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
If '/' is replaced by 'X' , then find the correct value of the following problem. (-2)/3X(-4)/1=?
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| Right Option : A | |||
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| Right Option : C | |||
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Multiplying a negative integer for odd times gives a _______ result. | |||
| Right Option : B | |||
| View Explanation | |||
Students / Parents Reviews [20]
The experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confidence to overcome competitive exams. One of the best institutes for secondary education.
Aman Kumar Shrivastava
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Cheshta
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8thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thThird consective year,my ward is in Abhyas with nice experience of admin and transport support.Educational standard of the institute recumbent at satisfactory level. One thing would live to bring in notice that last year study books was distributed after half of the session was over,though study ...
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Archit Segal
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Shreya Shrivastava
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