Multiplication of Rational Numbers Class 8...Class 8 Multiplication of Rational Numbers For more...

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:

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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:

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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:

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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 .

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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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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 .

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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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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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