How to Calculate Integer Multiplication Operations

A. Integer multiplication operations

B. Commutative (exchange)

C. Associative (grouping)

D. Distributive (spread)

E. Mixed integer operations


A. Integer multiplication operations

Integers contain positive integers (+) and negative integers (-).
Formula :



Example:

a. 4 x 3 = 12

b. 2 x (-3) = -6

c. -5 x 2 = -10

d. -3 x (-7) = 21

B. Commutative (exchange)

The product of two integers is always the same.

a x b = b xa

Example:

a. 3 x (-2) = (-2) x 3 = -6

b. -4 x (-6) = -6 x (-4) = 24


C. Associative (grouping)

a x (b x c) = (a x b) x c

Example:

3 x [(-4) x 5] = 3 x (-20)
                   = -60

[3 x (-4)] x 5 = -12 x 5
                    = -60


D. Distributive (distribution)

1. Distributive of multiplication to addition

a x (b x c) = (a x b) + (a x c)

Example:

a. 4 x (3 + 2) = (4 x 3) + (4 x 2)
    4 x 5 = 12 + 8
    20 = 20

b. 3 x [(2 + (-5)] = (3 + 2) + [3 x (-5)]
    3 x (-3) = 6 + (-15)
    -9 = -9

2. Distributive of multiplication to subtraction

a x (b - c) = (a x b) - (a x c)

Example:

a. 2 x (5-3) = (2 x 5) - (2 x3)
    2 x 2 = 10 - 6
    4 = 4


b. 5 x [4- (2)] = (5x4) - [5x (-2)]
     5 x 6 = 20 - (-10)
     30 = 30

E. Mixed integer operations

In solving the mixed integer operation, the following should be considered:

1. If in a mixed operation of integers there is a count operation in parentheses, then the operation in brackets must be done first.

2. If there is an addition (+) and subtraction (-) operation, they are both equal, so do the arithmetic operation on the left first.

3. What if there are multiplication (x) and division (:) operations both of them are equal, so that the arithmetic operation on the left is done first

4. If there are multiplication (x) and division (:) operations as well as addition (+) and subtraction (-) operations then the multiplication (x) and division (:) operations are stronger, so that the multiplication (x) and division calculation operations are carried out (:) first.

Example:

a.) 21 - 6: 2 + 4 x (-5) = 21 -3 + 4 x (-5)
                                     = 21 - 3 + (-20)
                                     = 18 + (-20)
                                     = -2

b.) 6 x (12 - 7) + (-8): 2 = 6 x 5 + (-8): 2
                                        = 6 x 5 + (-4)
                                        = 30 + (-4)
                                        = 26