Multiplication and Division of Integers
When We Multiply:
Example | |||
(+) × (+) | Two Positives make a Positive: | (+) | 3 × 2 = 6 |
(-) × (-) | Two Negatives make a Positive: | (+) | (−3) × (−2) = 6 |
(-) × (+) | A Negative and a Positive make a Negative: | (-) | (−3) × 2 = −6 |
(+) × (-) | A Positive and a Negative make a Negative: | (-) | 3 × (−2) = −6 |
Yes indeed, two negatives make a positive, and we will explain why, with examples! (source: https://www.mathsisfun.com/multiplying-negatives.html)
Division of Integers
Dividing integers is the opposite of multiplying integers. It is the process by which one is trying to know how many times a number is contained into another.
Example: 36÷12 =
You are trying to determine how many times 12 is contained into 36
Since 12 x 3 = 36, so 12 is contained into 36 three times.
Thus: 36 ÷ 12 = 3
Bear in mind that:
quotient × divisor = dividend
dividend ÷ divisor = quotient
dividend ÷ quotient = divisor
In other words, the product of 45 × 2 = 90
Then, dividing the product, which is 90 by 2 gives you back 45
However, dividing the product (90) by 45 gives you back 2
We can use this fact to find the rule for dividing integers
12 × 5 = 60
60 ÷ 5 = 12
12, 5, and 60 are positive, so: Positive ÷ Positive = Positive
For:
12 × -5 = -60
-60 ÷ -5 = 12
60 and 5 are negative, but 12 is positive, so Negative ÷ Negative = Positive
In the previous example, notice that -60 ÷ 5 = -12
60 is negative, 5 is positive, but 12 is negative, so: Negative ÷ Positive = Negative
Finally, consider:
-2 × – 6 = 12
12 ÷ -2 = -6
12 is positive, 2 is negative, and 6 is negative, so: Positive ÷ Negative = Negative
Take Note:
The rule for division of integers is the same for multiplying integers. Therefore, if you remember the rule for multiplying integers, you already know it for division.
The division of two integers with the same signs is positive
The division of two integers with different signs is Negative
Practice:
Comments
Unit I. Integers for 7th Grade (Bilingual Class) 15 June – 19 June
Weeks: 1 & 2
Complete your lesson notes in the Math Lesson Notebooks
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