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Q: Why is it that when subtracting an integer gives the same result as adding the opposite?

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The result of adding and integer and its opposite is negation. A + (-A) = 0 For all real integers. It has the effect of adding 0 to a sum. Example: 32 + 16 + (-16) + 5 = 37 = 32 + 0 + 5.

A rational number is always the result of dividing an integer when the divisor is nonzero.

When subtracting one fraction to another, one or both fractions are renamed so that they have the same denominators. Then the result of the subtraction is the equal to the subtraction of the numerators divided by the common denominator.

Just multiply 209 by any integer. The result is - by definition - a multiple of 209.

Divide 7 into 291. If the result is an integer, 7 is a factor.

Related questions

adding its opposite?

Zero

The result of adding and integer and its opposite is negation. A + (-A) = 0 For all real integers. It has the effect of adding 0 to a sum. Example: 32 + 16 + (-16) + 5 = 37 = 32 + 0 + 5.

Difference. A sum is the result of adding two numbers, and a difference is the result of subtracting two numbers.

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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.

Yes because you are always adding.

Subtracting a negative is like adding a positive; the result will be positive.

All integers belong to the set {..., -2, -1, 0, 1, 2, ...}. The absolute value of any integer results in a whole number {0, 1, 2, ...}. Adding and subtracting integers always results in an integer. Multiplying integers always results in an integer. Dividing integers can sometimes not result in an integer.

It doesn't always. 3 - (-3) = 6

Adding a negative integer is like subtracting a positive one. If you accept that 7 - 7 = 0 (because anything minus itself equals zero) then it stands to reason that 7 + -7 would equal zero as well.

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