Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 1 Rational Numbers Questions Solution. In this chapter, there is total 40 math problems. We have given each questions solution step by step.
1.) Find the value of: / + (− /)
ANSWER:
/ + (− /)
We make denominator same.
We make denominator 77.
x 7/ x 7 + (− x 11 / x 11)
28 /77 – 55 / 77
28-55/77
/ + (− /) = -27/77
2.) Find the value of: /–/
ANSWER:
/ – /
We make denominator same.
We make denominator 12.
/ – x 4/ x 4
/ – 8 / 12
4 – 8 / 12
= -4 / 12
/ – / = -1 / 3
3). Find the value of: − /–/
ANSWER:
− / – /
We make denominator same.
We make denominator 12.
− / – 5 x 2 / 6 x 2
− / – 10 / 12
− – 10 / 12
− / – / = -17 / 12 = -1 (5/12)
4.) Find the value of: − / − (− /)
ANSWER:
− / − (− /)
We make denominator same.
We make denominator 18.
− / − (− x 2 / x 2)
− / + 10 / 18
− + 10 / 18
− / − (− /) = 5 / 18
5.) Find the value of: − (−/ −) + (/)
ANSWER:
− (−/ −) + (/)
We make denominator same.
We make denominator 24.
− (- x 3/ − x 3) + ( x 2/ x 2)
− (-33 /-24) + (26/24)
− 33 + 26 / 24
-7 / 24
− (−/ −) + (/) = -7 / 24
6.) Find the value of: −/ ÷ (/ −)
ANSWER:
−/ ÷ (/ −)
We change ÷ into x and reverse the fraction.
−/ x −25/7
By cross multiplication,
-1 x -1
−/ ÷ (/ −) = 1
7.) Find the value of: −/ ÷ (− /)
ANSWER:
−/ ÷ (− /)
We change ÷ into x and reverse the fraction.
−/ x (− 87/58)
By cross multiplication,
-1/27 x -87 /2
−/ ÷ (− /) = 87 / 54
8.) Find the value of: (−)/ × / × ()/
ANSWER:
(−)/ × / × ()/
We multiply numerator and denominator of all fraction.
(−) x 3 x 110 / (5 x 10 x 144)
-12 x 110 / / (5 x 10 x 144)
-1 x 11 / 5 x 12
(−)/ × / × ()/ = -11 / 60
9.) Find the value of: −/ × / × /
ANSWER:
−/ × / × /
We multiply numerator and denominator of all fraction.
-11 x 4 x 14 / (21 x 7 x 33)
-1 x 4 x 2 /21 x 3
−/ × / × / = -8 / 63
10.) Find the value of: / ÷ (/−)
ANSWER:
/ ÷ (/−)
We change ÷ into x and reverse the fraction.
/ x (5/-33)
By cross multiplication,
1/3 x 1/-3
/ ÷ (/−) = -1/9
11.) Find the additive inverse of (− / + )
ANSWER:
(− / + ) We convert this in fraction.
= -1 / 8
We know, for additive inverse,
The sum of additive inverse and fraction is 0.
(− / + ) + Additive inverse of (− / + ) = 0
Additive inverse of (− / + ) = 1 / 8
12.) Find the additive inverse of ((−/−) − )
ANSWER:
((−/−) − )We convert this in fraction.
= 1/7
We know, for additive inverse,
The sum of additive inverse and fraction is 0.
((−/−) − ) + Additive inverse of ((−/−) − ) = 0
Additive inverse of ((−/−) − ) = -1/7
13.) Find the multiplicative inverse of (− / + /).
ANSWER:
(− / + /)
We convert this in fraction.
We make denominator 24.
(− / + x 8 / x 8)
(− / + 8/24)
1/24
Now, we know, multiplication of multiplicative inverse and its fraction is 1.
1/24 x multiplicative inverse (1/24) = 1
Multiplicative inverse of (− / + /) = 24
14.) Find the multiplicative inverse of (−/ ÷ /−).
ANSWER:
(−/ ÷ /−).
We convert this in fraction.
(−/ x 5 /-11)
= 25 /121
Now, we know, multiplication of multiplicative inverse and its fraction is 1.
(−/ ÷ /−).x multiplicative inverse(−/ ÷ /−) = 1
Multiplicative inverse of (−/ ÷ /−) = 121/25
15.) Find the value of – / + / + (− /) + /
ANSWER:
– / + / + (− /) + /
Here, we make common denominator by LCM.
We make denominator 30.
-2 x 6 + 5 x 5 + (-3 x 6) + 7 x 2 /30
= -12 + 25 -18 + 14 / 30
= 9/30
– / + / + (− /) + / = 3/10
16.) The sum of two rational numbers is – /. if one of them is – / , find the other.
ANSWER:
Given that, sum of two rational numbers is – /.
Let the other rational number is x.
– / + x = – /
X = – / + /
X = -6 /27
X = -2/9
The other rational number is-2/9.
17.) What number should be added to / to get – /?
ANSWER:
Let, the number is x.
X + / = – /
X = – / – /
X = -6 -9 / 14
X = -15 / 14
The number is-15 / 14.
18.) What number should be subtracted from – / so as to get /?
ANSWER:
Let, the number is x.
– / – x = /
-x = /+/
-x = 6 + 5 /8
-x = 11 /8
X = -11/8
The number is -11/8.
19.) What number should be subtracted from – / to get /?
ANSWER:
Let, the number is x.
– / – x = /
– x = / + /
– x = 15 / 6
X = – 15 /6
X = -5/2
The number is-5/2.
20.) What number should be added to (/ + /) to get 1?
ANSWER:
Let, the number is x.
(/ + /) + x = 1
X = 1 – (/ + /)
X = 1 – 5/6
X = 1/6
The number is1/6.
21.) What number should be added to -1 so as to get /?
ANSWER:
Let, the number is x.
-1 + x = /
X = / + 1
X = 12 / 7
The number is12 / 7.
22.) The product of two rational numbers is − /. If one of the them is – /, find the other.
ANSWER:
Given that, the product of two rational numbers is − /.
One of the them is – /.
Let, the other is y.
– / x y = − /.
y =− x 3 / -4 x 9
y = -48 / -36
y = 4/3
The other rational number is 4/3.
23.) What number should be multiplied by – / to obtain /?
ANSWER:
Let, the number is y.
– / x y = /
Y = 1 x 39 / 78 x -8
Y = 1/-16
The number is1/-16.
24.) Find three rational numbers between / and /.
ANSWER:
We have to find three rational numbers between / and /.
By adding,
/ + / = 5 / 7
/ + 5 / 7 = 7 / 10
/ + 7 / 10 = 9/13
25.) Find five rational numbers between / and /.
ANSWER:
We have to find five rational numbers between / and /
Here, we make denominator 60.
x 15 / x 15 = 15 / 60
x 20 / x 20 = 20 / 60
Rational numbers between / and / are 16/60, 17/60, 18/60, 19/60.
26.) The product of two rational numbers is – /. If one of them is /, then find the other.
ANSWER:
Given that, the product of two rational numbers is – /.
One of the them is /
Let, the other is y.
/ x y = – /.
y =– x 27 / x 14
y = -2 / 3
The other number is-2 / 3.
27.) Find the product of additive inverse and multiplicative inverse of – /.
ANSWER:
We find additive inverse and multiplicative inverse of – /.
Additive inverse– / = 1/2
Multiplicative inverse of – / = -2
The product of additive inverse and multiplicative inverse of – /
= 1/2 x -2 = -1
The product of additive inverse and multiplicative inverse of – / is -1.
28.) Find the value of : / ÷ = − /
ANSWER:
/ ÷ = − /
/ x1/ = − /
1/ =− / x 8/9
1/ = -24 / 18
1/ = -4/3
X = -3 / 4
29.) Find the value of : (−) ÷ = − /.
ANSWER:
(−) ÷ = − /.
(−) x1/ =− /.
1/ =− / x 1/ (-12)
1/ = 1/10
X = 10
30.) Divide the sum of / and – / by their difference.
ANSWER:
/ +(– /) / / -(– /)
54 – 7 / 15 / 54 + 7 / 15
/ + (– /) / / – (– /) = 47 / 61
31.) After reading / of a book, 20 pages are left. How many pages are there in the book?
ANSWER:
Let, the pages of books is x.
We form equation.
2x / 3 + 20 = x
2x + 60 = 3x
3x – 2x = 60
X = 60
But, x is pages of books.
The pages of books is 60.
32.) Amit has Rs.1400 with him. He spent / of his money on notebooks and / of his money on stationery. How much money is left with him?
ANSWER:
Given that,
Amit has Rs.1400.
He spent / of his money on notebooks and / of his money on stationery.
1/2 + 1/4 = 3/4.
3/4th of 1400 = ¾ x 1400 =Rs.1050
Money is left with him = Rs.1400 – Rs.1050
Money is left with him = Rs.350
33.) One litre of petrol costs Rs.175. What is the cost of (/) litres of petrol?
ANSWER:
Given that,
One litre of petrol costs Rs.175.
We have find cost of (/) litres of petrol
(/) litres = 16 / 5 litres.
Rs.175 x 16 / 5 litres
= Rs.35 x 16
= Rs.560
Cost of (/) litres of petrol is Rs.560
34.) If 6 shirts of equal sizes can be made out of 15 meter of cloth, how much cloth is needed for making one shirt?
ANSWER:
Given that,
6 shirts of equal sizes can be made out of 15 meter of cloth.
We have to find cloth is needed for making one shirt.
Cloth is needed for making one shirt = 15 meter of cloth / 6 shirts of equal sizes
Cloth is needed for making one shirt = 5 / 2 metre.
Cloth is needed for making one shirt = 2 (1/2) metre.
35.) (/) of long rope is cut into 11 equal pieces. What is the length of each piece?
ANSWER:
Given that,
(/) of long rope is cut into 11 equal pieces.
We have to findthe length of each piece.
The length of each piece = (/) / 11
The length of each piece = ½ m = 0.5 m
36.) The product of two fractions is (/). If one of the fraction is /, find the other.
ANSWER:
Given that, product of two fractions is (/) = 48 / 5.
One of the fraction is /.
Let, other fraction is y.
/ x y = 48/5
y =48 x 7 /5 x 48
y = 7/5. = 1 (2/5)
Other fraction is7/5 = 1 (2/5)
37.) At a football match / of the spectators were in covered place while remaining 12000 were in open. Find the total number of spectators.
ANSWER:
Given that,
At a football match / of the spectators were in covered place while remaining 12000 were in open.
We have to findthe total number of spectators.
Let, the total number of spectators is x.
x/ + 12000 = x
3x + 84000 = 7x
7x – 3x = 84000
4x = 84000
X = 84000 / 4
X = 21000
The total number of spectators is21000.
38.) A drum full of sugar weighs (/) kilogram. If the empty drum weighs / kilogram, find the weight of sugar.
ANSWER:
Given that,
A drum full of sugar weighs (/) kilogram = 152/5 kg.
The empty drum weighs / kilogram.
We have to find the weight of sugar.
The weight of sugar = A drum full of sugar – The empty drum
The weight of sugar = 152/5 kg – / kilogram.
The weight of sugar = 80 / 5 kg.
The weight of sugar = 16 kg.
39.) An aeroplane covers 780 kilometers in an hour. How much distance will it cover in (/) hours?
ANSWER:
Given that,
An aeroplane covers 780 kilometers in an hour.
We have to finddistance will it cover in (/) hours = 5/2 hours.
Distance will it cover in (/) hours = 780 kilometers x 5/2 hours.
Distance will it cover in (/) hours = 1950 kilometers.
40.) In a school, / of the students are girls. If there are 240 boys, find the number of girls in the school.
ANSWER:
Given that,
/ of the students are girls.
There are 240 boys.
We have to findthe number of girls in the school
From / = 8 is total number of students. And 5 is number of girls.
Number of boys are 3/8 which is 240.
1 part is 80.
5 part is 80 x 5 = 400 girls.
the number of girls in the school is 400.