Rational Numbers Class 8 RS Aggarwal Exe-1B Goyal Brothers Prakashan ICSE Foundation Maths Solutions. We provide step by step Solutions of lesson-1 Rational Numbers about Addition and subtraction on rational numbers . Our Solutions contain all type Questions of Exe-1B to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.
Rational Numbers Class 8 RS Aggarwal Exe-1B Goyal Brothers ICSE Maths Solutions
| Board | ICSE |
| Publications | Goyal Brothers Prakshan |
| Subject | Maths |
| Class | 8th |
| writer | RS Aggarwal |
| Book Name | Foundation |
| Topics | addition subtraction on rational numbers |
| Edition | 2024-2025 |
Addition and Subtraction on Rational Numbers
Rational Numbers Class 8 RS Aggarwal Exe-1B Goyal Brothers Prakashan ICSE Foundation Maths Solutions
.Page- 16
Exercise- 1B
(Addition and Subtraction on Rational Numbers)
Que-1: Find the additive inverse of :
(i) 9/13 (ii) 16/7 (iii) -3/23 (iv) 8/-11 (v) -22/15 (vi) -11/-9
Solution- we know that Additive inverse is a number which on getting added to the original number results in zero
(i) -9/13
(ii) -16/7
(iii) 3/23
(iv) 8/11
(v) 22/15
(vi) -11/9
Que-2: Find the sum :
(i) -7/17 + 6/17 (ii) -5/12 + 7/-12 (iii) 8/15 + 5/12 (iv) -11/18 + 5/-12 (v) -11/6 + -3/4 + 5/8 + -7/3 (vi) 4/7 + 2/-3 + 5/21 + -8/9
Solution- (i) -7/17 + 6/17
= (-7 + 6)/17
= -1/17
(ii) -5/12 + 7/-12
= (-5 + (-7))/12
= -12/12 = -1
(iii) 8/15 + 5/12
take lcm of 15 and 12 is 60.
[(8×4)+(5×5)]/60
(32+25)/60
57/60
(iv) on taking LCM of 12 and 18 is 36.
= [(-11×2)-(5×3)]/36
= -22-15/36
= -37/36 = -1*(1/36)
(v) LCM of 6,4,8 and 3 is 24.
−11/6×4/4 = −44/24
−3/4×6/6 = −18/24
5/8×3/3 = 15/24
−7/3×8/8 = −56/24
Now, we can add them together:
(−44/24) + (−18/24) + (15/24) + (−56/24)
=[(−44)+(−18)+15+(−56)]/24
= (−44−18+15−56)/24
= -103/24 = -4*(7/24) Ans.
(vi) The common denominator for 7, -3, 21, and 9 is 63
Then, rewrite each fraction with the common denominator:
= 4/7×9/9 = 36/63
= 2/−3×21/21 = −42/63
= 5/21×3/3 = 15/63
= −8/9×7/7 = −56/63
Now, add these fractions together:
36/63+(−42/63)+(15/63)+(−56/63)
= (36−42+15−56)/63
= −47/63
Que-3: Subtract :
(i) 2/3 from 5/6 (ii) -2/5 from -5/7 (iii) 4/9 from -7/8 (iv) -11/6 from 8/3
Solution- (i) 5/6 – 2/3
Taking LCM of 3 and 6 is 6
5/6 x 1/1 = 5/6
2/3 x 2/2 = 4/6
= 5/6 – 4/6
= 1/6
(ii) -5/7 – (-2/5)
Taking LCM of 5 and 7 is 35.
-5/7 x 5/5 = -25/35
-2/5 x 7/7 = -14/35
= -25/35 – (-14/35)
= -25/35 + 14/35
= -11/35
(iii) -7/8 – 4/9
Taking LCM of 8 and 9 is 72.
-7/8 x 9/9 = -63/72
4/9 x 8/8 = 32/72
= -63/72 – 32/72
= -95/72 = -1*(23/72)
(iv) 8/3 – (-11/6)
Taking LCM of 3 and 6 is 6.
8/3 x 2/2 = 16/6
-11/6 x 1/1 = -11/6
= 16/6 – (-11/6)
= 16/6 + 11/6
= 27/6 = 9/2 = 4*(1/2)
Que-4: The sum of two rational numbers is -4/9. If one of them is 13/6, then find the other.
Solution- According to the problem, the sum of two rational numbers is −4/9. So, we can write the equation:
13/6+x = −4/9
To find x, let’s isolate it on one side of the equation.
x = −4/9−13/6
To add these fractions, we need to find a common denominator, which is 18.
x = (−4×2)/(9×2)−(13×3(/(6×3)
x = −8/18−39/18
x = (−8−39)/18
x = −47/18 Ans.
Que-5: What number should be added to -2/3 to get -1/7 ?
Solution- According to the question:
let other number be x
sum of – 2 / 3 and a number = – 1 / 7
x + ( – 2 / 3 ) = – 1 / 7
x – 2 / 3 = – 1 / 7
x = ( – 1 / 7 ) + ( 2 / 3 )
x = { – ( 1 x 3 ) / ( 7 x 3 ) } + { ( 2 x 7 ) / ( 3 x 7 ) }
x = ( – 3 / 21 ) + ( 14 / 21 )
x = ( – 3 + 14 ) / 21
x = 11 / 21
Que-6: What number should be subtracted from -2 to get 7/11 ?
Solution- Let x be the number that needs to be subtracted from -2.
Then, the equation becomes:
−2−x = 7/11
Now, let’s solve for x:
x = −2−7/11
To subtract fractions, we need a common denominator, which is 11:
x = −22/11−7/11
x = (−22+7)/11
x = −29/11 = -2*(7/11) Ans.
Que-7: What number should be added to -1 so as to get 5/7 ?
Solution-Let x be the number that needs to be added to -1.
Then, the equation becomes:
−1+x = 5/7
Now, let’s solve for x:
x = 5/7+1
To add fractions, we need a common denominator, which is 7:
x = 5/7+7/7
x = (5+7)7
x = 12/7 Ans.
Que-8: What number should be subtracted from -2/3 to get -1/6 ?
Solution- Let x be the number that needs to be subtracted from −2/3.
Then, the equation becomes:
−2/3−x = −1/6
Now, let’s solve for x:
x = −1/6+2/3
To subtract fractions, we need a common denominator, which is 6:
x = −1/6+4/6
x = (−1+4)/6
x = 3/6
x = 1/2 Ans.
Que-9: State whether each of the following statements is true or false ?
(i) The difference of two rational numbers is always a rational number.
(ii) 2/3 – 3/5 = 3/5 – 2/3
(iii) 1 is the additive identity for rational numbers.
(iv) Subtraction is commutative on rational numbers.
(v) There exists a rational number which is its own additive inverse.
(vi) 19/-5 + -3/11 = 19/5 + 3/11
Solution- (i) True
(ii) False
(iii) False
(iv) False
(v) True
(vi) False
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