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.
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Std |
Maharashtra Class 7 |
| Subject |
Math Solution |
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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
