Chapter 8 – Rational Numbers

Class 7 Mathematics · 106 questions · 95 with answers

Solved examples

example-1Multiple choice

Which of the following rational numbers is equivalent to ? 3 4 4 9

(a)
(b)
(c)
(d)2 9 6 4

Show solution

Solution: Correct answer is (c).

example-2Multiple choice

Which of the following rational numbers is in standard form? 20 10 1 1

(a)
(b)
(c)
(d)30 4 2 –3

Show solution

Solution: Correct answer is (c). −3 1

example-3Multiple choice

The sum of and is 2 2

(a)–1
(b)–2
(c)4
(d)3

Show solution

Solution: Correct answer is (a). 4 –1

example-4Multiple choice

The value of − – is 3 3

(a)– 2
(b)– 3
(c)2
(d)–1

Show solution

Solution: Correct answer is (d). RATIONAL NUMBERS 233 15-04-2018 MATHEMATICS In Examples 5 and 6, fill in the blanks to make the statements true.

example-5Fill in the blanks

There are _______ number of rational numbers between two rational numbers.

Show solution

Solution: Unlimited

example-6Fill in the blanks

The rational number _________ is neither positive nor negative.

Show solution

Solution: 0 (Zero). In Examples 7 to 9, state whether the statements are True or False.

example-7Short answer

In any rational number , denominator is always a non- zero integer.

Show solution

Solution: True. Reading Strategy: Read a Lesson for Understanding You need to be actively involved as you work through each lesson in your textbook. To begin with, find the lesson’s objective given as main concepts and results. Lesson Features 15-04-2018 UNIT 8

example-8Short answer

“To reduce the rational number to its standard form, we divide its numerator and denominator by their HCF”.

Show solution

Solution: True.

example-9Short answer

“All rational numbers are integers”.

Show solution

Solution: False. Solve • Choose an Operation To decide whether to add, subtract, multiply, or divide to solve a problem, you need to determine the action taking place in the problem. • Subtracted from • Divided by • Minus • Quotient • Difference • Less than • Divided into • Decreased by • Multiplied by • Added to • Times • Plus • Product • Sum • Groups of • More than 4 5

example-10Short answer

List three rational numbers between and . 5 6 4 5

Show solution

Solution: We convert the rational numbers and into rational 5 6 numbers with the same denominators. 4 4 6 24 5 5 5 25 = × = ; = × = 5 5 6 30 6 6 5 30 RATIONAL NUMBERS 235 15-04-2018 MATHEMATICS −7 3 + − 8 8 24 24 4 25 25 4 So, = × and = × 30 30 4 30 30 4 96 100 = = 120 120 96 97 98 99 100 Here, < < < < . So, the required numbers 120 120 120 120 120 97 98 99 are , and 120 120 120 Alternate solution A rational number between 4 5 and is 5 6 1  4 5  49 = + = 2  5 6  60 another rational number 1  4 49  97 = + = 2  5 60  120 one more rational number 15-04-2018 UNIT 8 1  49 5  99 33 =  + = = 2  60 6  120 40 4 5 Therefore, three rational numbers between and are 5 6 49 97 33 , and 60 120 40 Note: There can be many set of answers. ADDING AND SUBTRACTING WITH LIKE DENOMINATORS Words Numbers Formula To add or subtract rational numbers with 1  −4  1 + (– 4) a b a +b the same denominator, + = + = 5  5  5 d d d add or subtract the numerators and keep −3 −3 = ,or the same denominator. 5 5 Example11: Which of the following pairs represent equivalent rational numbers ? 7 28 –2 –16 (i) and (ii) –3 and 24 12 48 Solution: 7 28 (i) and 12 48 Now, first rational number is and it is already in the standard form because there is no common factor in 7 and 12 other than 1. So, is in its standard form (a) Now, Consider 28 = 2 × 2 × 7 48 = 2 × 2 × 2 × 2 × 3 HCF = 2 × 2 = 4 RATIONAL NUMBERS 237 15-04-2018 MATHEMATICS Now, to reduce the rational numbers to its standard form, we divide the numerator and denominator by their HCF. First we take HCF of 28 and 48: 28 28 ÷ 4 7 Now, = = (b) 48 48 ÷ 4 12 From (a) and (b), we can say that the rational numbers 7 28 and are equivalent. 12 48 –2 –16 (ii) –3 and 24 –2 First we multiply the numerator and denominator of –3 by (–1), we get –2 (–2) × (–1) 2 = = (a) –3 (–3) × (–1) 3 Now it is in its standard form. Now, Consider HCF of 16 and 24 is 2 × 2 × 2 = 8 16 = 2 × 2 × 2 × 2 24 = 2 × 2 × 2 × 3 HCF = 2 × 2 × 2 = 8 –16 –16 ÷ 8 –2 So, = = (b) 24 24 ÷ 8 3 From (a) and (b), we can say that the rational numbers –2 –16 –3 24 are not equivalent. Action Operation Combining numbers or putting numbers together Addition Taking away or finding out how far apart two numbers are Subtraction Combining groups Multiplication Splitting things into equal groups or finding how many Division equal groups you can make 15-04-2018 UNIT 8

example-12Fill in the blanks

Write four more rational numbers to complete the pattern: –1 –2 –3 , , 3 6 9 , ______, ______, _______, _______.

Show solution

Solution: By observing the above pattern, we find that denominator is multiple of 3. So we will increase this pattern in this way. –2 –1 × 2 –3 –1 × 3 –4 –1 × 4 = , = = 6 3×2 9 3 × 3 , 12 3×4 –1 × 1 –1 = , 3 ×1 3 , –1 × 4 –4 = 3 × 4 12 Thus, we observe a pattern in these numbers. So, the other numbers would be –1 × 5 –5 –1 × 6 –6 –1 × 7 –7 –1 × 8 – 8 = , = , = and = 3 × 5 15 3 × 6 18 3 × 7 21 3 × 8 24 DIVIDING RATIONAL NUMBERS IN FRACTION FORM Words Numbers Algebra To divide by a 1 4 1 5 5 fraction, multiply by ÷ = × = a c a d ad 7 5 7 4 28 ÷ = × = the reciprocal b d b c bc 5 3

example-13Short answer

Find the sum of – 4 and – 7 . 6 4 5  3

Show solution

Solution: −4 +  −7  6  4 – 29  – 31  – 29 –31 = +  = + 6  4  6 4 RATIONAL NUMBERS 239 15-04-2018 MATHEMATICS –29 × 2 –31 × 3 = + . [Since LCM of 6 and 4 is 12]. 12 12 –29 × 2 – 31 × 3 = –58 – 93 = –151 = –151 So, the required sum is 12 . Think and Discuss 1. Give an example of two denominators with no common factors. 1  3  2. Tell if −2 −  −2  is positive or negative. Explain. 5  16  2 1 3. Explain how to add 2 + 9 , without first writing them as improper 5 2 fractions. 3 6

example-14Short answer

Find the product of –2 and 5 . 4 7 3 6 –11 41

Show solution

Solution: –2 ×5 = × 4 7 4 7 Now, product of two rational numbers Product of numerators = Product of denominators 3 6 –11 41 –11 × 41 – 451 So, – 2 ×5 = × = = 4 7 4 7 4×7 28 15-04-2018 UNIT 8 Think and Discuss 1. Explain how you can be sure that a fraction is simplified. 2. Give the sign of a rational number in which the numerator is negative and the denominator is negative.

example-15Multiple choice

Match column I to column II in the following: Column I Column II 3 3 (i) ÷

(a)–1 4 4 1 4 –2 (ii) ÷
(b)2 3 3 2 3 (iii) ÷ (–1)
(c)3 2 3 1 3 (iv) ÷
(d)4 2 8 5  –5  (v) ÷ (e) 1 7  7 

Show solution

Solution: (i) ↔ (e), (ii) ↔ (d), (iii) ↔ (b), (iv) ↔ (c), (v) ↔ (a) Application on Problem Solving Strategy

example-16Short answer

2 5 Find the reciprocal of ÷– . 11 55

Show solution

Solution : Understand and Explore the Problem • What are you trying to find? The reciprocal of the given number. Plan a Strategy • You know the division of rational numbers and the meaning of reciprocal. Apply this knowledge to find the reciprocal. RATIONAL NUMBERS 241 15-04-2018 MATHEMATICS Solve 2 −5 2 55 • Given expression = ÷ = ×– =– 2 11 55 11 5 • Now find out the reciprocal of – 2 The reciprocal of – 2 is − . Revise • Multiply – 2 and − and check whether you get 1 or not. –2× − = 1 Hence, our answer is correct, since we know that the product of a rational number with its reciprocal is always 1. Think and Discuss 2 5 1. Can you find the reciprocal of × ? 11 55 2. Can you compare this reciprocal with the orignal number?

Questions

Q1Multiple choice

A rational number is defined as a number that can be expressed in the form , where p and q are integers and

(a)q = 0
(b)q=1
(c)q ≠ 1
(d)q ≠ 0 15-04-2018 UNIT 8

Show answer

(d) q ≠ 0 15-04-2018 UNIT 8

Q2Multiple choice

Which of the following rational numbers is positive? –8 19 –21

(a)
(b)
(c)–3
(d)7 –13 –4 13

Show answer

Q3Multiple choice

Which of the following rational numbers is negative?

(a) –3 
(b)–5
(c)9
(d)3 –   7 –8 8 –7

Show answer

(d) 3 –   7 –8 8 –7

Q4Multiple choice

In the standard form of a rational number, the common factor of numerator and denominator is always:

(a)0
(b)1
(c)– 2
(d)2

Show answer

(b) 1

Q5Multiple choice

Which of the following rational numbers is equal to its reciprocal?

(a)1
(b)2
(c)
(d)0

Show answer

(a) 1

Q6Multiple choice

The reciproal of is

(a)3
(b)2
(c)– 1
(d)0 –48

Show answer

(b) 2

Q7Multiple choice

The standard form of is 48 –60 −4 −4

(a)
(b)
(c)
(d)60 48 5 −5 Number Reciprocal Product 3 4 34 4 3   =1 43 5 12 5  12  − − − –  =1 12 5 12  5  1 1 6 6   =1 6 6 RATIONAL NUMBERS 243 15-04-2018 MATHEMATICS

Show answer

(c)

Q8Multiple choice

Which of the following is equivalent to ? 5 16 16 15

(a)
(b)
(c)
(d)4 25 20 25

Show answer

(c)

Q9Multiple choice

How many rational numbers are there between two rational numbers?

(a)1
(b)0
(c)unlimited
(d)100

Show answer

Q10Multiple choice

In the standard form of a rational number, the denominator is always a

(a)0
(b)negative integer
(c)positive integer
(d)1

Show answer

Q11Multiple choice

To reduce a rational number to its standard form, we divide its numerator and denominator by their

(a)LCM
(b)HCF
(c)product
(d)multiple

Show answer

(b) HCF

Q12Multiple choice

Which is greater number in the following: –1 1

(a)
(b)0
(c)
(d)– 2 2 2 RULES FOR MULTIPYING TWO RATIONAL NUMBERS If the signs of the factors are the same, the product is positive. (+) . (+) = (+) or (–) . (–) = (+) If the signs of the factors are different, the product is negative (+) . (–) = (–) or (–) . (+) = (–) In Questions 13 to 46, fill in the blanks to make the statements true.

Show answer

(c)

Q13Fill in the blanks

– 3 is a ______ rational number.

Show answer

negative

Q14Fill in the blanks

1 is a ______ rational number. 15-04-2018 UNIT 8 –8

Show answer

positive

Q15Fill in the blanks

The standard form of is ______. –36

Q16Fill in the blanks

The standard form of 18 is ______. –24 –1

Q17Fill in the blanks

On a number line, is to the ______ of zero (0).

Show answer

left

Q18Fill in the blanks

On a number line, is to the ______ of zero (0).

Show answer

right 7 4 −2 1

Q19Fill in the blanks

– 1 is ______ than 1 . 2 5

Show answer

smaller

Q20Fill in the blanks

– 3 is ______ than 0. –16

Show answer

smaller

Q21Fill in the blanks

and 20 represent ______ rational numbers.

Show answer

different

Q24Fill in the blanks

–16 –27 –3 22. and represent ______ rational numbers. 45 5 23. Additive inverse of 2 is ______. –3 2 24. + = ______. 5 5 –5 –1

Show answer

− 3 5 −1

Q25Fill in the blanks

+ = ______. 6 6 3  –2 

Show answer

– 1

Q26Fill in the blanks

× = ______. 4  3  –5  –3 

Q27Fill in the blanks

× =______. 3  5  –6

Show answer

Q28Short answer

= 7 42

Show answer

– 36

Q29Short answer

1 = 6 –2 7

Show answer

Q30Fill in the blanks

– = _______. 9 9 RATIONAL NUMBERS 245 15-04-2018 MATHEMATICS In questions 31 to 35, fill in the boxes with the correct symbol >,< or =. 7 8

Show answer

– 1

Q31Short answer

–8 9 3 –5

Show answer

Q32Short answer

7 6

Show answer

Q33Short answer

5 8 6 4 –9 4

Show answer

Q34Short answer

7 –7 8 2

Show answer

Q35Short answer

8 2

Show answer

Q36Fill in the blanks

The reciprocal of ______ does not exist.

Show answer

zero 9 −5

Q37Fill in the blanks

The reciprocal of 1 is ______. –3  –7 

Show answer

Q38Fill in the blanks

÷ = ______. 7  3   –5 

Q39Fill in the blanks

0 ÷   = ______.  6  –5 

Show answer

Q40Fill in the blanks

0 ×   = ______.  6

Show answer

Q41Fill in the blanks

______ ×  –2   = 1.  5

Q42Fill in the blanks

The standard form of rational number –1 is ______. a a ÷m

Show answer

– 1 49 2 OSKNRKPNOV

Q43Fill in the blanks

If m is a common divisor of a and b, then = b ____

Show answer

b ÷ m

Q44Fill in the blanks

If p and q are positive integers, then is a ______ rational number and is a ______ rational number. –q

Show answer

positive, negative

Q45Fill in the blanks

Two rational numbers are said to be equivalent or equal, if they have the same ______ form.

Show answer

simplest

Q46Fill in the blanks

If is a rational number, then q cannot be ______. 15-04-2018 UNIT 8 State whether the statements given in question 47 to 65 are True or False.

Show answer

zero

Q47Short answer

Every natural number is a rational number but every rational number need not be a natural number.

Show answer

True

Q48Short answer

Zero is a rational number.

Show answer

True

Q49Short answer

Every integer is a rational number but every rational number need not be an integer.

Show answer

True

Q50Short answer

Every negative integer is not a negative rational number.

Show answer

False

Q51Short answer

If is a rational number and m is a non-zero integer, then p p ×m = q q ×m

Show answer

True

Q52Short answer

If is a rational number and m is a non-zero common divisor of p p ÷m p and q, then = . q q ÷m

Show answer

True

Q53Short answer

In a rational number, denominator always has to be a non-zero inte- ger. p p ×m

Show answer

True

Q54Short answer

If is a rational number and m is a non-zero integer, then is q q ×m a rational number not equivalent to .

Show answer

False

Q55Short answer

Sum of two rational numbers is always a rational number.

Show answer

True

Q56Short answer

All decimal numbers are also rational numbers.

Show answer

True

Q57Short answer

The quotient of two rationals is always a rational number.

Show answer

True

Q58Short answer

Every fraction is a rational number.

Show answer

True

Q59Short answer

Two rationals with different numerators can never be equal.

Show answer

False

Q60Short answer

8 can be written as a rational number with any integer as denomi- nator. 4 2

Show answer

False

Q61Short answer

is equivalent to . 6 3 –3

Show answer

True

Q62Short answer

The rational number lies to the right of zero on the number line.

Show answer

False

Q63Short answer

The rational numbers –12 and –7 are on the opposite sides of zero on the number line. –5 17 RATIONAL NUMBERS 247 15-04-2018 MATHEMATICS

Show answer

True

Q64Short answer

Every rational number is a whole number.

Show answer

False

Q65Short answer

Zero is the smallest rational number.

Show answer

False

Q66Multiple choice

Match the following: Column I Column II a a –a (i) ÷

(a)b b b (ii) ÷
(b)–1 (iii) ÷ (–1)
(c)1 a –a bc (iv) ÷
(d)b b ad b d  ad (v) ÷  (e) a c  bc

Show answer

(a) b b b (ii) ÷

(b) –1 (iii) ÷ (–1)

(d) b b ad b d  ad (v) ÷  (e) a c  bc

Q67Short answer

Write each of the following rational numbers with positive denomi- 5 15 –17 nators: , , . –8 –28 –13

Show answer

, ,

Q68Multiple choice

Express 3 as a rational number with denominator:

(i)36
(ii)– 80

Show answer

(i) 36

(ii) – 80

Q69Multiple choice

Reduce each of the following rational numbers in its lowest form:

(i)– 60
(ii)91

Show answer

(i) – 60

(ii) 91

Q72Multiple choice

– 364 70. Express each of the following rational numbers in its standard form:

(i)–12
(ii)14
(iii)–15
(iv)299 – 30 – 49 35 – 161 71. Are the rational numbers –8 and equivalent? Give reason. 28 –112 72. Arrange the rational numbers –7 , 5 , 2 , –1 , –3 in ascending order. 10 –8 –3 4 5

Show answer

, , , , . 10 −3 −8 5 4

Q73Short answer

Represent the following rational numbers on a number line: 3 –7 22 . , , 8 3 –6 15-04-2018 UNIT 8 –5 x

Q74Short answer

If = , find the value of x. 7 28

Show answer

– 20 −6 −9 −12 14 21 28

Q75Multiple choice

Give three rational numbers equivalent to:

(i)–3 7
(ii)4 11

Show answer

(i) –3 7

(ii) 4 11

Q76Multiple choice

Write the next three rational numbers to complete the pattern: 4 8 12 16

(i), , , , ______, ______,______. −5 –10 –15 –20
(ii)–8 –16 –24 –32 , ______, ______, ______. , , , 7 14 21 28 5 7

Show answer

(i) , , , , ______, ______,______. −5 –10 –15 –20

(ii) –8 –16 –24 –32 , ______, ______, ______. , , , 7 14 21 28 5 7

Q77Short answer

List four rational numbers between and . 7 8

Show answer

, , , 56 56 56 56 127 83 9

Q78Multiple choice

Find the sum of 8 3 7 –4

(i)and
(ii)and 13 11 3 3

Show answer

(i) and

(ii) and 13 11 3 3

Q79Multiple choice

Solve:

(i)29 30
(ii)5 –8 – – 4 7 13 26

Show answer

(i) 29 30

(ii) 5 –8 – – 4 7 13 26

Q80Multiple choice

Find the product of: –4 –5 –22 –21

(i)and
(ii)and 5 12 11 11

Show answer

(i) and

(ii) and 5 12 11 11

Q81Multiple choice

Simplify:

(i)13 × –14 + × –7 + –13 × 34
(ii)6 × 3 – 1 × 3 11 5 11 5 11 5 5 7 5 7

Show answer

(i) 13 × –14 + × –7 + –13 × 34

(ii) 6 × 3 – 1 × 3 11 5 11 5 11 5 5 7 5 7

Q82Short answer

Simplify: 3  21  (ii) 1 ÷  –  (i) ÷  7  –55   2

Show answer

(i) (ii) – 2

Q83Multiple choice

Which is greater in the following? 3 7

(i),
(ii)–3 5 ,3 1 4 8 7 9

Show answer

(i) ,

(ii) –3 5 ,3 1 4 8 7 9

Q84Short answer

Write a rational number in which the numerator is less than ‘–7 × 11’ and the denominator is greater than ‘12 + 4’. 1 –3

Show answer

It has more than one answer like , . 17 18 −11 19 3 −4

Q85Short answer

If x = and y = , then 10 8 evaluate x + y, x – y, x × y and x ÷ y. RATIONAL NUMBERS 249 15-04-2018 MATHEMATICS

Show answer

(i) , ,− , 40 40 80 15 8 4641 −4 −3

Q86Multiple choice

Find the reciprocal of the following: 1 1  + 1  20 4

(i) ×   × 6
(ii)× 2 4 2  51 91 3 –4  12   2
(iii)÷
(iv) –5 ×  –  –3 ×  13 65  15   9

Show answer

(i)  ×   × 6

(ii) × 2 4 2  51 91 3 –4  12   2

(iii) ÷

(iv)  –5 ×  –  –3 ×  13 65  15   9

Q87Short answer

Complete the following table by finding the sums: 1 4 −5 + − 9 11 6 5 −39 − 4 44 −

Show answer

1 4 5 + − − 9 11 6 2 5 34 1 − 3 9 33 6 5 49 39 25 − − − − 4 36 44 12 1 4 1 7 − − − 3 9 33 6 6 7 1 1 0 5 m

Q88Multiple choice

Write each of the following numbers in the form , where p and q are integers:

(a)six-eighths
(b)three and half
(c)opposite of 1
(d)one-fourth (e) zero (f) opposite of three-fifths

Show answer

, , , , ,

Q89Short answer

If p = m × t and q = n × t, then = p r

Show answer

8 2 1 4 1 3 n p r p r

Q90Multiple choice

Given that and are two rational numbers with different q s denominators and both of them are in standard form. To compare these rational numbers we say that:

(a)< , if p × s < r × q 15-04-2018 UNIT 8
(b)= , if ________ = _______
(c)> , if p × s > r × q

Show answer

(a) < , if p × s < r × q 15-04-2018 UNIT 8

(b) = , if ________ = _______

Q91Multiple choice

In each of the following cases, write the rational number whose numerator and denominator are respectively as under:

(a)5 – 39 and 54 – 6
(b)(–4) × 6 and 8 ÷ 2
(c)35 ÷ (–7) and 35 –18
(d)25 + 15 and 81 ÷ 40

Show answer

(a) 5 – 39 and 54 – 6

(b) (–4) × 6 and 8 ÷ 2

(d) 25 + 15 and 81 ÷ 40

Q92Multiple choice

Write the following as rational numbers in their standard forms:

(a)35%
(b)1.2
(c)–6
(d)240 ÷ (– 840) (e) 115 ÷ 207

Show answer

(a) 35%

(b) 1.2

(d) 240 ÷ (– 840) (e) 115 ÷ 207

Q93Multiple choice

Find a rational number exactly halfway between: −1 1 1 1 5 −7 1 1

(a)and
(b)and
(c)and
(d)and 3 3 6 9 −13 9 15 12 −4 5 7

Show answer

(a) and

(b) and

(d) and 3 3 6 9 −13 9 15 12 −4 5 7

Q94Multiple choice

Taking x = ,y = and z = , find : 9 12 18

(a)the rational number which when added to x gives y.
(b)the rational number which subtracted from y gives z.
(c)the rational number which when added to z gives us x.
(d)the rational number which when multiplied by y to get x. (e) the reciprocal of x + y. (f) the sum of reciprocals of x and y. (g) (x ÷ y) × z (h) (x – y) + z (i) x + (y + z) (j) x ÷ (y ÷ z) (k) x – (y + z) –1

Show answer

(a) the rational number which when added to x gives y.

(b) the rational number which subtracted from y gives z.

(d) the rational number which when multiplied by y to get x. (e) the reciprocal of x + y. (f) the sum of reciprocals of x and y. (g) (x ÷ y) × z (h) (x – y) + z (i) x + (y + z) (j) x ÷ (y ÷ z) (k) x – (y + z) –1

Q95Short answer

What should be added to to obtain the nearest natural number? –2

Q96Short answer

What should be subtracted from to obtain the nearest integer? –5

Q97Short answer

What should be multiplied with to obtain the nearest integer?

Q98Short answer

What should be divided by to obtain the greatest negative integer? RATIONAL NUMBERS 251 15-04-2018 MATHEMATICS

Q99Short answer

From a rope 68 m long, pieces of equal size are cut. If length of one piece is 4 m, find the number of such pieces.

Show answer

16 4 2 3 5 2 −3 −6 −9 −10 −15

Q100Short answer

If 12 shirts of equal size can be prepared from 27m cloth, what is length of cloth required for each shirt?

Show answer

2.25m

Q101Multiple choice

Insert 3 equivalent rational numbers between –1 1

(i)and
(ii)0 and –10 2 5

Show answer

(i) and

(ii) 0 and –10 2 5

Q102Multiple choice

Put the (√), wherever applicable Number Natural Whole Integer Fraction Rational Number Number Number

(a)– 114
(b)
(c)
(d)–19 (e) (f) 0

Q103Short answer

‘a’ and ‘b’ are two different numbers taken from the numbers 1 – 50. a −b What is the largest value that can have? What is the largest a +b a +b value that can have? a −b

Show answer

, 99

Q104Short answer

150 students are studying English, Maths or both. 62 per cent of the students are studying English and 68 per cent are studying Maths. How many students are studying both? 15-04-2018 UNIT 8

Show answer

Q105Short answer

A body floats of its volume above the surface. What is the ratio of the body submerged volume to its exposed volume? Re-write it as a rational number. Find the odd one out of the following and give reason. 4 3 −3 −2

Show answer

7 : 2;

Q106Multiple choice

(a)×
(b)× 3 4 2 3 1 −1 3
(c)2×
(d)× 2 3 1 4 −16

Show answer

(d) × 2 3 1 4 −16

Q107Multiple choice

(a)
(b)−9 36 −20 28
(c)
(d)−45 −63 −4 −7

Show answer

(c)

Q108Multiple choice

(a)
(b)3 6 −10 −8
(c)
(d)3 7 −3 −9

Show answer

(b) 3 6 −10 −8

Q109Multiple choice

(a)
(b)7 15 +24 +35
(c)
(d)20 25

Show answer

(a)

Q110Fill in the blanks

What’s the Error? Chhaya simplified a rational number in this −25 −5 manner = . What error did the student make? −30 6 RATIONAL NUMBERS 253 15-04-2018 MATHEMATICS (D) Applications 1. Moving from start to finish by going from smaller to bigger rational numbers. Start 2. Replace ‘*’ by inserting an appropriate rational number between the given rational numbers. 15-04-2018 UNIT 8 3. Three monkeys are climbing upstairs. They can only move ahead if they eat a banana with the common factor of their numerator and denominator on it. Which of the three monkeys will be able to reach till the end? 4. Crossword Puzzle Solve the given crossword and then fill up the given boxes. Clues are given below for across as well as downward filling. Also, for across and down clues. clue number is written at the corner of boxes. Answers of clues have to be filled in their respective boxes. 2 −5 Down 1: and are numbers. 3 4 a a Down 2: The inverse of is − . f f Down 3: The addition and multiplication of whole numbers, integers and rational numbers is Down 4: Since, is not defined, hence 0 has no . RATIONAL NUMBERS 255 15-04-2018 MATHEMATICS Down 5: Reciprocal is also known as multiplicative . Down 6 : The number line extends on both the sides. Down 7: The of two integers may not lead to the formation of another integer. Down 8: The multiplication of a number by its reciprocal gives . Across 1: There are rational numbers between two integers. Across 2: The multiplication of rational numbers is commutative and . Across 3: The addition and of two whole numbers lead to the formation of another whole number. Across 4: All the positive integers excluding 0 are known as numbers. Across 5: For any rational number a; a ÷ 0 is . Across 6: Rational numbers can be represented on a line. 15-04-2018

Show answer

She divided numerator by 5 but denominator by –5 OSKNRKPNOV −2