8th Maths : Chapter 1 : Numbers : Basic Arithmetic Operations on Rational Numbers : Exercise 1.2 : Text Book Back Exercises Questions with Answers, Solution

**Exercise 1.2**

** **

**Fill in the blanks:**

(i) The value
of = ________._{ } **[Answer: 1/20 ]**

(ii) The
value of is ________._{ }**[Answer:
1 ]**

(iii) The
value of is ________._{ }**[Answer:
1 ]**

(iv) The
rational number ________ does not have a reciprocal._{ }**[Answer:
0 ]**

(v) The multiplicative
inverse of –1 is ________._{ }**[Answer:
**−**1 ]**

2. **Say True or False:**

(i) All rational
numbers have an additive inverse.**[Answer: True ]**

(ii) The
rational numbers that are equal to their additive inverses are 0 and –1. **[Answer: False ]**

(iii) The
additive inverse of −11/−17 is 11/17. **[Answer: False ]**

(iv) The
rational number which is its own reciprocal is –1.**[Answer: True ]**

(v) The multiplicative
inverse exists for all rational numbers. **[Answer: False ]**

**3. Find the sum:**

**Solution:**

**(i)**** 7/5 + 3/5** = [7+3] / 5 = 10/5 = 2

**(ii)**** 7/5 + 5/7** = [ 7×7 + 5×5] / 35 = [49 + 25] / 35 = 74/35

**(iii) ****6/5 + (−14/15) **= [ 6×3 + (14)] / 15 = [18 + (−14)] / 5 = 4/5

**(iv) ****−4 (2/3) + 7 (5/12) **= [14/3] + [18/12] = [−14 × 4 + 89] / 12 = [−56 +89] / 12 = −33/12
= −11/4

**4. Subtract : **

**Solution:**

−17/11 – (−8/44) = [−17/11] + [8/44] = [−17 × 4 + 8] /
44 = [−68 + 8] / 44 = 60/44 = −15 / 11

**5. Evaluate : **

**Solution:**

**(i)** [9 / 132] × [−11 / 3] = −1 / 4

** (ii) [**−7 / 27] × [24 / −35] = 8/45

**6. Divide : **

**Solution:**

**(i)**** −21/5 ÷ −7/−10** = −21/5 × 10/7 = −6

**(ii)**** −3/13 ÷ −3** = −3/13 × −1/3 = [−3 × −1] / [13 × 3] = 3/39

**(iii) ****−2 ÷ [−6/15]** = −2 × [15/−6] = [−2 × 15] / −6
= −30 / −6 = 5

**7. Find ( a + b) ÷ (a - b) if **

**(i) a = 1/2 , b = 2/3 (ii) a = - 3/5
, b = 2/15 **

**Solution:**

**(i) a = 1/2, b = 2/3**

* a + b* = [1/2] + [2/3] = [1×3 +
2×2] / 6 = [3 + 4] / 6 = 7/6

*a – b *= (1/2) − (2/3) = [1×3 − 2×2] / 6 = [3 – 4] / 6 = −1/6

(*a + b*) ÷ (*a − b*) = [7/6] ÷ [−1/6] = [7/6] × [6/−1]
= −7

**(ii) a = −3/5, b = 2/15**

*a + b* = −3/5 + 2/15 = [ −3×3 + 2] / 15 = [−9
+ 2] / 15 = −7/15

*a − b* = (−3/5) – (2/15) = [−3 × 3 – 2] /
15 = [−9 – 2] / 15 = −11/15

(*a + b*) ÷ (*a − b*) = [−7/15] ÷ [−11/15] = [−7/15] ×
[15/−11] = 7/11

**8. Simplify : **** and show that
it is a rational number between 11 and 12.**

**Solution:**

(1/2) + (3/2 – 2/5) ÷ (3/10)
× 3 = 1/2 + ([15 – 4] / 10 ) ÷ 3/10 × 3
= 1/2 + 11/10 × 10/3 × 3

= 1/2 + 11 = 11 (1/2) = 23/2

**9. Simplify :**

Solution:

**10. A student had multiplied a number
by 4/3 instead of dividing it by 4/3 and got than the correct answer. Find the number.
**

**Solution:**

Let the number =* a*

[ *a* × 4/3 ] – [ *a* ÷ 4/3 ] = 70

[* a* × 4/3 ] – [ *a* × 3/4 ] = 70

*a* [4/3 – 3/4] = 70

*a* [ (4×4 – 3×3) / 12] = 70

*a* [ 16–9 / 12] = 70

*a* [7 / 12] = 70

*a*
= 70 × (12/7) = 120

*a* = 120

** **

**Objective
Type Questions**

11. The standard form of sum is _________

**[Answer: (A) 1]**

**Solution:**

3/4 + 5/6 + (−7/12) = [ (3 × 3) + (5 × 2) + (−7) ] / 12 = [ 9 +
10 + (−7) ] / 12 = [19 – 7 ] / 12 = 12 /
12 = 1

**[Answer: (C) 5/8 ]**

**Solution:**

(3/4 – 5/8) + 1/2 = ( [3 × 2 – 5] / 8) + 1/2 = [6 – 5] / 8 + 1/2
= 1/8 + 1/2

= [1 + 1 × 4] / 8 = [1 + 4] / 8 = 5/8

**[Answer: (B) 2/3]**

**Solution:**

3/4 ÷ (5/8 + 1/2) = 3/4 ÷ ( [5 ÷ (1 × 4)] / 8 ) = 3/4 ÷ ([5+4]/8)
= 3/4 ÷ 9/8 = [3/4] × [8/9] = 2/3

**[Answer: (D) 15/16]**

**Solution:**

3/4 × ( 5/8 ÷ 1/2) = 3/4 × (5/8 × 2/1) = 3/4 × 5/4 = 3×5 / 4×4 =
15/16

**15. Which of these rational numbers which
have additive inverse?**

(A) 7

(B) −5/7

(C) 0

(D) all of
these

**[Answer: (D) all of these]**

**Solution:**

Additive inverse of 7 is −7.

Additive inverse of −5/7 is 5/7.

Additive inverse of 0 is 0.

** **

__Answer: Exercise
1.2__

**1. (i) 1/20 (ii) 1 (iii)
1 (iv) 0 (v) –1 **

**2. (i) True (ii) False
(iii) False (iv) True (v) False **

**3. (i) 2 (ii) 74/35 (iii)
4/15 (iv) 2 3/4**

**4. −15/11 **

**5. (i) −1/4 (ii) 8/45**

**6. (i) − 6 (ii) 1/13 (iii)
5 **

**7. (i) –7 (ii) 7/11 **

**8. 23/2 (≈11 1/2) and hence
lies between 11 and 12. **

**9. (i) 133/60 (ii) −5/2
**

**10. 120 **

**11. (A) 1 **

**12. (C) 5/8 **

**13. (B) 2/3 **

**14. (D) 15/16 **

**15. (D) all of these**

Tags : Questions with Answers, Solution | Numbers | Chapter 1 | 8th Maths , 8th Maths : Chapter 1 : Numbers

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8th Maths : Chapter 1 : Numbers : Exercise 1.2: Basic Arithmetic Operations on Rational Numbers | Questions with Answers, Solution | Numbers | Chapter 1 | 8th Maths

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