Multiplication of two or more than two integers

Multiplication of two or more than two integers

Multiplication of Integers is very simple.

Remember only one rule to multiply integers correctly.

Rule: (1) Multiply the given integers without taking their signs into consideration.

(2) Now, count the number of negative signs (–). This means count the number of negative integers.

(a) If total number of negative signs is equal to odd number, then product is negative.

(b) And if total number of negative signs (–) is equal to even number, then their product is positive (+).

(c) If number of negative signs (–) is equal to zero (0). This means if there is no negative sign and all signs are positive, then their product will be positive.

[Here negative signs means negative integers.]

Precisely:

Count the number of negative integers. If number of positive integers (i.e. positive signs) is equal to odd number, then product will be a negative integers, otherwise product will be positive integer.

In other words, if number of negative integers is an odd number, then assign negative sign to their product, otherwise assign a positive sign to their product.

Example::

(a) Suppose number of negative integers = 1, 3, 5, 7, 9, 11, ????

Then, their product will be a negative integer.

Otherwise, in all case, i.e. if number of negative integers = 0, 2, 4, 6, 8, 10, ????.

Then their product will be a positive integer.

Example (1) 2 × 4 × 3

Solution:

Step: 1: Multiply the given integers without taking their sign into consideration.

2 × 4 × 3 = 24

Step: 2: Now, count the number of negative integers.

Here, number of negative integers = 0.

[This means number of negative sign = 0 or there are no negative integers.]

Since, number of negative integers = 0, thus, product will be positive.

Thus,

2 × 4 × 3 = 24 Answer

Example (2) 2 × 4 × 3 × (– 2)

Solution:

Step (1) Multiply the given number without taking their sign into consideration

2 × 4 × 3 × (– 2) = 48

Step (2) Count the number of negative integers.

Here, number of negative integers = 1

Since, number of negative integers is equal to one (1), which is an odd number.

This means number of negative integers is an odd number, thus their product is negative.

Thus, assign a neative sign to their product.

2 × 4 × 3 × (– 2)

= – 48 Answer

Multiplication of Integers Exercise 2

Question: (1) Solve 2 × (–4)

Solution:

Given, 2 × (–4)

Step: 1. Multiply the given integers without taking their sign into consideration.

2 × (–4) = 8

Step: 2. Now, count the number of negative integers.

Here number of negative integers = 1

Since 1 is an odd number, thus product will be negative.

Now, assign a negative sign to the product.

Thus, 2 × (–4) = –8 Answer

Question: (2) – 4 × 5 × (– 4)

Solution:

[Strategy to solve: (1) multiply the given integers without taking their sign into consideration.

(2) Count the number of negative integers. If number of negative integers is an odd number, then assign negative sign to the product otherwise assign positive sign to the product.]

Given, – 4 × 5 × (– 4)

Here, number of negative integers = 2. Which is an even number. Thus product will be positive integer.

Thus,

– 4 × 5 × (– 4)

= 80 Answer

Question: (3) – 5 × 5 × (– 4)

Solution:

[[Strategy to solve: (1) multiply the given integers without taking their sign into consideration.

(2) Count the number of negative integers. If number of negative integers is an odd number, then assign negative sign to the product otherwise assign positive sign to the product, that is if number of negative integers is equal to even number or zero, then assign positive sign to the product.]]

Given, – 5 × 5 × (– 4)

Here, number of negative integers is equal to 2. Since 2 is an even number thus, product will be positive integer.

Thus, – 5 × 5 × (– 4)

= 100 Answer

Question: (4) – 5 × (–5) × (– 4)

Solution:

Given, – 5 × (–5) × (– 4)

Step (i) Multiply the given integers without taking their sign into considerations.

Step (ii) count the number of negative integers. If the number of negative integers is an odd number, then product will be negative integer. And if number of negative integer is an even number or zero, then product will be positive integer.

Here, number of negative integers = 3.

Since, 3 is an odd number, thus product (result of product) will be negative integer.

Thus,

– 5 × (–5) × (– 4)

= –100 Answer

Question: (5) – 6 × (–5) × (– 4)

Solution:

Given, – 6 × (–5) × (– 4)

Here, Number of negative integers = 3

Since, number of negative integers is an odd number, thus product will be negative integer.

– 6 × (–5) × (– 4)

= –120 Answer

Question: (6) 6 × 5 × 4 × 10

Solution:

Given, 6 × 5 × 4 × 10

Here, number of negative integers = 0, thus product of the given integer will be a positive integer.

Thus, 6 × 5 × 4 × 10

= + 1200

For convenience positive sign is not given to the positive integer.

Thus, 6 × 5 × 4 × 10 = 1200 Answer

Question (7) – 5 × 4 × (–1) × (–1) × (–1)

Solution:

Given, – 5 × 4 × (–1) × (–1) × (–1)

Here, Number of negative integers = 4.

Since, 4 is an even number, thus product of four even number will be positive integer.

Thus, – 5 × 4 × (–1) × (–1) × (–1)

= + 20

For convenience positive sign is not given to a positive integer.

= 20 Answer

Question: (8) – 5 × (– 4) × (–1) × (–1) × (–1)

Solution:

Given, – 5 × (– 4) × (–1) × (–1) × (–1)

Here, number of negative integers = 5

Since, number of negative integer is an odd number, thus their product will be a negative integer.

– 5 × (– 4) × (–1) × (–1) × (–1)

= – 20 Answer

Question (9) 9 × 2 × (–2)

Solution:

Given, 9 × 2 × (–2)

Here, number of negative integers = 1

Since, 1 one is an odd number, thus product will have negative sign, that is product will be a negative integer.

Thus, 9 × 2 × (–2)

= – 36  Answer

Question (10) – 1 × 20 × (–1)

Solution:

Given, – 1 × 20 × (–1)

Here, number of negative integers = 2

Since number of negative integers (2) is an even number, thus their product will be a positive integer

Thus, – 1 × 20 × (–1)

= 20 Answer

Question (11) 2× (–1) × (–1) × 5 × (–1) × (–5)

Solution:

Given, 2× (–1) × (–1) × 5 × (–1) × (–5)

Here number of negative integers = 4

We know that when number of negative integers is an even number, then result of their multiplication will be a positive integer.

Here, since number of negative integers is equal to 4, which is an even number, thus the product will be a positive integer.

Thus,

2× (–1) × (–1) × 5 × (–1) × (–5)

= 50 Answer

Question (12) – 5 × ( – 2 ) × (– 1) × (– 1) ×(– 1) × (– 2)

Solution:

Given,

– 5 × ( – 2 ) × (– 1) × (– 1) ×(– 1) × (– 2)

Here, number of negative integers = 6

We know that when number of negative integers is an even number, then result of their multiplication will be a positive integer.

Here, since number of negative integers is equal to 6, which is an even number, thus the product will be a positive integer.

Thus, – 5 × ( – 2 ) × (– 1) × (– 1) ×(– 1) × (– 2)

= 20 Answer

Question (13) – 6 × 2 × (–1) × (–1) × (–2) × (–5)

Solution:

Given, – 6 × 2 × (–1) × (–1) × (–2) × (–5)

Here, total number of negative integers = 5

We know that when number of negative integers is an odd number, then result of their multiplication will be a negative integer.

Here, since number of negative integers is equal to 5, which is an odd number, thus the product will be a negative integer.

Thus,

Given, – 6 × 2 × (–1) × (–1) × (–2) × (–5)

= – 120 Answer

Question (14) –1 × (–1) × (–5) × (–1) × 5 × (–5) × (–3) × (–4)

Solution:

Given, –1 × (–1) × (–5) × (–1) × 5 × (–5) × (–3) × (–4)

Here, number negative integers = 7

We know that when number of negative integers is an odd number, then result of their multiplication will be a negative integer.

Here, since number of negative integers is equal to 7, which is an odd number, thus the product will be a negative integer.

Thus,

Given, –1 × (–1) × (–5) × (–1) × 5 × (–5) × (–3) × (–4)

= – 1500 Answer

Question (15) –2 × (–1) × (–4) × (–5)

Given,

–2 × (–1) × (–4) × (–5)

Here, number of negative integers = 4

We know that when number of negative integers is an even number, then result of their multiplication will be a positive integer.

Here, since number of negative integers is equal to 4, which is an even number, thus the product will be a positive integer.

Thus,

–2 × (–1) × (–4) × (–5)

= 40 Answer

Question (16) 2 × 1 × 3 × 1

Solution:

Given, 2 × 1 × 3 × 1

Here number of negative integers = 0

We know that when number of negative integers is equal to zero, then result of their multiplication will be a positive integer.

Here, since number of negative integers is equal to 0, thus the product will be a positive integer.

Thus, 2 × 1 × 3 × 1

= 6 Answer

Question (17) 2 × 1 × 3 × (–1)

Solution:

Given, 2 × 1 × 3 × (–1)

Here, number of negative integers = 1

We know that when number of negative integers is an odd number, then result of their multiplication will be a negative integer.

Here, since number of negative integers is equal to 1, which is an odd number, thus the product will be a negative integer.

Thus, 2 × 1 × 3 × (–1)

= – 6 Answer

Question (18) 2 × (–1) × 3 × (–1)

Given, 2 × (–1) × 3 × (–1)

Here, number of negative integers = 2

We know that when number of negative integers is an even number, then result of their multiplication will be a positive integer.

Here, since number of negative integers is equal to 2, which is an even number, thus the product will be a positive integer.

Thus, 2 × (–1) × 3 × (–1)

= 6 Answer

Question (19) 3 × (–5) × 3 × 1

Solution:

Given, 3 × (–5) × 3 × 1

Here, number of negative integers = 1

We know that when number of negative integers is an odd number, then result of their multiplication will be a negative integer.

Here, since number of negative integers is equal to 1, which is an odd number, thus the product will be a negative integer.

Thus, 3 × (–5) × 3 × 1

= – 45 Answer

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