## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 2 Exponents and Powers Ex 2.2

Question 1.
Express the following numbers in standard form:
(i) 0.0000000000085
(ii) 0.000000000000942
(iii) 6020000000000000
(iv) 0.00000000837
Solution:

Question 2.
Express the following numbers in the usual form:
(i) 3.02 × 10-6
(ii) 1-007 × 1011
(iii) 5.375 × 1014
(iv) 7.579 × 10-14
Solution:

Question 3.
Express the number appearing in the following statements in standard form:
(i) The mass of a proton is 0.000000000000000000000001673 gram.
(ii) The thickness of a piece of paper is 0.0016 cm.
(iii) The diameter of a wire on a computer chip is 0.000003 m.
(iv) A helium atom has a diameter of $$\frac { 22 }{ 100000000000 }$$ m
(v) Mass of a molecule of hydrogen gas is about 0.00000000000000000000334 tons.
(vi) The human body has 1 trillion cells which vary in shapes and sizes.
(vii) The distance from the Earth of the Sun is 149,600,000,000 m.
(viii) The speed of light is 300,000,000 m/sec.
(ix) Mass of the Earth is 5,970,000,000,000,000,000,000,000 kg.
(x) Express 3 years in seconds.
(xi) Express 7 hectares in cm2.
(xii) A sugar factory has annual sales of 3 billion 720 million kilograms of sugar.
Solution:

Question 4.
Compare the following:
(i) Size of a plant cell to the thickness of a piece of paper.
(ii) Size of a plant cell to the diameter of a wire on a computer chip.
(iii) The thickness of a piece of paper to the diameter of a wire on a computer chip.
Given size of plant cell = 0.00001275 m
Thickness of a piece of paper = 0.0016 cm
Diameter of a wire on a computer chip = 0.000003 m
Solution:

Question 5.
The number of red blood cells per cubic millimetre of blood is approximately 5.5 million. If the average body contains 5 litres of blood, what is the total number of red cell in the body? (1 litre = 1,00,000 mm3)
Solution:

Question 6.
Mass of Mars is 6.42 × 1029 kg and the mass of the sun is 1.99 × 1030 kg. What is the total mass?
Solution:

Question 7.
A particular star is at a distance of about 8.1 × 1013 km from the Earth. Assuming that the light travels at 3 × 108 m/sec, find how long does light take from that star to reach the Earth.
Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 2 Exponents and Powers Ex 2.1

Question 1.
Evaluate:

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Find the multiplicative inverse of the following:

Solution:

Question 4.
(i) Express 16-2 as a power with base 2.
(ii) Express 125-4 as a power with base 5.
Solution:

Question 5.
Write the following numbers in expanded form using exponents:
(i) 2789.453
(ii) 3007.805
Solution:

Question 6.
Simplify and write in exponential form with positive exponent:

Solution:

Question 7.
Simplify and write the following in exponential form:

Solution:

Question 8.
Simplify and write in exponential form with negative exponent:

Solution:

Question 9.
Simplify:

Solution:

Question 10.
By what number should $$\left( \frac { 3 }{ -2 } \right) ^{ -3 }$$ be divided to get $$\left( \frac { 2 }{ 3 } \right) ^{ 2 }$$ ?
Solution:

Question 11.
Find the value of m for which 9m ÷ 3-2 = 94.
Solution:

Question 12.

Solution:

Question 13.

Solution:

Question 14.

Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Check Your Progress

Question 1.
Evaluate the following:

Solution:

Question 2.
What number should be added to $$\frac { -4 }{ 11 }$$ to get $$\frac { -3 }{ 8 }$$?
Solution:

Question 3.
What rational number should be subtracted from the sum of $$\frac { 3 }{ 14 }$$ and $$\frac { -4 }{ 7 }$$ to get $$\frac { 13 }{ 21 }$$?
Solution:

Question 4.
If the product of two rational numbers is $$\frac { 25 }{ 42 }$$ and one of them -2$$\frac { 6 }{ 7 }$$, find the other.
Solution:

Question 5.
Divide the sum of $$\frac { 4 }{ 13 }$$ and $$\frac { -3 }{ 2 }$$ by their product.
Solution:

Question 6.
Using the appropriate properties of operations of rational numbers, evaluate the following:

Solution:

Question 7.
Find the additive inverse of the following:
(i) -13$$\frac { 7 }{ 8 }$$
(ii) 4$$\frac { 3 }{ 6 }$$
Solution:

Question 8.
Find the multiplicative inverse of the following:
(i) $$\frac { -23 }{ 46 }$$
(ii) 0
Solution:

Question 9.
Represent the following rational numbers on the number line:
(i) $$\frac { -3 }{ 11 }$$
(ii) $$\frac { 5 }{ 17 }$$
Solution:

Question 10.
Insert five rational numbers between $$\frac { -3 }{ 7 }$$ and $$\frac { 2 }{ 5 }$$
Solution:

Question 11.
If p = $$\frac { -4 }{ 9 }$$ , q = $$\frac { 2 }{ 3 }$$ and r = $$\frac { -8 }{ 11 }$$, then verily the foflowing:
(i) p + (q + r) = (p + q) + r
(ii) p × q = q × p
(iii) p × (q + r) = p × q + p × r
(iv) (p + q) ÷ r = p ÷ r + q ÷ r.
Solution:

Question 12.
A wedding cake weighed 8 kg. If $$\frac { 2 }{ 5 }$$ th of its weight was flour, $$\frac { 5 }{ 16 }$$ th was sugar, $$\frac { 1 }{ 4 }$$ thwas cream and the rest were nuts, find the weight of nuts.
Solution:

## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 1 Rational Numbers Objective Type Questions

Mental Maths

Question 1.
Fill in the blanks:
(i) The product of two rational numbers is a ……….
(ii) Subtraction of rational numbers is …….. commutative.
(iii) The rational number $$\frac { -7 }{ 4 }$$ lies ……. of zero on the number line.
(iv) Division of rational numbers is ……… associative.
(v) $$\frac { p }{ q }$$ ÷ 0 is ……..
(vi) Negative of a rational number is called its ………
(vii) Multiplicative identity of rational numbers is ……….
(viii) Multiplication of rational numbers is ……. over addition.
(ix) Division of a rational number by a non-zero rational number is a ………..
(x) The rational number which is additive inverse of itself is …………
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) $$\frac { -5 }{ 9 }$$ is the additive inverse of $$\frac { 5 }{ 9 }$$.
(ii) Every integer is a rational number.
(iii) Zero has its multiplicative inverse.
(iv) Every rational number is an integer.
(v) Division of two rational numbers is alwasy closed.
(vi) Non-terminating, non-recurring decimal numbers are rational numbers.
(vii) 0 is the multiplicative identity of rational numbers.
(viii) Non-terminating recurring decimal numbers are not rational numbers.
(ix) Subtraction of two rational numbers is not associative.
(x) Reciprocal of 1 is 1.
(xi) The multiplicative inverse is also called a reciprocal.
(xii) Between two different rational numbers, there are infinitely many number of rational numbers.
Solution:

Multiple Choice Questions

Choose the correct answer from the given four options (3 to 18):
Question 3.
Additive inverse of $$\frac { -2 }{ -5 }$$ is
(a) $$\frac { 2 }{ 5 }$$
(b) $$\frac { 5 }{ 2 }$$
(c) $$\frac { 2 }{ -5 }$$
(d) $$\frac { 5 }{ -2 }$$
Solution:

Question 4.
Multiplicative inverse of $$\frac { -3 }{ 7 }$$ is
(a) $$\frac { 7 }{ 3 }$$
(b) $$\frac { -7 }{ 3 }$$
(c) $$\frac { 3 }{ 7 }$$
(d) None of these
Solution:

Question 5.
Sum of a rational number and its additive inverse is
(a) 1
(b) 0
(c) -1
(d) None of these
Solution:

Question 6.
Rational numbers are not closed under
(b) subtraction
(c) multiplication
(d) division
Solution:

Question 7.
0 ÷ $$\frac { 2 }{ 3 }$$ is equal to
(a) $$\frac { 2 }{ 3 }$$
(b) $$\frac { 3 }{ 2 }$$
(c) 0
(d) not defined
Solution:

Question 8.
$$\frac { 2 }{ 3 }$$ ÷ 0 is equal to
(a) $$\frac { 2 }{ 3 }$$
(b) $$\frac { 3 }{ 2 }$$
(c) 0
(d) not defined
Solution:

Question 9.
$$\frac { p }{ q } +\left( \frac { r }{ s } +\frac { t }{ u } \right) =\left( \frac { p }{ q } +\frac { r }{ s } \right) +\frac { t }{ u }$$ is called
(a) commutative property
(b) associative property
(c) distributive property
(d) None of these
Solution:

Question 10.
Multiplication of a non-zero rational number and its reciprocal is
(a) 0
(b) 1
(c) -1
(d) None of these
Solution:

Question 11.
Product of rational number $$\frac { -2 }{ 5 }$$ and its additive inverse is
(a) 0
(b) 1
(c) $$\frac { -4 }{ 25 }$$
(d) $$\frac { -5 }{ 2 }$$
Solution:

Question 12.
Sum of rational number $$\frac { 4 }{ 7 }$$ and its reciprocal is
(a) $$\frac { 28 }{ 65 }$$
(b) $$\frac { 65 }{ 28 }$$
(c) $$\frac { -28 }{ 65 }$$
(d) $$\frac { -65 }{ 28 }$$
Solution:

Question 13.
Sum of two rational numbers is 0, if one ofthem is $$\frac { -4 }{ 5 }$$, then other is
(a) $$\frac { 5 }{ 4 }$$
(b) $$\frac { 4}{ 5 }$$
(c) $$\frac { -5 }{ 4 }$$
(d) $$\frac { -4 }{ 5 }$$
Solution:

Question 14.
Product of two rational numbers is 1, if one of them is $$\frac { 10 }{ 3 }$$, then other is
(a) $$\frac { 3 }{ 10 }$$
(b) $$\frac { -3}{ 10 }$$
(c) $$\frac { 10 }{ 3 }$$
(d) None of these
Solution:

Question 15.
Rational number represented by the point P on the number line is

(a) $$\frac { -5 }{ 7 }$$
(b) $$\frac { -3}{ 7 }$$
(c) $$\frac { -5 }{ 8 }$$
(d) $$\frac { -4 }{ 8 }$$
Solution:

Question 16.
What should be subtracted from $$\frac { -5 }{ 3 }$$ to get $$\frac { -2 }{ 7 }$$?
(a) $$\frac { 29 }{ 21 }$$
(b) $$\frac { -21}{ 29 }$$
(c) $$\frac { -29 }{ 21 }$$
(d) $$\frac { 21 }{ 29 }$$
Solution:

Question 17.
Reciprocal of a negative number is
(a) positive
(b) negative
(c) can not say
(d) does not exist
Solution:

Question 18.
Which of the following statement is true?

Solution:

Value Based Questions

Question 1.
Ram donated $$\frac { 1 }{ 10 }$$ of his salary to an orphanage, $$\frac { 1 }{ 3 }$$ of his salary spent on food, $$\frac { 1 }{ 4 }$$ of salary on rent and electricity and $$\frac { 1 }{ 20 }$$ of his salary on telephone. This month he donated ₹ 5000 in Prime Minister relief fund for Uttarakhand victims. He was left with ₹ 3000 with him, find his monthly salary. Should we donate the money for needy people? What values are being promoted?
Solution:

Question 2.
In an Examination $$\frac { 1 }{ 3 }$$ of the total students used unfair means and out of which $$\frac { 1 }{ 4 }$$ caught red handed while cheating. If 5 students caught red handed then find the total number of students appeared in exam.
Why should we not use unfair means in an examination?
What values are being promoted?
Solution:

Higher Order Thinking Skills (HOTS)

Question 1.
Area ol a square is 4 sq. in more than $$\frac { 2 }{ 3 }$$ of the area of a rectangle. If the area of square is 64 sq. m, then find the dimensions of the rectangle, given that breadth is $$\frac { 2 }{ 5 }$$ of length.
Solution:

Question 2.
Rahul can do $$\frac { 2 }{ 7 }$$ of a certain work in 6 days while Suresh can do $$\frac { 3 }{ 5 }$$ of the same work in 9 days. They started work together but after 7 days Rahul left the work. Find in how many days Suresh can complete the remaining work?
Solution:

## 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?
Solution:

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?
Solution:

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?
Solution:

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 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 $$\frac { 2 }{ 3 }$$
Solution:

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 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 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 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 Chapter 1 Rational Numbers Ex 1.1

Question 1.

Solution:

Question 2.
Simplify:

Solution:

Question 3.
Verify commutative property of addition for the following pairs of rational numbers:

Solution:

Question 4.
Find the additive inverse of the following rational numbers:
(i) $$\frac { 2 }{ -3 }$$
(ii) $$\frac { -7 }{ -12 }$$
Solution:

Question 5.
Verify that -(-x) = x for
(i) x = $$\frac { 10 }{ 13 }$$
(ii) x = $$\frac { -15 }{ 17 }$$
Solution:

Question 6.
Using appropriate properties of addition, find the following:

Solution:

Question 7.
Fill in the following blanks:

Solution:

Question 8.
If a = $$\frac { -11 }{ 27 }$$, b = $$\frac { 4 }{ 9 }$$ and c = $$\frac { -5 }{ 18 }$$, then verify that a + (b + c) = (a + b) + c.
Solution: