How Are Integers Added?


Quick Answer

Integers with the same sign are added and the sum takes the sign of the integers, while integers with different signs are subtracted and the difference takes the sign of the number with the highest absolute value. The set of integers include all the counting numbers, zero and the negatives of the counting numbers.

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Full Answer

There are several types of numbers in mathematics: counting, whole, integer, fraction, rational, irrational, real, imaginary and complex. Counting numbers include 1, 2, 3, 4, 5 and so on, while whole numbers are counting numbers including zero.

Fractions are ratios of two integers, where one integer is divided by another integer that is not zero. Rational numbers are numbers that can be expressed as a fraction, while irrational numbers are non-repeating, non-terminating numbers. Real numbers include all the rational and irrational numbers. An imaginary number is any number that when multiplied by itself gives a negative real number. Complex numbers are combinations of real and imaginary numbers.

On a number line, the integers are represented by the negative numbers, zero and positive numbers that extend infinitely in either direction. When adding integers, certain rules are followed. When adding integers having the same sign, +3 + +5 = +8. The sum of 8 takes the sign of both positive integers. In case of integers with different signs, -4 + +1 = -3. The difference of 3 takes the sign of -4, which is the integer with the larger absolute value.

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