# NCERT solutions for Mathematics Exemplar Class 8 chapter 1 - Rational Numbers [Latest edition]

## Chapter 1: Rational Numbers

Exercise
Exercise [Pages 8 - 27]

### NCERT solutions for Mathematics Exemplar Class 8 Chapter 1 Rational Numbers Exercise [Pages 8 - 27]

#### Choose the correct alternative:

Exercise | Q 1 | Page 8

A number which can be expressed as p/q where p and q are integers and q ≠ 0 is ______.

• Natural number

• Whole number

• Integer

• Rational number

Exercise | Q 2 | Page 9

A number of the form p/q is said to be a rational number if ______.

• p and q are integers

• p and q are integers and q ≠ 0

• p and q are integers and p ≠ 0

• p and q are integers and p ≠ 0 also q ≠ 0

Exercise | Q 3 | Page 9

The numerical expression 3/8 + ((-5))/7 = (-19)/56 shows that ______.

• Rational numbers are closed under addition

• Rational numbers are not closed under addition

• Rational numbers are closed under multiplication

• Addition of rational numbers is not commutative

Exercise | Q 4 | Page 9

Which of the following is not true?

• Rational numbers are closed under addition

• Rational numbers are closed under subtraction

• Rational numbers are closed under multiplication

• Rational numbers are closed under division

Exercise | Q 5 | Page 9

- 3/8 + 1/7 = 1/7 + ((-3)/8) is an example to show that ______.

• Addition of rational numbers is commutative

• Rational numbers are closed under addition

• Addition of rational number is associative

• Rational numbers are distributive under addition

Exercise | Q 6 | Page 9

Which of the following expressions shows that rational numbers are associative under multiplication?

• 2/3 xx ((-6)/7 xx 3/5) = (2/3 xx (-6)/7) xx 3/5

• 2/3 xx ((-6)/7 xx 3/5) = 2/3 xx (3/5 xx (-6)/7)

• 2/3 xx ((-6)/7 xx 3/5) = (3/5 xx 2/3) xx (-6)/7

• (2/3 xx (-6)/7) xx 3/5 = ((-6)/7 xx 2/3) xx 3/5

Exercise | Q 7 | Page 10

Zero (0) is ______.

• The identity for addition of rational numbers

• The identity for subtraction of rational numbers

• The identity for multiplication of rational numbers

• The identity for division of rational numbers

Exercise | Q 8 | Page 10

One (1) is ______.

• The identity for addition of rational numbers

• The identity for subtraction of rational numbers

• The identity for multiplication of rational numbers

• The identity for division of rational numbers

Exercise | Q 9 | Page 10

The additive inverse of (-7)/19 is ______.

• (-7)/19

• 7/19

• 19/7

• (-19)/7

Exercise | Q 10 | Page 10

Multiplicative inverse of a negative rational number is ______.

• A positive rational number

• A negative rational number

• 0

• 1

Exercise | Q 11 | Page 10

If x + 0 = 0 + x = x, which is rational number, then 0 is called ______.

• Identity for addition of rational numbers

• Multiplicative inverse of x

• Reciprocal of x

Exercise | Q 12 | Page 10

To get the product 1, we should multiply 8/21 by ______.

• 8/21

• (-8)/21

• 21/8

• (-21)/8

Exercise | Q 13 | Page 11

– (–x) is same as ______.

• – x

• x

• 1/x

• (-1)/x

Exercise | Q 14 | Page 11

The multiplicative inverse of - 1/7 is ______.

• 8/7

• (-8)/7

• 7/8

• 7/(-8)

Exercise | Q 15 | Page 11

If x be any rational number then x + 0 is equal to ______.

• x

• 0

• – x

• Not defined

Exercise | Q 16 | Page 11

The reciprocal of 1 is ______.

• 1

• –1

• 0

• Not defined

Exercise | Q 17 | Page 11

The reciprocal of –1 is ______.

• 1

• –1

• 0

• Not defined

Exercise | Q 18 | Page 11

The reciprocal of 0 is ______.

• 1

• –1

• 0

• Not defined

Exercise | Q 19 | Page 11

The reciprocal of any rational number p/q, where p and q are integers and q ≠ 0, is ______.

• p/q

• 1

• 0

• q/p

Exercise | Q 20 | Page 11

If y be the reciprocal of rational number x, then the reciprocal of y will be ______.

• x

• y

• x/y

• y/x

Exercise | Q 21 | Page 11

The reciprocal of (-3)/8 xx ((-7)/13) is ______.

• 104/21

• (-104)/21

• 21/104

• (-21)/104

Exercise | Q 22 | Page 11

Which of the following is an example of distributive property of multiplication over addition for rational numbers?

• -1/4 xx {2/3 + ((-4)/7)} = [-1/4 xx 2/3] + [-1/4 xx ((-4)/7)]

• -1/4 xx {2/3 + ((-4)/7)} = [1/4 xx 2/3] - ((-4)/7)

• -1/4 xx {2/3 + ((-4)/7)} = 2/3 + (-1/4) xx (-4)/7

• -1/4 xx {2/3 + ((-4)/7)} = {2/3 + ((-4)/7)} - 1/4

Exercise | Q 23 | Page 12

Between two given rational numbers, we can find ______.

• One and only one rational number

• Only two rational numbers

• Only ten rational numbers

• Infinitely many rational numbers

Exercise | Q 24 | Page 13

(x + y)/2 is a rational number ______.

• Between x and y

• Less than x and y both

• Less than x and y both

• Less than x but greater than y

Exercise | Q 25 | Page 13

Which of the following statements is always true?

• (x - y)/2 is a rational number between x and y

• (x + y)/2 is a rational number between x and y

• (x xx y)/2 is a rational number between x and y

• (x ÷ y)/2 is a rational number between x and y

#### Fill in the blank:

Exercise | Q 26 | Page 13

The equivalent of 5/7, whose numerator is 45 is ______.

Exercise | Q 27 | Page 13

The equivalent rational number of 7/9, whose denominator is 45 is ______.

Exercise | Q 28 | Page 13

Between the numbers 15/20 and 35/40, the greater number is ______.

Exercise | Q 29 | Page 13

The reciprocal of a positive rational number is ______.

Exercise | Q 30 | Page 13

The reciprocal of a negative rational number is ______.

Exercise | Q 31 | Page 13

Zero has ______ reciprocal.

Exercise | Q 32 | Page 13

The numbers ______ and ______ are their own reciprocals

Exercise | Q 33 | Page 13

If y be the reciprocal of x, then the reciprocal of y2 in terms of x will be ______.

Exercise | Q 34 | Page 13

The reciprocal of 2/5 xx ((-4)/9) is ______.

Exercise | Q 35 | Page 13

(213 xx 657)^-1 = 213^-1 xx ______.

Exercise | Q 36 | Page 13

The negative of 1 is ______.

Exercise | Q 37 | Page 15

For rational numbers a/b, c/d and e/f we have a/b xx (c/d + e/f) = ______ + ______.

Exercise | Q 38 | Page 15

(-5)/7 is ______ than –3.

Exercise | Q 39 | Page 15

There are ______ rational numbers between any two rational numbers.

Exercise | Q 40 | Page 15

The rational numbers 1/3 and (-1)/3are on the ______ sides of zero on the number line.

Exercise | Q 41 | Page 15

The negative of a negative rational number is always a ______ rational number.

Exercise | Q 42 | Page 15

Rational numbers can be added or multiplied in any ______.

Exercise | Q 43 | Page 15

The reciprocal of (-5)/7 is ______.

Exercise | Q 44 | Page 15

The multiplicative inverse of 4/3 is ______.

Exercise | Q 45 | Page 15

The rational number 10.11 in the from p/q is ______.

Exercise | Q 46 | Page 15

1/5 xx [2/7 + 3/8] = [1/5 xx 2/7] = ______.

Exercise | Q 47 | Page 15

The two rational numbers lying between –2 and –5 with denominator as 1 are ______ and ______.

#### State whether the following statement is True or False:

Exercise | Q 48 | Page 15

If x/y is a rational number, then y is always a whole number.

• True

• False

Exercise | Q 49 | Page 15

If p/q is a rational number, then p cannot be equal to zero.

• True

• False

Exercise | Q 50 | Page 15

If r/s is a rational number, then s cannot be equal to zero.

• True

• False

Exercise | Q 51 | Page 15

5/6 lies between 2/3 and 1.

• True

• False

Exercise | Q 52 | Page 16

5/10 lies between 1/2 and 1.

• True

• False

Exercise | Q 53 | Page 16

(-7)/2 lies between –3 and –4.

• True

• False

Exercise | Q 54 | Page 16

9/6 lies between 1 and 2.

• True

• False

Exercise | Q 55 | Page 16

If a ≠ 0, the multiplicative inverse of a/b is b/a.

• True

• False

Exercise | Q 56 | Page 16

The multiplicative inverse of (-3)/5 is 5/3.

• True

• False

Exercise | Q 57 | Page 16

The additive inverse of 1/2 is –2.

• True

• False

Exercise | Q 58 | Page 16

If x/y is the additive inverse of c/d, then x/y + c/d = 0.

• True

• False

Exercise | Q 59 | Page 16

For every rational number x, x + 1 = x.

• True

• False

Exercise | Q 60 | Page 16

If x/y is the additive inverse of c/d, then x/y - c/d = 0

• True

• False

Exercise | Q 61 | Page 16

The reciprocal of a non-zero rational number q/p is the rational number q/p.

• True

• False

Exercise | Q 62 | Page 16

If x + y = 0, then –y is known as the negative of x, where x and y are rational numbers.

• True

• False

Exercise | Q 63 | Page 16

The negative of any rational number is the number itself.

• True

• False

Exercise | Q 64 | Page 16

The negative of 0 does not exist.

• True

• False

Exercise | Q 65 | Page 16

The negative of 1 is 1 itself.

• True

• False

Exercise | Q 66 | Page 16

For all rational numbers x and y, x – y = y – x.

• True

• False

Exercise | Q 67 | Page 16

For all rational numbers x and y, x × y = y × x.

• True

• False

Exercise | Q 68 | Page 17

For every rational number x, x × 0 = x.

• True

• False

Exercise | Q 69 | Page 17

For every rational numbers x, y and z, x + (y × z) = (x + y) × (x + z).

• True

• False

Exercise | Q 70 | Page 17

For all rational numbers a, b and c, a (b + c) = ab + bc.

• True

• False

Exercise | Q 71 | Page 17

1 is the only number which is its own reciprocal.

• True

• False

Exercise | Q 72 | Page 17

–1 is not the reciprocal of any rational number.

• True

• False

Exercise | Q 73 | Page 17

For any rational number x, x + (–1) = –x.

• True

• False

Exercise | Q 74 | Page 17

For rational numbers x and y, if x < y then x – y is a positive rational number.

• True

• False

Exercise | Q 75 | Page 17

If x and y are negative rational numbers, then so is x + y

• True

• False

Exercise | Q 76 | Page 17

Between any two rational numbers there are exactly ten rational numbers.

• True

• False

Exercise | Q 77 | Page 17

Rational numbers are closed under addition and multiplication but not under subtraction.

• True

• False

Exercise | Q 78 | Page 17

Subtraction of rational number is commutative.

• True

• False

Exercise | Q 79 | Page 17

3/4 is smaller than –2.

• True

• False

Exercise | Q 80 | Page 17

0 is a rational number.

• True

• False

Exercise | Q 81 | Page 17

All positive rational numbers lie between 0 and 1000.

• True

• False

Exercise | Q 82 | Page 17

The population of India in 2004 - 05 is a rational number.

• True

• False

Exercise | Q 83 | Page 17

There are countless rational numbers between 5/6 and 8/9.

• True

• False

Exercise | Q 84 | Page 17

The reciprocal of x–1 is 1/x.

• True

• False

Exercise | Q 85 | Page 17

The rational number 57/23 lies to the left of zero on the number line.

• True

• False

Exercise | Q 86 | Page 17

The rational number 7/(-4) lies to the right of zero on the number line.

• True

• False

Exercise | Q 87 | Page 17

The rational number (-8)/(-3) lies neither to the right nor to the left of zero on the number line.

• True

• False

Exercise | Q 88 | Page 18

The rational numbers 1/2and –1 are on the opposite sides of zero on the number line.

• True

• False

Exercise | Q 89 | Page 18

#### State whether the following statement is True or False:

Every fraction is a rational number.

• True

• False

Exercise | Q 90 | Page 18

Every integer is a rational number

• True

• False

Exercise | Q 91 | Page 18

The rational numbers can be represented on the number line.

• True

• False

Exercise | Q 92 | Page 18

The negative of a negative rational number is a positive rational number.

• True

• False

Exercise | Q 93 | Page 18

If x and y are two rational numbers such that x > y, then x – y is always a positive rational number.

• True

• False

Exercise | Q 94 | Page 18

0 is the smallest rational number.

• True

• False

Exercise | Q 95 | Page 18

Every whole number is an integer.

• True

• False

Exercise | Q 96 | Page 18

Every whole number is a rational number.

• True

• False

Exercise | Q 97 | Page 18

0 is whole number but it is not a rational number.

• True

• False

Exercise | Q 98 | Page 18

The rational numbers 1/2 and - 5/2 are on the opposite sides of 0 on the number line.

• True

• False

Exercise | Q 99 | Page 18

Rational numbers can be added (or multiplied) in any order (-4)/5 xx (-6)/5 = (-6)/5 xx (-4)/5

• True

• False

Exercise | Q 100 | Page 18

Solve the following: Select the rational numbers from the list which are also the integers.

9/4, 8/4, 7/4, 6/4, 9/3, 8/3, 7/3, 6/3, 5/2, 4/2, 3/1, 3/2, 1/1, 0/1, (-1)/1, (-2)/1, (-3)/2, (-4)/2, (-5)/2, (-6)/2

Exercise | Q 101 | Page 18

Select those which can be written as a rational number with denominator 4 in their lowest form:

7/8, 64/16, 36/(-12), (-16)/17, 5/4, 140/28

Exercise | Q 102.(a) | Page 19

Using suitable rearrangement and find the sum:

4/7 + ((-4)/9) + 3/7 + ((-13)/9)

Exercise | Q 102.(b) | Page 19

Using suitable rearrangement and find the sum:

-5 + 7/10 + 3/7 + (-3) + 5/14 + (-4)/5

Exercise | Q 103.(i) | Page 19

Verify – (– x) = x for x = 3/5

Exercise | Q 103.(ii) | Page 19

Verify – (– x) = x for x = (-7)/9

Exercise | Q 103.(iii) | Page 19

Verify – (– x) = x for x = 13/(-15)

Exercise | Q 104 | Page 19

Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

Exercise | Q 105.(a) | Page 19

Verify the property x + y = y + x of rational numbers by taking

x = 1/2, y = 1/2

Exercise | Q 105.(b) | Page 19

Verify the property x + y = y + x of rational numbers by taking

x = (-2)/3, y = (-5)/6

Exercise | Q 105.(c) | Page 19

Verify the property x × y = y × z of rational numbers by using

x = (-5)/7 and y = 14/15

Exercise | Q 105.(d) | Page 19

Verify the property x + y = y + x of rational numbers by taking

x = (-2)/5, y = (-9)/10

Exercise | Q 106.(a) | Page 19

Simplify the following by using suitable property. Also name the property.

[1/2 xx 1/4] + [1/2 xx 6]

Exercise | Q 106.(b) | Page 19

Simplify the following by using suitable property. Also name the property.

[1/5 xx 2/15] + [1/5 xx 2/5]

Exercise | Q 106.(c) | Page 19

Simplify the following by using suitable property. Also name the property.

(-3)/5 xx {3/7 + ((-5)/6)}

Exercise | Q 107 | Page 19

Tell which property allows you to compute 1/5 xx [5/6 xx 7/9] as [1/5 xx 5/6] xx 7/9

Exercise | Q 108.(a) | Page 1

Verify the property x × y = y × z of rational numbers by using

x = 7 and y = 1/2

Exercise | Q 108.(b) | Page 1

Verify the property x × y = y × z of rational numbers by using

x = 2/3 and y = 9/4

Exercise | Q 108.(c) | Page 19

Verify the property x × y = y × z of rational numbers by using

x = (-5)/7 and y = 14/15

Exercise | Q 108.(d) | Page 19

Verify the property x × y = y × z of rational numbers by using

x = (-3)/8 and y = (-4)/9

Exercise | Q 109.(a) | Page 19

Verify the property x × (y × z) = (x × y) × z of rational numbers by using and What is the name of this property?
x = 1, y = (-1)/2 and z = 1/4
and What is the name of this property?

Exercise | Q 109.(b) | Page 19

Verify the property x × (y × z) = (x × y) × z of rational numbers by using and What is the name of this property?
x = 2/3, y = (-3)/7 and z = 1/2
and What is the name of this property?

Exercise | Q 109.(c) | Page 19

Verify the property x × (y × z) = (x × y) × z of rational numbers by using
x = (-2)/7, y = (-5)/6 and z = 1/4
and What is the name of this property?

Exercise | Q 110.(a) | Page 20

Verify the property x × (y + z) = x × y + x × z of rational numbers by taking.

x = (-1)/2, y = 3/4, z = 1/4

Exercise | Q 110.(b) | Page 20

Verify the property x × (y + z) = x × y + x × z of rational numbers by taking.

x = (-1)/2, y = 2/3, z = 3/4

Exercise | Q 110.(c) | Page 20

Verify the property x × (y + z) = x × y + x × z of rational numbers by taking.

x = (-1)/2, y = 2/3, z = 3/4

Exercise | Q 110.(d) | Page 20

Verify the property x × (y + z) = x × y + x × z of rational numbers by taking.

x = (-1)/5, y = 2/5, z = (-3)/10

Exercise | Q 111.(a) | Page 20

Use the distributivity of multiplication of rational numbers over their addition to simplify:

3/5 xx [35/24 + 10/1]
Exercise | Q 111.(b) | Page 20

Use the distributivity of multiplication of rational numbers over their addition to simplify:

(-5)/4 xx [8/5 + 16/15]
Exercise | Q 111.(c) | Page 20

Use the distributivity of multiplication of rational numbers over their addition to simplify:

2/7 xx [7/16 - 21/4]
Exercise | Q 111.(d) | Page 20

Use the distributivity of multiplication of rational numbers over their addition to simplify:

3/4 xx [8/9 - 40]
Exercise | Q 112.(a) | Page 20

Simplify 32/5 + 23/11 xx 22/15

Exercise | Q 112.(b) | Page 20

Simplify 3/7 xx 28/15 ÷ 14/5

Exercise | Q 112.(c) | Page 20

Simplify 3/7 + (-2)/21 xx (-5)/6

Exercise | Q 112.(d) | Page 20

Simplify 7/8 + 1/16 - 1/12

Exercise | Q 113 | Page 20

Identify the rational number that does not belong with the other three. Explain your reasoning

(-5)/11, (-1)/2, (-4)/9, (-7)/3

Exercise | Q 114 | Page 20

The cost of 19/4 metres of wire is Rs. 171/2. Find the cost of one metre of the wire.

Exercise | Q 115 | Page 20

A train travels 1445/2 km in 17/2 hours. Find the speed of the train in km/h.

Exercise | Q 116 | Page 21

If 16 shirts of equal size can be made out of 24 m of cloth, how much cloth is needed for making one shirt?

Exercise | Q 117 | Page 21

7/11 of all the money in Hamid’s bank account is Rs. 77,000. How much money does Hamid have in his bank account?

Exercise | Q 118 | Page 21

A 117 1/3 m long rope is cut into equal pieces measuring 7 1/3 each. How many such small pieces are these?

Exercise | Q 119 | Page 21

1/6 of the class students are above average, 1/4 are average and rest are below average. If there are 48 students in all, how many students are below average in the class?

Exercise | Q 120 | Page 21

2/5 of total number of students of a school come by car while 1/4 of students come by bus to school. All the other students walk to school of which 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 that school?

Exercise | Q 121 | Page 21

Huma, Hubna and Seema received a total of Rs. 2,016 as monthly allowance from their mother such that Seema gets 1/2 of what Huma gets and Hubna gets 1 2/3 times Seema’s share. How much money do the three sisters get individually?

Exercise | Q 122 | Page 21

A mother and her two daughters got a room constructed for Rs. 62,000. The elder daughter contributes 3/8 of her mother’s contribution while the younger daughter contributes 1/2 of her mother’s share. How much do the three contribute individually?

Exercise | Q 123 | Page 21

Tell which property allows you to compare
2/3 xx [3/4 xx 5/7] and [2/3 xx 5/7] xx 3/4.

Exercise | Q 124.(i) | Page 22

Name the property used in the following

-7/11 xx (-3)/5 = (-3)/5 xx (-7)/11

Exercise | Q 124.(ii) | Page 22

Name the property used in the following

-2/3 xx [3/4 + (-1)/2] = [(-2)/3 + 3/4] + [(-2)/3 xx (-1)/2]

Exercise | Q 124.(iii) | Page 22

Name the property used in the following

1/3 + [4/9 + ((-4)/3)] = [1/3 + 4/9] + [(-4)/3]

Exercise | Q 124.(iv) | Page 22

Name the property used in the following.

(-2)/7 + 0 = 0 + (-2)/7 = - 2/7

Exercise | Q 124.(v) | Page 22

Name the property used in the following.

3/8 xx 1 = 1 xx 3/8 = 3/8

Exercise | Q 125.(i) | Page 22

Find the multiplicative inverse of -1 1/8

Exercise | Q 12.(ii) | Page 22

Find the multiplicative inverse of 3 1/3

Exercise | Q 126 | Page 22

Arrange the numbers 1/4, 13/16, 5/8 in the descending order.

Exercise | Q 127 | Page 22

The product of two rational numbers is (-14)/27. If one of the numbers be 7/9, find the other.

Exercise | Q 128 | Page 22

By what numbers should we multiply (-15)/20 so that the product may be (-5)/7?

Exercise | Q 129 | Page 22

By what number should we multiply (-8)/13 so that the product may be 24?

Exercise | Q 130 | Page 22

The product of two rational numbers is –7. If one of the number is –5, find the other?

Exercise | Q 131 | Page 22

Can you find a rational number whose multiplicative inverse is –1?

Exercise | Q 132 | Page 22

Find five rational numbers between 0 and 1.

Exercise | Q 133 | Page 22

Find two rational numbers whose absolute value is 1/5.

Exercise | Q 134 | Page 23

From a rope 40 metres long, pieces of equal size are cut. If the length of one piece is 10/3 metre, find the number of such pieces.

Exercise | Q 135 | Page 23

5 1/2 metres long rope is cut into 12 equal pieces. What is the length of each piece?

Exercise | Q 136 | Page 23

Write the following rational numbers in the descending order.

8/7, (-9)/8, (-3)/2, 0, 2/5

Exercise | Q 137.(i) | Page 23

Find 0 ÷ 2/3

Exercise | Q 137.(ii) | Page 23

Find 1/3 xx (-5)/7 xx (-21)/10

Exercise | Q 138 | Page 23

On a winter day the temperature at a place in Himachal Pradesh was –16°C. Convert it in degree Fahrenheit (0F) by using the formula.

C/5 = (F - 32)/9

Exercise | Q 139 | Page 23

Find the sum of additive inverse and multiplicative inverse of 7.

Exercise | Q 140 | Page 23

Find the product of additive inverse and multiplicative inverse of - 1/3.

Exercise | Q 141.(a) | Page 23

The diagram shows the wingspans of different species of birds. Use the diagram to answer the question given below:

How much longer is the wingspan of an Albatross than the wingspan of a Sea gull?

Exercise | Q 141.(b) | Page 23

The diagram shows the wingspans of different species of birds. Use the diagram to answer the question given below:

Exercise | Q 142 | Page 24

Shalini has to cut out circles of diameter 1 1/4 cm from an aluminium strip of dimensions 8 3/4 cm by 1 1/4 cm. How many full circles can Shalini cut? Also calculate the wastage of the aluminium strip.

Exercise | Q 143 | Page 24

One fruit salad recipe requires 1/2 cup of sugar. Another recipe for the same fruit salad requires 2 tablespoons of sugar. If 1 tablespoon is equivalent to 1/16 cup, how much more sugar does the first recipe require?

Exercise | Q 144.(a) | Page 24

Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.

 Name Distance covered (km) Seema 1/25 Nancy 1/32 Megha 1/40 Soni 1/20

How farther did Soni hop than Nancy?

Exercise | Q 144.(b) | Page 24

Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.

 Name Distance covered (km) Seema 1/25 Nancy 1/32 Megha 1/40 Soni 1/20

What is the total distance covered by Seema and Megha?

Exercise | Q 144.(c) | Page 24

Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.

 Name Distance covered (km) Seema 1/25 Nancy 1/32 Megha 1/40 Soni 1/20

Who walked farther, Nancy or Megha?

Exercise | Q 145.(a) | Page 24

The table given below shows the distances, in kilometres, between four villages of a state. To find the distance between two villages, locate the square where the row for one village and the column for the other village intersect.

Compare the distance between Himgaon and Rawalpur to Sonapur and Ramgarh?

Exercise | Q 145.(b) | Page 24

The table given below shows the distances, in kilometres, between four villages of a state. To find the distance between two villages, locate the square where the row for one village and the column for the other village intersect.

If you drove from Himgaon to Sonapur and then from Sonapur to Rawalpur, how far would you drive?

Exercise | Q 146.(a) | Page 25

The table shows the portion of some common materials that are recycled.

 Material Recycled Paper 5/11 Aluminium cans 5/8 Glass 2/5 Scrap 3/4

Is the rational number expressing the amount of paper recycled more than 1/2 or less than 1/2?

Exercise | Q 146.(b) | Page 25

The table shows the portion of some common materials that are recycled.

 Material Recycled Paper 5/11 Aluminium cans 5/8 Glass 2/5 Scrap 3/4

Which items have a recycled amount less than 1/2?

Exercise | Q 146.(c) | Page 25

The table shows the portion of some common materials that are recycled.

 Material Recycled Paper 5/11 Aluminium cans 5/8 Glass 2/5 Scrap 3/4

Is the quantity of aluminium cans recycled more (or less) than half of the quantity of aluminium cans?

Exercise | Q 146.(d) | Page 25

The table shows the portion of some common materials that are recycled.

 Material Recycled Paper 5/11 Aluminium cans 5/8 Glass 2/5 Scrap 3/4

Arrange the rate of recycling the materials from the greatest to the smallest.

Exercise | Q 147 | Page 26

The overall width in cm of several wide-screen televisions are 97.28 cm, 98 4/9 cm 98 1/25 cm and 97.94 cm. Express these numbers as rational numbers in the form p/q and arrange the widths in ascending order.

Exercise | Q 148 | Page 26

Roller Coaster at an amusement park is 2/3 m high. If a new roller coaster is built that is 3/5 times the height of the existing coaster, what will be the height of the new roller coaster?

Exercise | Q 149 | Page 26

Here is a table which gives the information about the total rainfall for several months compared to the average monthly rains of a town. Write each decimal in the form of rational number p/q.

 Month Above/Below normal (in cm) May 2.6924 June 0.6096 July – 6.9088 August – 8.636
Exercise | Q 150 | Page 26

The average life expectancies of males for several states are shown in the table. Express each decimal in the form p/q and arrange the states from the least to the greatest male life expectancy. State-wise data are included below; more indicators can be found in the “FACTFILE” section on the homepage for each state.

 State Male p/q form Lowest terms Andhra Pradesh 61.6 Assam 57.1 Bihar 60.7 Gujarat 61.9 Haryana 64.1 Himachal Pradesh 65.1 Karnataka 62.4 Kerala 70.6 Madhya Pradesh 56.5 Maharashtra 64.5 Orissa 57.6 Punjab 66.9 Rajasthan 59.8 Tamil Nadu 63.7 Uttar Pradesh 58.9 West Bengal 62.8 India 60.8

Source: Registrar General of India (2003) SRS Based Abridged Lefe Tables. SRS Analytical Studies, Report No. 3 of 2003, New Delhi: Registrar General of India. The data are for the 1995-99 period; states subsequently divided are therefore included in their pre-partition states (Chhatisgarh in MP, Uttaranchal in UP and Jharkhand in Bihar)

Exercise | Q 151 | Page 27

A skirt that is 35 7/8 cm long has a hem of 3 1/8 cm. How long will the skirt be if the hem is let down?

Exercise | Q 152 | Page 27

Manavi and Kuber each receives an equal allowance. The table shows the fraction of their allowance each deposits into his/her saving account and the fraction each spends at the mall. If allowance of each is Rs. 1260 find the amount left with each.

 Where money goes Fraction of allowance Manavi Kuber Saving Account 1/2 1/3 Spend at mall 1/4 3/5 Left over ? ?

Exercise

## NCERT solutions for Mathematics Exemplar Class 8 chapter 1 - Rational Numbers

NCERT solutions for Mathematics Exemplar Class 8 chapter 1 (Rational Numbers) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics Exemplar Class 8 solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics Exemplar Class 8 chapter 1 Rational Numbers are Closure Property of Rational Numbers, Commutative Property of Rational Numbers, Identity of Addition and Multiplication of Rational Numbers, Associative Property of Rational Numbers, Distributive Property of Multiplication Over Addition for Rational Numbers, Rational Numbers Between Two Rational Numbers, Rational Numbers, Negative Or Additive Inverse of Rational Numbers, Reciprocal Or Multiplicative Inverse of Rational Numbers, Rational Numbers on a Number Line.

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