Maharashtra Board Class 7 Math Chapter 5 Operations on Rational Numbers Solution

Maharashtra Board Class 7 Math Solution Chapter 5 – Operations on Rational Numbers

Balbharati Maharashtra Board Class 7 Math Solution Chapter 5: Operations on Rational Numbers. Marathi or English Medium Students of Class 7 get here Operations on Rational Numbers full Exercise Solution.

Std

Maharashtra Class 7
Subject

Math Solution

Chapter

Operations on Rational Numbers


Practice Set 22

1.) Carry out the following additions of rational numbers.

(i) 5/ 36 + 6/ 42

ANS:

To carry out addition we have made denominator same.

For that we are performing cross multiplication.

5 x 42 + 36 x 6 / ( 36 x 42 )

210 + 216 / 1512

426 / 1512

By dividing 6 we get,

71/252

(ii) 1 (2/ 3) + 2 (4 /5)

ANS:

Firstly we arrange given in numerator and denominator form.

5 / 3  + 14 / 5

To carry out addition we have made denominator same.

For that we are performing cross multiplication.

5 x 5 + 3 x 14 / (3 x 5)

25 + 42 / 15

67 / 15

(iii) 11/ 17 + 13/ 19

ANS:

To carry out addition we have made denominator same.

For that we are performing cross multiplication.

11 x 19 + 17 x 13 / (17 x 19)

209 + 221 / 323

430 / 323

(iv) 2 (3 /11) + 1 (3 /77)

ANS:

Firstly we arrange given in numerator and denominator form.

25/11 + 80/77

To carry out addition we have made denominator same.

For that we are performing cross multiplication.

25 x 77 + 11 x 80 / (11 x 77)

1925 + 880 / 847

2805 / 847

By dividing 11, we get

255/77

2.) Carry out the following subtractions involving rational numbers.

(i) 7 /11 – 3/ 7

ANS:

To carry out subtraction we have made denominator same.

For that we are performing cross multiplication.

7 x 7 – 11 x 3 / (11 x 7)

49 – 33 / 77

16 / 77

(ii) 13 /36 – 2 /40

ANS:

To carry out subtraction we have made denominator same.

For that we are performing cross multiplication.

13 x 40 – 36x 2 / (36 x 40)

520 – 72/ 1440

448 / 1440

Dividing by 32, we get

14/ 45

(iii) 1 (2/ 3) – 3 (5/ 6)

ANS:

Firstly we arrange given in numerator and denominator form.

5/3 – 23/6

To carry out subtraction we have made denominator same.

For that we are performing cross multiplication.

5 x 6 – 3 x 23 / (3 x 6)

30 – 69/ 18

-39 / 18

Dividing by 3, we get

-13/6

(iv) 4 (1/ 2) – 3 (1/ 3)

ANS:

Firstly we arrange given in numerator and denominator form.

9/2 – 10/3

To carry out subtraction we have made denominator same.

For that we are performing cross multiplication.

9 x 3 – 2 x 10 / (2 x 3)

27 – 20 / 6

7 / 6

3.) Multiply the following rational numbers.

(i) 3 /11 × 2/ 5

ANS:

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

3 /11 × 2/ 5

= 3 x 2 / 11 x 5

= 6 / 55

(ii) 12 /5 × 4 /15

ANS:

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

12 x 4 / 5 x 15

= 48 / 75

By dividing 3, we get

16/25

(iii) (−8)/ 9 × 3/ 4

ANS:

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

(−8) x 3 / 9 x 4

When any one number have –ve sign the answer contain –ve sign.

= -24 / 36

By dividing 12, we get

= -2 / 3

(iv) 0 /6 × 3/ 4

ANS:

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

0 x 3 / 6 x 24

0 / 24

= 0

4.) Write the multiplicative inverse.

(i) 2/ 5

ANS:

In multiplicative inverse we have to replace numerator with denominator and denominator with numerator and place of sign is as it is.

Multiplicative inverse of 2/ 5 is 5/ 2

(ii) -3 /8

ANS:

In multiplicative inverse we have to replace numerator with denominator and denominator with numerator and place of sign is as it is.

Multiplicative inverse of-3 /8 is -8 / 3.

(iii) -17 /39

ANS:

In multiplicative inverse we have to replace numerator with denominator and denominator with numerator and place of sign is as it is.

Multiplicative inverse of-17 /39 is -39 /17

(iv) 7

ANS:

In multiplicative inverse we have to replace numerator with denominator and denominator with numerator and place of sign is as it is.

Multiplicative inverse of 7 is 1/7

(v) – 7 (1/3)

ANS:

Firstly we make in numerator and denominator form.

3 x (-7) + 1 / 3

-22 /3

In multiplicative inverse we have to replace numerator with denominator and denominator with numerator and place of sign is as it is.

Multiplicative inverse of-22 /3 is -3 /22

5.) Carry out the divisions of rational numbers.

(i) 40 /12 ÷ 10/ 4

ANS:

To carry out divisions of rational numbers we have to made ÷ sign as x and inverse the next fraction.

40 /12 x 4/ 10

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

40 x 4 / 12 x 10

160 / 120

By dividing 40, we get

4 / 3

(ii) -10/ 11 ÷ -11/ 10

ANS:

To carry out divisions of rational numbers we have to made ÷ sign as x and inverse the next fraction.

-10/ 11 x -10/ 11

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

-10 x -10 / 11 x 11

When two –ve sign number are multiply the answer we get is + ve sign.

=100 / 121

(iii) -7/ 8 ÷ -3/ 6

ANS:

To carry out divisions of rational numbers we have to made ÷ sign as x and inverse the next fraction.

-7/ 8 x -6/ 3

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

-7 x -6 / 8 x 3

When two –ve sign number are multiply the answer we get is + ve sign.

42 / 24

By dividing 6, we get

7 / 4

(iv) 2/ 3 ÷ (- 4)

ANS:

To carry out divisions of rational numbers we have to made ÷ sign as x and inverse the next fraction.

2/ 3 x – 1 / 4

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

2 x -1 / 3 x 4

When any one number have –ve sign the answer contain –ve sign.

-2 / 12

By dividing 2, we get

-1 / 6

(v) 2 (1/5) ÷ 5 (3/6)

ANS:

Firstly we arrange given in numerator and denominator form.

11 /5 ÷ 33 /6

To carry out divisions of rational numbers we have to made ÷ sign as x and inverse the next fraction.

11 /5 x 6 /33

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

11 x 6 / 5 x 33

66 / 165

By dividing 33, we get

2 / 5

(vi) -5 /13 ÷ 7 /26

ANS:

To carry out divisions of rational numbers we have to made ÷ sign as x and inverse the next fraction.

-5 /13 x 26 /7

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

-5 x 26 / 13 x 7

When any one number have –ve sign the answer contain –ve sign.

-130 / 91

By dividing 13, we get

-10 / 7

(vii) 9 /11 ÷ (−8)

ANS:

To carry out divisions of rational numbers we have to made ÷ sign as x and inverse the next fraction.

9 /11 x (−1) / 8

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

9 x -1 / 11 x 8

When any one number have –ve sign the answer contain –ve sign.

-9 / 88

(viii) 5 ÷ 2/ 5

ANS:

To carry out divisions of rational numbers we have to made ÷ sign as x and inverse the next fraction.

5/1 x 5/ 2

We are directly multiply numerator with numerator and denominator with denominator and simplify it.

5 x 5 / 1 x 2

= 25 / 2

Practice Set 23

 ¤ Write three rational numbers that lie between the two given numbers.

(i) 2/ 7, 6/ 7

ANS:

To find rational numbers that lie between the two given numbers we have to add numerator with numerator and denominator with denominator.

2 + 6 / 7 + 7

8 / 14

By simplifying we get,

4 / 7

Now we add 2/ 7 and 4 / 7

2 + 4 / 7 + 7

6 / 14

By simplifying we get,

3 / 7

Now we add 6/ 7 and 4 / 7

6 + 4 / 7 + 7

10 / 14

By simplifying we get,

5 / 7

Three rational numbers that lie between2/ 7, 6/ 7 is 3/ 7, 4/ 7, 5/ 7

 

(ii) 4 /5, 2/ 3

ANS:

Firstly we made denominator same.

We multiply 4 /5 by 3

12 / 15

And we multiply2/ 3 by 5

10/15

To find rational numbers that lie between the two given numbers we have to add numerator with numerator and denominator with denominator.

12 + 10 / 15 + 15

22 / 30

By simplifying we get,

11 / 15

Now we add 12 / 15 and11 / 15

12 + 11 / 15 + 15

23 / 30

Now we add10/15and 11 / 15

10 + 11 / 15 + 15

21 / 30

Three rational numbers that lie between4 /5, 2/ 3 is 23/ 30, 22/ 30, 21/ 30

 

(iii) – 2/ 3, 4/ 5

ANS:

Firstly we made denominator same.

We multiply -2 /3 by 5

-10 / 15

And we multiply 4/ 5 by 3

12/15

To find rational numbers that lie between the two given numbers we have to add numerator with numerator and denominator with denominator.

-10 + 12 / 15 + 15

2 / 30

By simplifying we get,

1 / 15

Now we add -10 / 15 and 1 / 15

-10 + 1 / 15 + 15

-9 / 30

Now we add 12/15 and 1 / 15

12 + 1 / 15 + 15

13 / 30

Three rational numbers that lie between – 2/ 3, 4/ 5is -9/30,2/30, 13/30

(iv) 7 /9, – 5/ 9

To find rational numbers that lie between the two given numbers we have to add numerator with numerator and denominator with denominator.

7 -5 / 9 + 9

2 / 18

By simplifying we get,

1/9

Now we add7 /9 and 1/9

7 + 1 / 9 + 9

8 / 18

By simplifying we get,

4 / 9

Now we add- 5/ 9and 1/9

-5 + 1 / 9 + 9

-4 / 9

Three rational numbers that lie between7 /9, – 5/ 9 is -4/9, 1/9, 4/9.

 

(v) -3/ 4, +5/ 4

To find rational numbers that lie between the two given numbers we have to add numerator with numerator and denominator with denominator.

-3 + 5 / 4 + 4

2 / 8

By simplifying we get,

1/4

Now we add-3/ 4 and 1/4

-3 + 1 / 4 + 4

-2 / 8

By simplifying we get,

-1 / 4

Now we add5/ 4and 1/4

5 + 1 / 4+ 4

6 / 8

By simplifying we get,

3/4

Three rational numbers that lie between-3/ 4, +5/ 4 is -1/4, 1/4, 3/4

 

(vi) 7/ 8, -5 /3

ANS:

Firstly we made denominator same.

We multiply 7 /8 by 3

21 / 24

And we multiply -5 / 3 by 8

-40/ 24

To find rational numbers that lie between the two given numbers we have to add numerator with numerator and denominator with denominator.

21 -40 / 24 + 24

-19 / 48

= -38 / 96

Now we add 7/ 8 and -19 / 48

Firstly we made denominator same.

We multiply 7 /8 by 6

42 / 48

Now we add42 / 48and -19 / 48

42 – 19 / 48 + 48

23 / 96

Now we add-5 /3and -19 / 48

Firstly we made denominator same.

We multiply -5 /3 by 16

-80 / 48

Now we add-80 / 48and -19 / 48

-80 + (-19) / 96

-99 / 96

Three rational numbers that lie between7/ 8, -5 /3 is -38 / 96, -99 / 96, 23 / 96

 

(vii) 5 /7, 11/ 7

ANS:

To find rational numbers that lie between the two given numbers we have to add numerator with numerator and denominator with denominator.

5 + 11 / 7 + 7

16 / 14

By simplifying we get,

8/7

Now we add5 /7 and 8/7

5 + 8 / 7 + 7

13 / 14

Now we add11/ 7and 8/7

11 + 8 / 7 + 7

19 / 14

Three rational numbers that lie between 5 /7, 11/ 7 is 13/14, 16 /14, 19 /14

Practice Set 24

¤ Write the following rational numbers in decimal form.

(i) 13/ 4

ANS:

Here we dividing by 4 to 13.

13/ 4 in decimal form is 3.125

(ii) -7/ 8

ANS:

-7/ 8in decimal form is -0.875

 

(iii) 7 (3/ 5)

ANS:

We first convert it into fraction form.

7 (3/ 5) = 38 / 5

38 / 5 in decimal form is 7.6

 

(iv) 5/ 12

ANS:

5/ 12 in decimal form is 4.16666

(v) 22 /7

ANS:

22 /7in decimal form is 3.142857

 

(vi) 4/ 3

ANS:

4/ 3in decimal form is 1.3333

 

(vii) 7/9

ANS:

7/9 in decimal form is 0.77777

Practice Set 25

¤ Simplify the following expressions.

1.) 50 × 5 ÷ 2 + 24

ANS:

Here we are using BODMAS rule.

B = BRACKET

O= OF

D= DIVISION

M= MULTIPLICATION

A= ADDITION

S=SUBTRACTION

50 × 5 ÷ 2 + 24

= 50 X (5/2) + 24

= 25 X 5 + 24

= 125 + 24

= 149

50 × 5 ÷ 2 + 24 = 149

 

2.) (13 × 4) ÷ 2-26

ANS:

Here we are using BODMAS rule.

B = BRACKET

O= OF

D= DIVISION

M= MULTIPLICATION

A= ADDITION

S=SUBTRACTION

(13 × 4) ÷ 2-26

WE FIRST SOLVE BRACKET.

52 /2 – 26

26 – 26

= 0

(13 × 4) ÷ 2-26 = 0

 

3.) 140 ÷ [(-11) × (-3) – (-42) ÷ 14 -1)]

ANS:

140 ÷ [(-11) × (-3) – (-42) ÷ 14 -1)]

We first solve bracket.

In bracket we first perform division, multiplication, addition and then subtraction.

140 ÷[(-11) × (-3) – (-42 / 14) – 1]

140 ÷[(-11) × (-3) + 3 – 1]

140 ÷[ 33 + 3 – 1 ]

140 ÷[ 36 – 1]

140 ÷ 35

= 4

140 ÷ [(-11) × (-3) – (-42) ÷ 14 -1)] = 4

 

4.) {(220-140) + [10 × 9 + (-2 × 5)]}-100

ANS:

We first solve bracket.

In bracket we first perform bracket, division, multiplication, addition and then subtraction.

{(220-140) + [10 × 9 + (-2 × 5)]}-100

{80 + [90 + (-10) ]} – 100

{80 + [90 -10]} – 100

{80 + 80} – 100

160 – 100

= 60

{(220-140) + [10 × 9 + (-2 × 5)]}-100 = 60

 

5.) 3/ 5 + 3/ 8 ÷ 6/ 4

ANS:

3/ 5 + 3/ 8 x 4 / 6

3 / 5 + (3 x 4 / 8 x 4 )

3 / 5 + (12/32)

3 / 5 + 3 /8

We are made denominator same.

3 x 8 + 5 x 3

———————-

5 x 8

= 24 + 15 / 40

= 39 / 40

3/ 5 + 3/ 8 ÷ 6/ 4 = 39 / 40

Updated: July 21, 2021 — 2:30 am

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