Math and Arithmetic

# Why you add an integer's opposite when you are subtracting integers?

012 ###### 2017-11-27 15:59:46

Because that is how the opposite of a number is defined.

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## Related Questions   adding and subtracting integers is when you add and minus 2 numbers Some do, some don't. The operations are equivalent and people do what they are more comfortable with. -You must memorize -To add 2 integers with different signs, find the difference of their absolute value -To subtract an integer, add it's opposite While solving problems with large integers, don't always rely on the number line. Using integer arithmetic we can solve the problem of large integer. We need a rule for subtracting integers and the rule is: Rule: To subtract an integer, add its opposite. When adding negative integers, you subtract. (2+-1=1) When subtracting negative integers, you add. (2--3=5)  Subtracting an integer is the same as adding the additive inverse. In symbols: a - b = a + (-b), where "-b" is the additive inverse (the opposite) of b.  To add two integers with opposite signs . . . -- Ignore the signs, and write the difference between the two numbers. -- Give it the same sign as the larger original number has. Adding two numbers with different signs means subtracting the two absolute integers (without sign) and vice versa. The subtacting integers is EWAN ko hahahah!! Integers are whole numbers, both positive and negative. Therefore, adding and subtracting integers would be adding and subtracting whole numbers. Examples: 8+2 -8+2 8-2 -8-2 Subtracting an integer is the same as adding its opposite.Examples:In the following examples, we convert the subtracted integer to its opposite, and add the two integers.7 - 4 = 7 + (-4) = 312 - (-5) = 12 + (5) = 17-8 - 7 = -8 + (-7) = -15-22 - (-40) = -22 + (40) = 18Note that the result of subtracting two integers could be positive or negative. Adding IntegersTo add integers, one must consider the following two rules to be a successful.If you want to think of it on the number line you start from 0 and when you add a positive number you go that much to the right, and when you add a negative number you go that much to the left. When adding two positive integers, just add like normal. When adding one positive integer, and one negative integer, it is like subtracting a positive number from a positive number. When adding two negative integers, it is like subtracting a positive number from a negative number. Two integerss add to zero when their absolute values are equal and they have opposite signs. Adding integers, if they have the same sign, add their absolute values and keep the same sign. Subtracting, change the sign of the 2nd number and the add using rules of addition. Multiplying and dividing, Divide the absolute values, if the signs are the same the answer is positive, if the signs are different the answer is negative. ADDING: same sign, add and keep that sign. opposite sides, subtract their absolute values and use the sign of the number with the larger absolute value SUBRTRACTING: change the sign of the subtrahend (2nd number) then ADD using rules above. Because of the definition of addition and subtraction. When looking at a real number line: when you add you move to the left or up, when you add the opposite of a number you move in the opposite direction.  Integers are the "counting numbers" and their negative counterparts, and zero. Opposite integers are the pairs of integers that have the same absolute value, or, in other words, are the same distance from zero. 10 and -10 are opposite integers. 43 and -43 are opposite integers. It's just that simple.   I would think that the commonality of adding and subtracting integers is that the answer itself will always be an integer. In other words, the answer is always gonna be a "whole number".

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