SEBA Class 7 Mathematics Chapter 9 Rational Number Comparing

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SEBA Class 7 Mathematics Chapter 9 Rational Number Comparing

Also, you can read the SCERT book online in these sections Solutions by Expert Teachers as per SCERT (CBSE) Book guidelines. SEBA Class 7 General Maths Textual Question Answer. These solutions are part of SCERT All Subject Solutions. Here we have given SEBA Class 7 Mathematics Chapter 9 Rational Number Comparing Solutions for All Subject, You can practice these here.

Rational Number Comparing

Chapter – 9

PART – II

Exercise – 9.1

1. Select the correct options from the following sentences –

(i) All natural numbers are integers.

Ans: True.

(ii) An integer may not be a natural number.

Ans: True.

(iii) If a number is rational then the number must be an integer.

Ans: False.

(iv) There are infinite numbers of rational numbers between two integers.

Ans: True.

(v) All fractions are integers.

Ans: False.

(vi) All fractions are rational numbers.

Ans: True.

(vii) 0 is a rational number.

Ans: True.

(viii) Each integer is rational.

Ans: True.

2. Write 3 equal rational numbers for the following fractions. (Keep in mind that there are infinite numbers of equivalent rational number for every number)

(i) -4/5

Ans: – 4/5 = (-4 × 2)/(2 × 5) = -8/10

-4/5 = (-4 × 3)/(3 × 5) = -12/15

-4/5 = (-4 × 4)/(4 × 5) = -16/20

(ii) 2/-3

Ans: 2/-3 = (2 × 2)/(2 × -3) = -4/6

2/-3 = (2 × 3)/(2 × -3) = -6/9

2/-3 = (2 × 4)/(2 × -3) = -8/12

(iii) -7/21

Ans: -7/21 = -7×1/21 ×1 = -1/3 

-7/21 = (-7 × 2)/(21 × 2) = -14/42

-7/21 = (-7 × 3)/(21 × 13) = -21/63

(iv) 1/-9

Ans: 1/-9 = (1 × 2)/(-9 × 2) = 2/-18

1/-9 = (1 × 3)/(-9× 3) = -3/27

1/-9 = (1 × 4)/(-9 × 4) = -4/36

(v) 40/64

Ans: 40/64 = (40 x 2)/(64 x 2) = 80/128

40/64 = (40 x 3)/(64 x 3) = 120/192

40/64 = (40 x 4)/(64 x 4) = 160/256

3. Are the following pairs equal?

(i) -3/13, 6/-26

Ans: Yes.

(ii) 7/-3, 1/-3

Ans: No.

4. Replace x and y in such a way so that the equity exists.

(i) 9/-40 = -9/x

Ans: 9x = 9 × 40

× = 9 × 40/9

× = 40

(ii) -5/35 = y/-70

Ans: 35y = 5 × 70

y = 5 × 70 /35

y = 10

5. Express in standard form.

(i) 5/-2

Ans: 5/-2 = -2 1/2 

(ii) 7/-14

Ans: 7/-14 = 7/(-7 × 2) = -1/2 

(iii) 25/-45

Ans: 25/-45 = (5 × 5)/(-5 × 9) = -5/9

(iv) 2 3/7

Ans: 2 3/7

(v) -18/10

Ans: -18/10 = (-2 × 9)/(2 × 5) = -9/5

6. Which is smaller in each of the pair of the following rational numbers.

(a) 7/14, -2/4

Ans: 7/14 = (7 × 2)/(14 × 2) = 14/28

-2/4 = (-2 × 7)/(4 × 7) = -14/28

∴ -2/4 Smaller Number.

(b) -1/3, -2/5 

Ans: -1/3 = (-1 × 5)/(3 × 5) = -5/15

-2/5 = (-2 × 3)/(5 × 3) = -6/15

∴ -6/15 < -5/15

∴ -2/5 < -1/3 ∴ -2/5 Smaller Number.

(c) -8/5, -7/4

Ans: -8/5 = (-8 × 4)/(5 × 4) = -32/20

-7/4 = (-7 × 5)/(4 × 5) = -35/20

Now, -35/20 < -32/20 ∴ -7/4 Smaller Number.

(d) -2/-3, 16/12

Ans: -2/-3 = 2/3 = (2 × 2)/(2 × 3) = 4/6

16/12 = 4/3

∴ -2/-3 Smaller Number.

7. Write 5 rational number between the following pair of numbers. (Keep in mind that there are several rational numbers in each of the following pairs)

(i) -1 and 1

Ans: 5 rational numbers between -1 and 1

Let, a = – 1 b = 1 a < b n = 5

d = 1 – (-1)/(5 + 1) = 2/6 = 1/3 

∴ -1 + 1 × 1/3, -1 + 2 × 1/3, -1 + 3 × 1/3, -1 + 4 × 1/3, – 1 × 5 × 1/3 

⇒ (-3 + 1)/3, (-3 + 2)/3, -1 + 1, (-3 + 4)/3, (-3 + 5)/3

⇒ -2/3, -1/3, 0, 1/3, 2/3

(ii) -3/4, 3/4

Ans: 

(iii) -3, -2

Ans: The 5 rational numbers between –3 and –2 

Are- -2.1, -2.2,-2.3, -2.5.

(iv) -2/5, -2/3

Ans: -2/5, -2/3 

-2 / 5 = 2 × 3/ 5  × 3 = – 6/ 15

-⅔ = -2 × 5 / 3  × 5 = – 10 / 15 

∴ The rational numbers are- -7/15 , -8/15 , – 8 .1/15 , -8.2/15 , -8.3/15

(v) 5/8, 3/7

Ans: 5/8, 3/7

5/8 = 0.625 = 0.63

3/7 = 0.428 = 0.43

∴ The rational numbers are- 0.44, 0.45, 0.46, 0.47, 0.62

8. Put the following rational numbers in number line –

(i) 2/3

Ans:

(ii) -4/7

Ans:

(iii) 3/8 

Ans: 

(iv) -2 3/5 

Ans:

(v) 3 4/9

Ans:

9. 31/5  is a rational lies to the right of 0. What is the rational number which lies at the left of 0 in same distance? What will be the rational number which lies to the centre of the two rational numbers?

Ans: 31/5, 0

10. (i) What will be the greatest integer among the integers which are smaller than 1/2?

Ans: 0

(ii) What will be the smallest integer among all the integers which are greater than 1/2?

Ans: 1

Exercise – 9.2

1. Find the sum:

(a) 3/6 + 5/3

Ans: 3/6 + 5/3

= (3 + 10)/6 = 13/6

(b) -5/6 + 4/7

Ans: -5/6 + 4/7

= (-35 + 24)/42 = -11/42

Ans:

= -8/15 – 3/20

= -32 – 9/60 = -41/60

Ans:

= 1 – 8/9

= 9 – 8/9 = 1/9

Ans:

= -8/21 – 4/35

= -40 – 12/105 = -52/105

(f) -3 4/5 + 2 1/6 

Ans: -3 4/5 + 2 1/6

= -19/5 + 13/6

= (-114 + 65)/30 = -49/30

Ans:

= -14/3 – 23/7 = (-98 – 69)/21 = -167/21 = -7 20/21

2. Subtract the following:

(i) 51/14 – 3/2

Ans: 51/14 – 3/2 

= 51 – 21/14

= 30/14 = 15/7 = 2 1/7

Ans:

= 2/3 + 1/3

= 2 + 1/3 = 3/3 = 1

Ans:

= 1 + 8/9

= 9 + 8/9 = 17/9 = 1 8/9

Ans:

= -14/3 + 23/7

= -98 + 69/21

= -29/21 = -1 8/21

Ans:

= -8/12 + 4/35 = -2/3 + 4/35

= -70 + 12/105

= -58/105 = – 58/105

(vi) -2 1/9 -5

Ans: -2 1/9 -5

= -19 – 45/9

= -64/9 = -7 1/9

Ans:

= 7 + 20/9

= (63 + 20)/9 = 83/9 = 9 2/9

3. Find the product:

(i) -15/14 × 2/3

Ans: -15/14 × 2/3 

= (-15 × 2)/(14 × 3)

= -30/42 = -5/7

(ii) 3/-11 × -2/5 

Ans: 3/-11 × -2/5 

= 3 × (-2)/(-11) × 5

= (3 × 2)/(11 × 5) = 6/55

Ans: 

= (-6) × 7/21 × (-8)

Ans:

= 6 × (-9)/5 × 11

= -54/55

Ans:

= (-7) × (-2)/12 × 13 = 7 × 2/12 × 13 = 7/6 × 13 = 7/78

Ans:

= 4/5 

Ans: 

= 6/7

Ans:

= -3/5

4. Find out the value:

(i) (-5) ÷ (-1)

Ans: (-5) ÷ (-1)

= -5/-1 = 5

Ans:

= -1 × 5/3 = -5/3 = -1 2/3

Ans: 

= -1 × (5/-3)

= 5/3 = 1 2/3 

Ans:

= -3/7 × 21/1 = -9

(v) 7/-3 ÷ (-21)

Ans: 7/-3 ÷ (-21)

= 7/-3 × 1/-21

= 7/3 × 21

= 1/3 × 3 = 1/9

Ans:

= 21 × 3/-7

= 21 × 3/-7

= 3 × (-3) 

= -9

Ans: 

= 6/13 × 65/-4

= 3 × 5/2

= -15/2 = -7 1/2 

Ans:

= -1/8 × 8/-1

= 1

5. Answer as per the instruction:

(i) What is Additive inverse of – 8/9.

Ans: 8/9

(ii) What is additive inverse of -1.

Ans: 1

(iii) 2/3 / (2/3) = 1 (Say correct or incorrect).

Ans: 2/3 / (2/3) = 1 [Correct]

(iv) 1 / (4/3) = 3/4 (Say correct or incorrect).

Ans: 1 / (4/3) = 3/4 [Correct].

(v) If a and b are two rational numbers then, a × (- b) = – (a × b) and – a × b = – (a × b) Now take any two rational numbers in place of a and b and verify the above equity.

Ans: Correct.

(vi) What is the reciprocal of – 3/7?

Ans: -7/3