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Class 8Sum of Rational Numbers
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(1) Solve the f ollowing and simplif y to lowest term:
A)
-5
5 +
3
6 +
-6
2 =
B)
-5
5 +
-3
3 +
-3
6 =
C)
6
3 +
-6
4 +
2
4 +
3
3 +
-6
4 =
D)
-4
2 +
3
5 +
1
4 +
3
2 +
-5
6 =
E)
2
3 +
5
5 +
-5
6 +
-3
4 +
1
3 =
(2) Solve the f ollowing and simplif y to lowest term:
A)
-4
2 +
1
4 +
4
4 +
-3
2 +
-3
6 =
B)
-5
3 +
-2
6 +
-2
5 =
(3) Solve the f ollowing and simplif y to lowest term:
ID : in-8-Sum-of-Rational-Numbers [1]
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A)
5
4 +
5
6 +
-1
2 =
B)
2
3 +
-1
2 +
-2
5 +
-1
4 +
-5
2 =
(4) Solve the f ollowing and simplif y to lowest term:
A)
5
3 +
-6
4 +
-3
6 +
4
5 =
B)
-4
4 +
-2
3 +
-1
2 =
(5) Solve the f ollowing and simplif y to lowest term:
A)
4
3 +
-5
4 +
-2
4 +
-6
4 =
B)
1
4 +
4
2 +
6
4 +
3
4 +
5
2 =
(6) Solve the f ollowing and simplif y to lowest term:
A)
-3
5 +
5
4 +
-5
4 =
B)
-5
4 +
1
6 +
4
3 +
4
3 =
(7) Solve the f ollowing and simplif y to lowest term:
ID : in-8-Sum-of-Rational-Numbers [2]
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A)
5
4 +
-6
3 +
-5
2 +
6
3 +
-4
6 =
B)
-5
2 +
-2
3 +
4
6 =
(8) Solve the f ollowing and simplif y to lowest term:
A)
-1
2 +
6
3 +
-5
6 +
4
4 =
B)
-2
2 +
-2
4 +
-1
3 =
(9) Solve the f ollowing and simplif y to lowest term:
A)
-5
5 +
2
3 +
6
3 =
B)
3
6 +
2
2 +
3
5 =
(10) Solve the f ollowing and simplif y to lowest term:
A)
-4
5 +
-5
3 +
1
2 +
-5
2 +
-1
4 =
B)
5
2 +
-2
2 +
4
5 =
(11) Solve the f ollowing and simplif y to lowest term:
ID : in-8-Sum-of-Rational-Numbers [3]
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A)
-1
5 +
-1
3 +
-4
2 +
5
3 =
B)
-1
4 +
5
4 +
-1
5 =
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ID : in-8-Sum-of-Rational-Numbers [4]
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Answers
(1) A)
-5
5 +
3
6 +
-6
2 =
-7
2
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-5
5 +
3
6 +
-6
2
= (-5 × 6) + (3 × 5) + (-6 × 15)
30
= -30 + 15 -90
30
= -105
30
Step 2
To simplif y -105
30 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -105 and 30 is 15.
Theref ore, -105
30 =
-105
15
30
15
= -7
2
Step 3
Thus, the simplif ied term is -7
2 .
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B)
-5
5 +
-3
3 +
-3
6 =
-5
2
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-5
5 +
-3
3 +
-3
6
= (-5 × 6) + (-3 × 10) + (-3 × 5)
30
= -30 -30 -15
30
= -75
30
Step 2
To simplif y -75
30 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -75 and 30 is 15.
Theref ore, -75
30 =
-75
15
30
15
= -5
2
Step 3
Thus, the simplif ied term is -5
2 .
ID : in-8-Sum-of-Rational-Numbers [6]
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C)
6
3 +
-6
4 +
2
4 +
3
3 +
-6
4 =
1
2
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
6
3 +
-6
4 +
2
4 +
3
3 +
-6
4
= (6 × 4) + (-6 × 3) + (2 × 3) + (3 × 4) + (-6 × 3)
12
= 24 -18 + 6 + 12 -18
12
= 6
12
Step 2
To simplif y 6
12 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 6 and 12 is 6.
Theref ore, 6
12 =
6
6
12
6
= 1
2
Step 3
Thus, the simplif ied term is 1
2 .
ID : in-8-Sum-of-Rational-Numbers [7]
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D)
-4
2 +
3
5 +
1
4 +
3
2 +
-5
6 =
-29
60
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-4
2 +
3
5 +
1
4 +
3
2 +
-5
6
= (-4 × 30) + (3 × 12) + (1 × 15) + (3 × 30) + (-5 × 10)
60
= -120 + 36 + 15 + 90 -50
60
= -29
60
Step 2
The HCF of -29 and 60 is 1, which means numerator and denominator does nothave common f actor and f raction cannot be simplif ied f urther
Step 3
Thus, the simplif ied term is -29
60 .
ID : in-8-Sum-of-Rational-Numbers [8]
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E)
2
3 +
5
5 +
-5
6 +
-3
4 +
1
3 =
5
12
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
2
3 +
5
5 +
-5
6 +
-3
4 +
1
3
= (2 × 20) + (5 × 12) + (-5 × 10) + (-3 × 15) + (1 × 20)
60
= 40 + 60 -50 -45 + 20
60
= 25
60
Step 2
To simplif y 25
60 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 25 and 60 is 5.
Theref ore, 25
60 =
25
5
60
5
= 5
12
Step 3
Thus, the simplif ied term is 5
12 .
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(2) A)
-4
2 +
1
4 +
4
4 +
-3
2 +
-3
6 =
-11
4
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-4
2 +
1
4 +
4
4 +
-3
2 +
-3
6
= (-4 × 6) + (1 × 3) + (4 × 3) + (-3 × 6) + (-3 × 2)
12
= -24 + 3 + 12 -18 -6
12
= -33
12
Step 2
To simplif y -33
12 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -33 and 12 is 3.
Theref ore, -33
12 =
-33
3
12
3
= -11
4
Step 3
Thus, the simplif ied term is -11
4 .
ID : in-8-Sum-of-Rational-Numbers [10]
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B)
-5
3 +
-2
6 +
-2
5 =
-12
5
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-5
3 +
-2
6 +
-2
5
= (-5 × 10) + (-2 × 5) + (-2 × 6)
30
= -50 -10 -12
30
= -72
30
Step 2
To simplif y -72
30 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -72 and 30 is 6.
Theref ore, -72
30 =
-72
6
30
6
= -12
5
Step 3
Thus, the simplif ied term is -12
5 .
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(3) A)
5
4 +
5
6 +
-1
2 =
19
12
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
5
4 +
5
6 +
-1
2
= (5 × 3) + (5 × 2) + (-1 × 6)
12
= 15 + 10 -6
12
= 19
12
Step 2
The HCF of 19 and 12 is 1, which means numerator and denominator does nothave common f actor and f raction cannot be simplif ied f urther
Step 3
Thus, the simplif ied term is 19
12 .
ID : in-8-Sum-of-Rational-Numbers [12]
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B)
2
3 +
-1
2 +
-2
5 +
-1
4 +
-5
2 =
-179
60
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
2
3 +
-1
2 +
-2
5 +
-1
4 +
-5
2
= (2 × 20) + (-1 × 30) + (-2 × 12) + (-1 × 15) + (-5 × 30)
60
= 40 -30 -24 -15 -150
60
= -179
60
Step 2
The HCF of -179 and 60 is 1, which means numerator and denominator does nothave common f actor and f raction cannot be simplif ied f urther
Step 3
Thus, the simplif ied term is -179
60 .
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(4) A)
5
3 +
-6
4 +
-3
6 +
4
5 =
7
15
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
5
3 +
-6
4 +
-3
6 +
4
5
= (5 × 20) + (-6 × 15) + (-3 × 10) + (4 × 12)
60
= 100 -90 -30 + 48
60
= 28
60
Step 2
To simplif y 28
60 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 28 and 60 is 4.
Theref ore, 28
60 =
28
4
60
4
= 7
15
Step 3
Thus, the simplif ied term is 7
15 .
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B)
-4
4 +
-2
3 +
-1
2 =
-13
6
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-4
4 +
-2
3 +
-1
2
= (-4 × 3) + (-2 × 4) + (-1 × 6)
12
= -12 -8 -6
12
= -26
12
Step 2
To simplif y -26
12 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -26 and 12 is 2.
Theref ore, -26
12 =
-26
2
12
2
= -13
6
Step 3
Thus, the simplif ied term is -13
6 .
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(5) A)
4
3 +
-5
4 +
-2
4 +
-6
4 =
-23
12
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
4
3 +
-5
4 +
-2
4 +
-6
4
= (4 × 4) + (-5 × 3) + (-2 × 3) + (-6 × 3)
12
= 16 -15 -6 -18
12
= -23
12
Step 2
The HCF of -23 and 12 is 1, which means numerator and denominator does nothave common f actor and f raction cannot be simplif ied f urther
Step 3
Thus, the simplif ied term is -23
12 .
ID : in-8-Sum-of-Rational-Numbers [16]
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B)
1
4 +
4
2 +
6
4 +
3
4 +
5
2 =
7
1
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
1
4 +
4
2 +
6
4 +
3
4 +
5
2
= (1 × 1) + (4 × 2) + (6 × 1) + (3 × 1) + (5 × 2)
4
= 1 + 8 + 6 + 3 + 10
4
= 28
4
Step 2
To simplif y 28
4 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 28 and 4 is 4.
Theref ore, 28
4 =
28
4
4
4
= 7
1
Step 3
Thus, the simplif ied term is 7
1 .
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(6) A)
-3
5 +
5
4 +
-5
4 =
-3
5
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-3
5 +
5
4 +
-5
4
= (-3 × 4) + (5 × 5) + (-5 × 5)
20
= -12 + 25 -25
20
= -12
20
Step 2
To simplif y -12
20 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -12 and 20 is 4.
Theref ore, -12
20 =
-12
4
20
4
= -3
5
Step 3
Thus, the simplif ied term is -3
5 .
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B)
-5
4 +
1
6 +
4
3 +
4
3 =
19
12
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-5
4 +
1
6 +
4
3 +
4
3
= (-5 × 3) + (1 × 2) + (4 × 4) + (4 × 4)
12
= -15 + 2 + 16 + 16
12
= 19
12
Step 2
The HCF of 19 and 12 is 1, which means numerator and denominator does nothave common f actor and f raction cannot be simplif ied f urther
Step 3
Thus, the simplif ied term is 19
12 .
ID : in-8-Sum-of-Rational-Numbers [19]
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(7) A)
5
4 +
-6
3 +
-5
2 +
6
3 +
-4
6 =
-23
12
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
5
4 +
-6
3 +
-5
2 +
6
3 +
-4
6
= (5 × 3) + (-6 × 4) + (-5 × 6) + (6 × 4) + (-4 × 2)
12
= 15 -24 -30 + 24 -8
12
= -23
12
Step 2
The HCF of -23 and 12 is 1, which means numerator and denominator does nothave common f actor and f raction cannot be simplif ied f urther
Step 3
Thus, the simplif ied term is -23
12 .
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B)
-5
2 +
-2
3 +
4
6 =
-5
2
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-5
2 +
-2
3 +
4
6
= (-5 × 3) + (-2 × 2) + (4 × 1)
6
= -15 -4 + 4
6
= -15
6
Step 2
To simplif y -15
6 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -15 and 6 is 3.
Theref ore, -15
6 =
-15
3
6
3
= -5
2
Step 3
Thus, the simplif ied term is -5
2 .
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(8) A)
-1
2 +
6
3 +
-5
6 +
4
4 =
5
3
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-1
2 +
6
3 +
-5
6 +
4
4
= (-1 × 6) + (6 × 4) + (-5 × 2) + (4 × 3)
12
= -6 + 24 -10 + 12
12
= 20
12
Step 2
To simplif y 20
12 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 20 and 12 is 4.
Theref ore, 20
12 =
20
4
12
4
= 5
3
Step 3
Thus, the simplif ied term is 5
3 .
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B)
-2
2 +
-2
4 +
-1
3 =
-11
6
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-2
2 +
-2
4 +
-1
3
= (-2 × 6) + (-2 × 3) + (-1 × 4)
12
= -12 -6 -4
12
= -22
12
Step 2
To simplif y -22
12 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -22 and 12 is 2.
Theref ore, -22
12 =
-22
2
12
2
= -11
6
Step 3
Thus, the simplif ied term is -11
6 .
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(9) A)
-5
5 +
2
3 +
6
3 =
5
3
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-5
5 +
2
3 +
6
3
= (-5 × 3) + (2 × 5) + (6 × 5)
15
= -15 + 10 + 30
15
= 25
15
Step 2
To simplif y 25
15 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 25 and 15 is 5.
Theref ore, 25
15 =
25
5
15
5
= 5
3
Step 3
Thus, the simplif ied term is 5
3 .
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B)
3
6 +
2
2 +
3
5 =
21
10
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
3
6 +
2
2 +
3
5
= (3 × 5) + (2 × 15) + (3 × 6)
30
= 15 + 30 + 18
30
= 63
30
Step 2
To simplif y 63
30 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 63 and 30 is 3.
Theref ore, 63
30 =
63
3
30
3
= 21
10
Step 3
Thus, the simplif ied term is 21
10 .
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(10) A)
-4
5 +
-5
3 +
1
2 +
-5
2 +
-1
4 =
-283
60
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-4
5 +
-5
3 +
1
2 +
-5
2 +
-1
4
= (-4 × 12) + (-5 × 20) + (1 × 30) + (-5 × 30) + (-1 × 15)
60
= -48 -100 + 30 -150 -15
60
= -283
60
Step 2
The HCF of -283 and 60 is 1, which means numerator and denominator does nothave common f actor and f raction cannot be simplif ied f urther
Step 3
Thus, the simplif ied term is -283
60 .
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B)
5
2 +
-2
2 +
4
5 =
23
10
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
5
2 +
-2
2 +
4
5
= (5 × 5) + (-2 × 5) + (4 × 2)
10
= 25 -10 + 8
10
= 23
10
Step 2
The HCF of 23 and 10 is 1, which means numerator and denominator does nothave common f actor and f raction cannot be simplif ied f urther
Step 3
Thus, the simplif ied term is 23
10 .
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(11) A)
-1
5 +
-1
3 +
-4
2 +
5
3 =
-13
15
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-1
5 +
-1
3 +
-4
2 +
5
3
= (-1 × 6) + (-1 × 10) + (-4 × 15) + (5 × 10)
30
= -6 -10 -60 + 50
30
= -26
30
Step 2
To simplif y -26
30 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -26 and 30 is 2.
Theref ore, -26
30 =
-26
2
30
2
= -13
15
Step 3
Thus, the simplif ied term is -13
15 .
ID : in-8-Sum-of-Rational-Numbers [28]
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B)
-1
4 +
5
4 +
-1
5 =
4
5
Step 1
Let’s add the given numbers by taking the LCM of the denominators:
-1
4 +
5
4 +
-1
5
= (-1 × 5) + (5 × 5) + (-1 × 4)
20
= -5 + 25 -4
20
= 16
20
Step 2
To simplif y 16
20 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 16 and 20 is 4.
Theref ore, 16
20 =
16
4
20
4
= 4
5
Step 3
Thus, the simplif ied term is 4
5 .
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