1) When adding numbers of the same sign, we add their absolute values, and give the result the same sign.
2 + 5.7 = 7.7
(-7.3) + (-2.1) = -(7.3 + 2.1) = -9.4
(-100) + (-0.05) = -(100 + 0.05) =
2) When adding numbers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the number with the larger absolute value.
7 + (-3.4) = ?
Subtracting the smaller from the larger gives 7 - 3.4 = 3.6, and since the larger value was 7, we give the result the same sign as 7, so 7 + (-3.4) = 3.6.
8.5 + (-17) = ?
Subtracting the smaller from the larger gives 17 - 8.5 = 8.5, and since the larger value was 17, we give the result the same sign as -17, so
8.5 + (-17) = -8.5.
-2.2 + 1.1 = ?
Subtracting the smaller from the larger gives 2.2 - 1.1 = 1.1, and since the larger value was 2.2, we give the result the same sign as -2.2, so
-2.2 + 1.1 = -1.1.
6.93 + (-6.93) = ?
Subtracting the smaller from the larger gives 6.93 - 6.93 = 0. The sign in this case does not matter, since 0 and -0 are the same. Note that 6.93 and -6.93 are opposite numbers. All opposite numbers have this property that their sum is equal to zero. Two numbers that add up to zero are also called additive inverses.
Subtracting Positive and Negative Numbers
Subtracting a number is the same as adding its opposite.
In the following examples, we convert the subtracted number to its opposite, and add the two numbers.
7 - 4.4 = 7 + (-4.4) = 2.6
22.7 - (-5) = 22.7 + (5) = 27.7
-8.9 - 1.7 = -8.9 + (-1.7) = -10.6
-6 - (-100.6) = -6 + (100.6) = 94.6
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