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Class 8Multiplication of Rational Numbers
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(1) Find the f ollowing and simplif y it to lowest term:
A)
-4
6 ×
-4
3 ×
-1
4 =
B)
5
6 ×
3
6 ×
5
4 ×
3
2 =
C)
1
3 ×
2
2 ×
4
2 ×
3
6 =
D)
-4
5 ×
1
5 ×
5
2 ×
-1
3 =
E)
4
2 ×
-4
3 ×
-3
5 =
(2) Find the f ollowing and simplif y it to lowest term:
A)
-2
5 ×
-4
2 ×
1
5 =
B)
-1
6 ×
5
6 ×
3
6 ×
-1
3 =
(3) Find the f ollowing and simplif y it to lowest term:
ID : in-8-Multiplication-of-Rational-Numbers [1]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
A)
-1
5 ×
4
3 ×
-2
6 ×
-4
4 =
B)
1
2 ×
5
5 ×
4
2 =
(4) Find the f ollowing and simplif y it to lowest term:
A)
-2
5 ×
-3
4 ×
-5
4 =
B)
-2
4 ×
4
2 ×
3
4 ×
-3
6 =
(5) Find the f ollowing and simplif y it to lowest term:
A)
-5
4 ×
2
3 ×
3
6 ×
1
4 =
B)
-4
5 ×
1
4 ×
-2
4 ×
5
5 =
(6) Find the f ollowing and simplif y it to lowest term:
A)
1
4 ×
5
6 ×
-4
3 ×
-3
5 =
B)
5
3 ×
-3
5 ×
1
6 =
(7) Find the f ollowing and simplif y it to lowest term:
ID : in-8-Multiplication-of-Rational-Numbers [2]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
A)
-3
3 ×
1
2 ×
-1
4 ×
2
6 =
B)
2
2 ×
-5
5 ×
2
2 ×
3
2 =
(8) Find the f ollowing and simplif y it to lowest term:
A)
3
5 ×
1
3 ×
-4
4 ×
-4
3 =
B)
-4
2 ×
-5
4 ×
-4
6 ×
5
3 =
(9) Find the f ollowing and simplif y it to lowest term:
A)
-4
6 ×
5
3 ×
-3
3 =
B)
-5
6 ×
4
3 ×
-3
2 ×
3
5 =
(10) Find the f ollowing and simplif y it to lowest term:
A)
-2
4 ×
-1
4 ×
2
4 =
B)
3
4 ×
1
2 ×
-2
2 ×
-3
4 =
(11) Find the f ollowing and simplif y it to lowest term:
ID : in-8-Multiplication-of-Rational-Numbers [3]
(C) 2016 Edugain (www.Edugain.com) Personal use only, commercial use is strictly prohibited
A)
-4
2 ×
-4
5 ×
-3
4 ×
1
4 =
B)
-1
5 ×
-3
6 ×
1
3 =
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Answers
(1) A)
-4
6 ×
-4
3 ×
-1
4 =
-2
9
Step 1
Let’s multiply the given numbers:
-4
6 ×
-4
3 ×
-1
4
= -2
3 ×
-4
3 ×
-1
4
= -8
36
Step 2
To simplif y -8
36 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -8 and 36 is 4.
Theref ore, -8
36 =
-8
4
36
4
= -2
9
Step 3
Thus, the simplif ied term is -2
9 .
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B)
5
6 ×
3
6 ×
5
4 ×
3
2 =
25
32
Step 1
Let’s multiply the given numbers:
5
6 ×
3
6 ×
5
4 ×
3
2
= 5
6 ×
1
2 ×
5
4 ×
3
2
= 75
96
Step 2
To simplif y 75
96 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 75 and 96 is 3.
Theref ore, 75
96 =
75
3
96
3
= 25
32
Step 3
Thus, the simplif ied term is 25
32 .
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C)
1
3 ×
2
2 ×
4
2 ×
3
6 =
1
3
Step 1
Let’s multiply the given numbers:
1
3 ×
2
2 ×
4
2 ×
3
6
= 1
3 ×
1
1 ×
2
1 ×
1
2
= 2
6
Step 2
To simplif y 2
6 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 2 and 6 is 2.
Theref ore, 2
6 =
2
2
6
2
= 1
3
Step 3
Thus, the simplif ied term is 1
3 .
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D)
-4
5 ×
1
5 ×
5
2 ×
-1
3 =
2
15
Step 1
Let’s multiply the given numbers:
-4
5 ×
1
5 ×
5
2 ×
-1
3
= -4
5 ×
1
5 ×
5
2 ×
-1
3
= 20
150
Step 2
To simplif y 20
150 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 20 and 150 is 10.
Theref ore, 20
150 =
20
10
150
10
= 2
15
Step 3
Thus, the simplif ied term is 2
15 .
ID : in-8-Multiplication-of-Rational-Numbers [8]
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E)
4
2 ×
-4
3 ×
-3
5 =
8
5
Step 1
Let’s multiply the given numbers:
4
2 ×
-4
3 ×
-3
5
= 2
1 ×
-4
3 ×
-3
5
= 24
15
Step 2
To simplif y 24
15 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 24 and 15 is 3.
Theref ore, 24
15 =
24
3
15
3
= 8
5
Step 3
Thus, the simplif ied term is 8
5 .
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(2) A)
-2
5 ×
-4
2 ×
1
5 =
4
25
Step 1
Let’s multiply the given numbers:
-2
5 ×
-4
2 ×
1
5
= -2
5 ×
-2
1 ×
1
5
= 4
25
Step 2
The HCF of 4 and 25 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 4
25 .
B)
-1
6 ×
5
6 ×
3
6 ×
-1
3 =
5
216
Step 1
Let’s multiply the given numbers:
-1
6 ×
5
6 ×
3
6 ×
-1
3
= -1
6 ×
5
6 ×
1
2 ×
-1
3
= 5
216
Step 2
The HCF of 5 and 216 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 5
216 .
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(3)ID : in-8-Multiplication-of-Rational-Numbers [11]
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B)
1
2 ×
5
5 ×
4
2 =
1
1
Step 1
Let’s multiply the given numbers:
1
2 ×
5
5 ×
4
2
= 1
2 ×
1
1 ×
2
1
= 2
2
Step 2
To simplif y 2
2 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 2 and 2 is 2.
Theref ore, 2
2 =
2
2
2
2
= 1
1
Step 3
Thus, the simplif ied term is 1
1 .
ID : in-8-Multiplication-of-Rational-Numbers [12]
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(4) A)
-2
5 ×
-3
4 ×
-5
4 =
-3
8
Step 1
Let’s multiply the given numbers:
-2
5 ×
-3
4 ×
-5
4
= -2
5 ×
-3
4 ×
-5
4
= -30
80
Step 2
To simplif y -30
80 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -30 and 80 is 10.
Theref ore, -30
80 =
-30
10
80
10
= -3
8
Step 3
Thus, the simplif ied term is -3
8 .
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B)
-2
4 ×
4
2 ×
3
4 ×
-3
6 =
3
8
Step 1
Let’s multiply the given numbers:
-2
4 ×
4
2 ×
3
4 ×
-3
6
= -1
2 ×
2
1 ×
3
4 ×
-1
2
= 6
16
Step 2
To simplif y 6
16 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 6 and 16 is 2.
Theref ore, 6
16 =
6
2
16
2
= 3
8
Step 3
Thus, the simplif ied term is 3
8 .
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(5) A)
-5
4 ×
2
3 ×
3
6 ×
1
4 =
-5
48
Step 1
Let’s multiply the given numbers:
-5
4 ×
2
3 ×
3
6 ×
1
4
= -5
4 ×
2
3 ×
1
2 ×
1
4
= -10
96
Step 2
To simplif y -10
96 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -10 and 96 is 2.
Theref ore, -10
96 =
-10
2
96
2
= -5
48
Step 3
Thus, the simplif ied term is -5
48 .
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B)
-4
5 ×
1
4 ×
-2
4 ×
5
5 =
1
10
Step 1
Let’s multiply the given numbers:
-4
5 ×
1
4 ×
-2
4 ×
5
5
= -4
5 ×
1
4 ×
-1
2 ×
1
1
= 4
40
Step 2
To simplif y 4
40 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 4 and 40 is 4.
Theref ore, 4
40 =
4
4
40
4
= 1
10
Step 3
Thus, the simplif ied term is 1
10 .
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(6) A)
1
4 ×
5
6 ×
-4
3 ×
-3
5 =
1
6
Step 1
Let’s multiply the given numbers:
1
4 ×
5
6 ×
-4
3 ×
-3
5
= 1
4 ×
5
6 ×
-4
3 ×
-3
5
= 60
360
Step 2
To simplif y 60
360 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 60 and 360 is 60.
Theref ore, 60
360 =
60
60
360
60
= 1
6
Step 3
Thus, the simplif ied term is 1
6 .
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B)
5
3 ×
-3
5 ×
1
6 =
-1
6
Step 1
Let’s multiply the given numbers:
5
3 ×
-3
5 ×
1
6
= 5
3 ×
-3
5 ×
1
6
= -15
90
Step 2
To simplif y -15
90 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -15 and 90 is 15.
Theref ore, -15
90 =
-15
15
90
15
= -1
6
Step 3
Thus, the simplif ied term is -1
6 .
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(7) A)
-3
3 ×
1
2 ×
-1
4 ×
2
6 =
1
24
Step 1
Let’s multiply the given numbers:
-3
3 ×
1
2 ×
-1
4 ×
2
6
= -1
1 ×
1
2 ×
-1
4 ×
1
3
= 1
24
Step 2
The HCF of 1 and 24 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 1
24 .
B)
2
2 ×
-5
5 ×
2
2 ×
3
2 =
-3
2
Step 1
Let’s multiply the given numbers:
2
2 ×
-5
5 ×
2
2 ×
3
2
= 1
1 ×
-1
1 ×
1
1 ×
3
2
= -3
2
Step 2
The HCF of -3 and 2 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 -3
2 .
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(8)ID : in-8-Multiplication-of-Rational-Numbers [20]
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B)
-4
2 ×
-5
4 ×
-4
6 ×
5
3 =
-25
9
Step 1
Let’s multiply the given numbers:
-4
2 ×
-5
4 ×
-4
6 ×
5
3
= -2
1 ×
-5
4 ×
-2
3 ×
5
3
= -100
36
Step 2
To simplif y -100
36 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of -100 and 36 is 4.
Theref ore, -100
36 =
-100
4
36
4
= -25
9
Step 3
Thus, the simplif ied term is -25
9 .
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(9) A)
-4
6 ×
5
3 ×
-3
3 =
10
9
Step 1
Let’s multiply the given numbers:
-4
6 ×
5
3 ×
-3
3
= -2
3 ×
5
3 ×
-1
1
= 10
9
Step 2
The HCF of 10 and 9 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 10
9 .
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B)
-5
6 ×
4
3 ×
-3
2 ×
3
5 =
1
1
Step 1
Let’s multiply the given numbers:
-5
6 ×
4
3 ×
-3
2 ×
3
5
= -5
6 ×
4
3 ×
-3
2 ×
3
5
= 180
180
Step 2
To simplif y 180
180 into lowest term, we need to divide the numerator and
denominator by their HCF.The HCF of 180 and 180 is 180.
Theref ore, 180
180 =
180
180
180
180
= 1
1
Step 3
Thus, the simplif ied term is 1
1 .
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(10) A)
-2
4 ×
-1
4 ×
2
4 =
1
16
Step 1
Let’s multiply the given numbers:
-2
4 ×
-1
4 ×
2
4
= -1
2 ×
-1
4 ×
1
2
= 1
16
Step 2
The HCF of 1 and 16 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 1
16 .
B)
3
4 ×
1
2 ×
-2
2 ×
-3
4 =
9
32
Step 1
Let’s multiply the given numbers:
3
4 ×
1
2 ×
-2
2 ×
-3
4
= 3
4 ×
1
2 ×
-1
1 ×
-3
4
= 9
32
Step 2
The HCF of 9 and 32 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 9
32 .
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(11)ID : in-8-Multiplication-of-Rational-Numbers [25]
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B)
-1
5 ×
-3
6 ×
1
3 =
1
30
Step 1
Let’s multiply the given numbers:
-1
5 ×
-3
6 ×
1
3
= -1
5 ×
-1
2 ×
1
3
= 1
30
Step 2
The HCF of 1 and 30 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 1
30 .
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