive inverse of  x= −1317 =  x= 1317

This equaliity

x = −1317+frac1317=0

=−(−x)=x

Question 4:

(i)  -12

(ii) −1913

(iii) 13

(iv)  −38∗−38

(v)  −1∗−35

Solutions:

1. The multiplicative inverse of  -12 is 112
2. The multiplicative inverse of −1913 is−1319
3. The multiplicative inverse of 13  is 31 = 3
4. The multiplicative inverse of  −1∗−35 is 53

Question 5:

Find out the multiplication property that is used in the following sums:

(i) −37∗1=1∗−37=−37

(ii) −1417∗−34=−34∗−1417

(iii) −1737∗37−17=1

Solutions:

1. This use the multiplicative identity property and the multiplicative identity is 1
2. This uses the commutativity property
3. This uses the multiplicative inverse property

Question 6:

Find the product of  715 and the reciprocal of −417

Solution:

Reciprocal of  −417 =  −1714

715∗−1714=11960

Question 7:

1. Which rational number does not have a reciprocal
2. Which rational number is equal to its own reciprocal
3. Which rational number is equal to its own negative

Solution:

1. Zero is the rational number that has no reciprocal
2. One and negative one are rational numbers that are equal to their own reciprocal
3. Zero is a rational number that is also equal to its own negative.

Question 8: Answer or complete the following sentences:

1. Does zero have a reciprocal?
2. The two numbers _____ and _________ are their own reciprocals.
3. What is the reciprocal of -6?
4. What is the reciprocal of ?
5. The product of two rational numbers is always a __________.
6. The reciprocal of a positive rational number is ___________.

Solutions:

1. No it doesn’t
2. 1, -1
3. -1/6
4. X
5. Rational number
6. Positive rational number

Question 9:

Find the multiplicative inverse of the following:

1. -12
2. −1218
3. 27
4. -1
5. −38∗−57
6. −2∗−27

Solutions:

1. −112
2. −1218
3. 72
4. -1
5. 5615
6. 72

Question 10:

Is 0.3 the multiplicative inverse of   313? Why or why not?

Answer:

313=103 0.3∗313=0.3∗103=310∗103=1

As proved above the product is one.

Therefore, 0.3 is the multiplicative inverse of  313