I. Calculating an algebraic sum
A. From left to right
In general, we calculate from left to right.Example: To work out (-2) + (-1.5) - (-0.3), first calculate (-2) + (-1.5), then subtract (-0.3) from the result.
We can present the calculations in the following manner, showing one stage of the calculation on each line:
A = (-2) + (-1.5) - (-0.3)
A = (-3.5) - (-0.3)
A = (-3.5) + (+0.3)
A = -3.2
B. By changing the order of the terms
It is possible to change the order of the terms in order to make calculations easier.Example with two terms:
B = (-24.8) - (-32.5) + (+24.8)
B = (-24.8) + (+24.8) - (-32.5)
B = 0 + (+32.5)
B = +32.5
II. Giving a simplified notation of an algebraic sum
A. Rules
1. For positive numbers, writing the + sign and brackets is optional.2. In a sum, if the first term is negative, the brackets are optional.
3. Adding a number is the same as subtracting its opposite (and subtracting a number is the same as adding its opposite).
B. Examples with two terms
(+7) - (+2) can be written 7 - 2, according to rule 1.We write: (+7) - (+2) = 7 - 2 = 5.
(-3) + (+1) can be written (-3) + 1, according to rule 1, then -3 + 1, according to rule 2.
We write: (-3) + (+1) = -3 + 1 = -2.
(+1) + (- 4) can be written (+1) - (+4), according to rule 3, then 1 - 4, according to rule 1.
We write: (+1) + (- 4) = 1 - 4 = -3.
C. Generalization
We want to simplify how the following expression is written:E = (-2) + (+3) + (-4) - (+5) - (-6).
This gives us:
E = (-2) + (+3) - (+4) - (+5) + (+6), according to rule 3.
E = -2 + 3 - 4 - 5 + 6, according to rule 2.
In practice and for speed, we can use the following rules for rewriting notation:
III. Calculating an expression with more than one set of brackets or parentheses
Start by completing the calculations inside the innermost brackets or parentheses.Examples with two terms:
C = (- 5) - ((-2) + (+7))
C = (-5) - (+5) = (-5) + (-5) = -10
D = [(-1.2) - (-2)] - [3 - (7.1 - (-8.5) + (-3)]
Using simplified notations:
D = [-1.2 + 2] - [3 - (7.1 + 8.5 - 3)]
D = 0.8 - [3 - 12.6]
D = 0.8 - [-9.6]
D = 0.8 + 9.6
D = 10.4
Read more:
Applying the Distributive Law
Calculating a Numerical Expression (1)
Determining the Common Factors of Two Integers
Recognizing a Proportional Relationship
Rounding to the Nearest Unit
Writing a Numerical Expression That Corresponds to a Sequence of Operations