OPERATIONS OF REAL NUMBERS
Operations refer to addition, subtraction, multiplication and division.
ADDITION/SUBTRACTION OF REAL NUMBERS
a) Two real numbers with the same signs, add and use the common sign
b) Two real numbers with different signs, subtract and use the sign of the larger number
EXAMPLES:
1) -5 + (-3) = -8 (same signs, add and use the common sign)
2) 3 + (-7) = -4 (different signs, subtract and use the sign of larger number)
3) -14 + 23 = 9 (different signs, subtract and use the sign of larger number)
4) 28 + (-12) = 16 (different signs, subtract and use the sign of larger number)
5) -42 - 21 = -43 (same signs, add and use the common sign)
can also be written as -42 + (-21) = -43
6) -3/5 + 2/5 = -1/5 (different signs, subtract and use the sign of larger number)
7) -4.5 + (-3.6) + (-1.1) = -9.2 (same signs, add and use the common sign)
8) -12 - 13 + 42 - 11 + 16 + (-12) + 15
(-12-13-11-12) + (42+16+15) (group the neg numbers and pos numbers)
-48 + 73
25
NOTE: when there are grouping symbols such as the absolute value and opposites, you must simplify those first and then add/subtract.
9) 8 - (-6) (first take the opposite of -6, then add/subtract)
8 + 6 = 14
10) 4.5 + (-6.0) - (-2.3) - 12 + 2.6 - (-2.1)
4.5 + (-6.0) + 2.3 - 12 + 2.6 + 2.1 (simplify the opposites)
(4.5 + 2.3 + 2.6 + 2.1) + (-6.0 -12) (group like terms)
11.5 + (-18)
-6.5
11) |-2| + (-6) + 12 - (-3)
2 + (-6) + 12 + 3 (simplify absolute value and opposites)
11
12) -(-6) - 26 - |-14| + 34 (simplify absolute value and opposites)
6 - 26 - 14 + 34 (note: - |-14| ≠ 14)
(6 + 34) + (-26 - 14)
40 + (-40)
0
MULTIPLICATION/DIVISION OF REAL NUMBERS
a) do the indicated operation
b) two positive numbers or two negative numbers, then answer is a positive
positive number and a negative number, then answer is a negative
EXAMPLES:
1) -12 · 5 = -60
2) (5)(-4)(-7) = 140
3) -1/2(-2/3)(-1) = -1/3 (recall how to multiply fractions)
4) (4/5) ÷ (-3/10) = -6/25 (recall how to divide fractions)
5) (-3)(-7)|-10| (this expression reads as -3 times -7 times the absolute value of -10)
(-3)(-8)(10) = 240 (simplify the absolute value, then multiply)
MORE EXAMPLES
The following examples will include all four operations.
Evaluate each expression:
1) -5 + (-3) - 6 2) -5(-3)(-6) 3) -16 ÷ |-10| 4) 15/32 · -4/5
5) (-2/5)(-1/3)(5)(-1/2) 6) -2/5 + 1/3 - 5 + 1/2
7) |-7/9| - (-5/6) + 1/3 8) |-11|(-2)|-10|
Answers:
1) -5 + (-3) - 6 = -14 (add/subtract)
2) -5(-3)(-6) = -90 (multiply)
3) -16 ÷ |-10| (simplify absolute value)
-16 ÷ 10 = -8/5 or -1 3/5 or -1.6 (divide)
4) 15/32 · -4/5 = -3/8 or -0.375 (multiply)
5) (-2/5)(-1/3)(-5)(-1/2) = 1/3 or 0.33 (multiply)
6) -2/5 + 1/3 - 5 + 1/2 = -4 17/30 or -137/30 or - 4.5667 (add/subtract)
7) |-7/9| - (-5/6) + 1/3 (simplify absolute value and opposites)
7/9 + 5/6 + 1/3 = 1 17/18 or 35/18 or 1.944 (add/subtract)
8) |-11|(-2)|-10| (simplify absolute value)
11· (-2) · 10 = -220 (multiply)