Multiplication Of Integers
Multiplication Of Integers
Multiplication of Integers: The rules that govern on how to multiply and divide integers are very similar. Rules on How to Multiply Integers:
Example: Multiply the integers (+4) and (-7)
Solution: (+4) x (-7) = -28. Multiply or find the product of the absolute values (4 x 7 = 28) . Now, determine the sign of the final answer. The rule states that if the signs of the two integers are different then the final answer will be negative. Hence, -28.
Example: The opposite of ( - 2) x 7 x ( - 1 ) is __________
Solution: Multiply the absolute values (2 x 7 x 1 = 14). The product of two negative integers is positive. The opposite of 14 is (-14).
Properties of Integers under Multiplication:
Example: Verify Closure Property of (+30) by (-5).
Solution: Multiply +30 x (-5) = -150. Hence, +30, -5 and -150 are integers.
Example: Verify Commutative Property of (+10) and (-5).
Solution: Let a = +10 and b = -5. LHS = a x b = (+10) x (-5) = -50 and RHS = b x a = (-5) x (+10) = -50. Hence Verified.
Associative Property: The multiplication of integers is associative, i.e., for any three integers a, b, c, we have: a × ( b × c) = (a × b) × c.
Example: Verify Associative Property of (+9) , (-5) and (-2)
Solution: Let a = +9 , b = -5 and c = -2. LHS = a × ( b × c) = +9 x (-5 x (-2)) = +9 x (+10) = +90
and RHS = (a × b) × c = (+9 x (-5)) x (-2) = (-45) x (-2) = +90. Hence Verified.
Multiplicative Identity Property: For every integer a, we have: a × 1 = a = 1 × a. The integer 1 is called the multiplicative identity for integers. For any integer, we have a × 0 = 0 = 0 × a.
Example: Simplify: a) (-18) x 1 b) (-7) x 0
Solution: a) (-18) x 1 = (-18) b) (-7) x 0 = 0
Multiplication of a negative integer for even times gives a _________ result. | |||
| Right Option : C | |||
| View Explanation | |||
If the expression [( - 43) x 109] can also be written as [a + ( - 387 ), what is the value of 'a' ? | |||
| Right Option : B | |||
| View Explanation | |||
68 x _______ = - 68 | |||
| Right Option : C | |||
| View Explanation | |||
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