the sum and difference of two positive integer is 15 and 9 respectively. find the smaller number
Answers
(+) × (+) = + Plus x Plus = Plus
(+) x (-) = – Plus x Minus = Minus
(-) × (+) = – Minus x Plus = Minus
(-) × (-) = + Minus x Minus = Plus
When two positive integers are multiplied then the result is positive.
When two negative integers are multiplied then also result is positive.
But when one positive and one negative integer is multiplied, then the result is negative.
When there is no symbol, then the integer is positive.
Addition of Integers
Addition of integers means there are three possibilities. They are:
Addition between two positive numbers,
Addition between two negative numbers; and
Addition between a positive number and a negative number.
Addition Rules for Integers
Type of Numbers Operation Result Example
Positive + Positive Add Positive (+) 10 + 15 = 25
Negative + Negative Add Negative (-) (-10) + (-15) = -25
Positive + Negative* Subtract Positive (+) (-10) + 15 =5
Negative + Positive* Subtract Negative (-) 10 + (-15)= -5
Whenever a positive number and a negative number are added, the sign of the greater number will decide the operation and sign of the result. In the above example 10 + (-15) = -5 and (-10) + 15 =5; here, without sign 15 is greater than 10 hence numbers will be subtracted and the answer will give the sign of the greater number.
Alternatively, to find the sum of a positive and a negative integer, take the absolute value (“absolute value” means to remove any negative sign of a number, and make the number positive) of each integer and then subtract these values. Take above example, 10 + (-15); absolute value of 10 is 10 and -15 is 15.
⇒ 10 – 15 = -5
Thus we can conclude the above table as follow:
Addition of two positive integers always gives a positive-sum.
Addition of two negative integers always gives a negative-sum.
Addition of a positive and a negative integer give either a positive or negative-sum depending on the value of the given numbers.
Note: The sum of an integer and it’s opposite is always zero. (For example, -5 + 5= 0)
Subtraction of Integers
Like addition, subtraction of integers also has three possibilities. They are:
Subtraction between two positive numbers,
Subtraction between two negative numbers; and
Subtraction between a positive number and a negative number.
For the ease of calculation, we need to renovate subtraction problems into addition problems. There are two steps to this:
Convert the subtraction sign into an addition sign.
After converting the sign, take the inverse of the number which comes after the sign.
Once the transformation is done, follow the rules of addition given above.
For example, find the value of: (-5) – (7)
Step 1: Change the subtraction sign into an addition sign
⇒ (-5) + (7)
Step 2: Take the inverse of the number which comes after the sign
⇒ –5 + (-7) (opposite of 7 is -7)
⇒ –5 + (-7) = -12 [Add and put the sign of greater number]