ICSE

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.6

Question 1.
In a bag, there are 20 kg of fruits. If 7\(\frac { 1 }{ 6 }\) kg of these fruits be oranges and 8\(\frac { 2 }{ 3 }\) kg of thee are apples and rest are grapes. Find the mass of the grapes in the bag.
Solution:

Question 2.
The population of a city is 6,63,432. If \(\frac { 1 }{ 2 }\) of the population are adult males and \(\frac { 1 }{ 3 }\) of the population are adult females, then find the number of children in the city.
Solution:

Question 3.
In an election of housing society, there are 30 voters. Each of them gives the vote. Three persons X, Y and Z are standing for the post of Secretary. If Mr X got \(\frac { 2 }{ 5 }\) of the total votes and Mr Z got \(\frac { 1 }{ 3 }\) of the total votes, then find the number of votes which Mr Y got.
Solution:

Question 4.
A person earns ₹ 100 in a day. If he spent ₹ 14\(\frac { 2 }{ 7 }\) on food and ₹ 30\(\frac { 2 }{ 3 }\) on petrol. How much did he save on that day?
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Question 5.
In an examination, 400 students appeared. If \(\frac { 2 }{ 3 }\) of the boys and all 130 girls passed in the examination, then find how many boys failed in an examination?
Solution:

Question 6.
A car is moving at the speed of 40\(\frac { 2 }{ 3 }\) km/h. Find how much distance will it cover in \(\frac { 9 }{ 10 }\) hrs?
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Question 7.
Find the area of a square lawn whose one side is 5\(\frac { 7 }{ 9 }\) m long.
Solution:

Question 8.
Perimeter of a rectangle is 15\(\frac { 3 }{ 7 }\) m. If the length is 4\(\frac { 2 }{ 7 }\) m, find its breadth.
Solution:

Question 9.
Rahul had a rope of 325\(\frac { 4 }{ 5 }\) m long. He cut off a 150\(\frac { 3 }{ 5 }\) m long piece, then he divided the rest of the rope into 3 parts of equal length. Find the length of each part.
Solution:

Question 10.
If 3\(\frac { 1 }{ 2 }\) litre of petrol costs ₹ 270\(\frac { 3 }{ 8 }\), then find the cost of 4 litre of petrol.
Solution:

Question 11.
Ramesh earns ₹ 40,000 per month. He spends \(\frac { 3 }{ 8 }\) of the income on food, \(\frac { 1 }{ 5 }\) of the remaining on LIC premium and then \(\frac { 1 }{ 2 }\) of the remaining on other expenses. Find how much money is left with him?
Solution:

Question 12.
A, B, C, D and E went to a restaurant for dinner. A paid \(\frac { 1 }{ 2 }\) of the bill, B paid \(\frac { 1 }{ 5 }\) of the bill and rest of the bill was shared equally by C, D and E. What fraction of the bill was paid by each?
Solution:

Question 13.
\(\frac { 2 }{ 5 }\) of total number of students of a school come by car while \(\frac { 1 }{ 4 }\) of students come by bus to school. All the other students walk to school of which \(\frac { 1 }{ 3 }\) walk on their own and the rest are escorted by their parents. If 224 students come to school walking on their own, how many students study in the school?
Solution:

Question 14.
A mother and her two sons got a room constructed for ₹ 60,000. The elder son contributes \(\frac { 3 }{ 8 }\) of his mother’s contribution while the younger son contributes \(\frac { 1 }{ 2 }\) of his mother’s share. How much do the three contribute individually?
Solution:

Question 15.
In a class of 56 students, the number of boys is \(\frac { 2 }{ 5 }\) th of the number of girls. Find the number of boys and girls.
Solution:

Question 16.
A man donated \(\frac { 1 }{ 10 }\) of his money to a school, \(\frac { 1 }{ 6 }\) th of the remaining to a church and the remaining money he distributed equally among his three children. If each child gets ₹ 50000, how much money did the man originally have?
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Question 17.
If \(\frac { 1 }{ 4 }\) of a number is added to \(\frac { 1 }{ 3 }\) of that number, the result is 15 greater than half of that number. Find the number.
Solution:

Question 18.
A student was asked to multiply a given number by \(\frac { 4 }{ 5 }\). By mistake, he divided the given number by \(\frac { 4 }{ 5 }\). His answer was 36 more than the correct answer. What was the given number?
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.5

Question 1.
Represent the following rational numbers on the number line:
(i) \(\frac { 11 }{ 4 }\)
(ii) 4\(\frac { 3 }{ 5 }\)
(iii) \(\frac { -9 }{ 7 }\)
(iv) \(\frac { -2 }{ -5 }\)
Solution:

Question 2.
Write the rational numbers for each point labelled with a letter:

Solution:

Question 3.
Find twenty rational numbers between \(\frac { -3 }{ 7 }\) and \(\frac { 2 }{ 3 }\)
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Question 4.
Find six rational numbers between \(\frac { -1 }{ 2 }\) and \(\frac { 5 }{ 4 }\)
Solution:

Question 5.
Find three rational numbers between -2 and -1.
Solution:

Question 6.
Write ten rational numbers which are greater than 0.
Solution:

Question 7.
Write five rational numbers which are smaller than -4.
Solution:

Question 8.
Identify the rational number which is different from the other three. Explain your reasoning

Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.4

Question 1.
Find the value of the following:

Solution:

Question 2.
State whether the following statements are true or false:
(i) \(\frac { -9 }{ 13 }\) ÷ \(\frac { 2 }{ 7 }\) is a rational number.

Solution:

Question 3.
The product of two rational numbers is \(\frac { -11 }{ 12 }\). If one of them is 2\(\frac { 4 }{ 9 }\), find the other.
Solution:

Question 4.
By what rational number should \(\frac { -7 }{ 12 }\) be multiplied to get the product as \(\frac { 5 }{ 14 }\) ?
Solution:

Question 5.
By what rational number should -3 is divided to get \(\frac { -9 }{ 13 }\)?
Solution:

Question 6.
Divide the sum of \(\frac { -13 }{ 8 }\) and \(\frac { 5 }{ 12 }\) by their difference.
Solution:

Question 7.
Divide the sum of \(\frac { 8 }{ 3 }\) and \(\frac { 4 }{ 7 }\) by the product of \(\frac { -3 }{ 7 }\) and \(\frac { 14 }{ 9 }\).
Solution:

Question 8.
If p = \(\frac { -3 }{ 2 }\), q = \(\frac { 4 }{ 5 }\) and r = \(\frac { -7 }{ 12 }\), then verify that (p ÷ q) ÷ r ≠ p ÷ (q ÷ r).
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.3

Question 1.
Multiply and express the result in the lowest form:

Solution:

Question 2.
Verify commutative property of multiplication for the following pairs of rational numbers:
(i) \(\frac { 4 }{ 5 }\) and \(\frac { -7 }{ 8 }\)
(ii) 13\(\frac { 1 }{ 3 }\) and 1\(\frac { 1 }{ 8 }\)
(iii) \(\frac { -7 }{ -20 }\) and \(\frac { 5 }{ -14 }\)
Solution:

Question 3.
Verify the following and name the property also:

Solution:

Question 4.
Find the multiplication inverse of the following:

Solution:

Question 5.
Using the appropriate properties of operations of rational numbers, evaluate the following:

Solution:

Question 6.
If p = \(\frac { -8 }{ 27 }\), q = \(\frac { 3 }{ 4 }\) and r = \(\frac { -12 }{ 15 }\), then verify that
(i) p × (q × r) = (p × q) × r
(ii) p × (q – r) = p × q – p × r
Solution:

Question 7.
Fill in the following blanks:

(ix) The reciprocal of 0 is …….
(x) The numbers ……… and ……. are their own reciprocals.
(xi) If y be the reciprocal of x, then the reciprocal of y² in terms of x will be ………
(xii) The product of a non-zero rational number and its reciprocal is ………
(xiii) The reciprocal of a negative rational number is ………..
Solution:

Question 8.
If \(\frac { 4 }{ 5 }\) the multiplicative inverse of -1\(\frac { 1 }{ 4 }\) ? Why or why not?
Solution:

Question 9.
Using distributivity, find

Solution:

Question 10.
Find the sum of additive inverse and multiplicative inverse of 9.
Solution:

Question 11.
Find the product of additive inverse and multiplicative inverse of \(\frac { -3 }{ 7 }\)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Ex 1.2

Question 1.
Subtract:

Solution:

Question 2.
Sum of two rational numbers is \(\frac { 3 }{ 5 }\). If one of them is \(\frac { -2 }{ 7 }\), find the other.
Solution:

Question 3.
What rational number should be added to \(\frac { -5 }{ 11 }\) to get \(\frac { -7 }{ 8 }\)?
Solution:

Question 4.
What rational number should be subtracted from -4\(\frac { 3 }{ 5 }\) to get -3\(\frac { 1 }{ 2 }\) ?
Solution:

Question 5.
Subtract the sum of \(\frac { -5 }{ 7 }\) and \(\frac { -8 }{ 3 }\) from the sum of \(\frac { 5 }{ 2 }\) and \(\frac { -11 }{ 12 }\).
Solution:

Question 6.
If x = \(\frac { -4 }{ 7 }\) and y = \(\frac { 2 }{ 5 }\), then verify that x – y ≠ y – x.
Solution:

Question 7.
If x = \(\frac { 4 }{ 9 }\), y = \(\frac { -7 }{ 12 }\) and z = \(\frac { -2 }{ 3 }\), then verify that x – (y – z) ≠ (x – y) – z
Solution:

Question 8.
Which of the following statement is true/fasle?
(i) \(\frac { 2 }{ 3 } -\frac { 4 }{ 5 }\) is not a rational number.
(ii) \(\frac { -5 }{ 7 }\) is the additive inverse of \(\frac { 5 }{ 7 }\).
(iii) 0 is the additive inverse of its own.
(iv) Commutative property holds for subtraction of rational numbers.
(v) Associative property does not hold for subtraction of rational numbers.
(vi) 0 is the identity element for subtraction of rational numbers.
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths