Arithmetic Expression
Given an arithmetic
expression without parentheses we perform operations moving from left to right in the following order:
| 1. Multiply or Divide
|
| 2. Add or Subtract
|
Example:
Convert the following expression into a number.
Solution:
- Perform multiplication and division.
|
- Perform addition and subtraction
|
-
Click on the following interactive demo to create more examples.
If an expression has
non-nested parentheses, this is, there is just one set of
parentheses.
The following steps must be used.
- 1.
-
Calculate the value of the
expression within the parentheses.
|
- 2.
-
Multiply and Divide.
|
- 3.
- Add and Subtract.
|
Example:
Convert the following expression into a number.
| 32-(5-68+15)-3×(5-12+40÷8) |
Solution:
- 1.
-
Calculate the value of the
expression within the parentheses.
| 32-(5-68+15)-3×(5-12+40÷8) |
-
|
- 2.
-
Multiply and Divide.
|
- 3.
- Add and Subtract.
|
-
Click on the following interactive demo to create more examples.
If a set of parentheses
lies within another set of parentheses, we eliminate the
interior parentheses first we repeat the same process for
the expression within parentheses until we can convert the
expression into a number.
Example 1.
Convert the following expression into a number.
Solution:
- 1.
- Obtain the value of
the expression within interior parentheses.
|
12 - 4×(5
- (11 - 12) + 7)) |
|
- 2.
-
Calculate the value of the
expression within exterior parentheses.
|
Example 2.
Convert the following expression into a number.
| -14 -
(5×(7-6
÷ 3+(-6-5+3)
) -3×(5
-(11×2-17)
- (15-7))) |
Solution:
- 1.
-
Calculate the value of the expression within internal
parentheses.
|
-14 -(5×(7-6
÷ 3+(-6-5+3)
) -3×(5-(11×2-17)
- (15-7))) |
|
-14 -
(5×(7-6
÷ 3+(-8)
) -3×(5
-(22-17) -
(8))) |
|
-14 -
(5×(7-2-8
) -3×(5
-5 - 8)) |
|
- 2.
- Calculate the value of the expression within
the next set of parentheses.
|
-14 -
(5×(7-2-8
) -3×(5
-5 - 8)) |
-
|
- 3.
- Calculate the value of the expression within
the next set of parentheses.
|
-
Sometimes there are
exercises where we found square brackets [ ] or round
bracket { } instead of parentheses ( ), but the way to solve
these exercises is the same just replace the brackets for
parenthesis .
|