Some expressions have more than one operation. The value of the expression depends on the order in which the operations are evaluated. What is the value of 9 ⋅ 5 + 4?
Method 1
9 ⋅ 5 + 4 = 45 + 4 Multiply 9 and 5.
= 49 Add
45 and 4.
Method 2
9 ⋅ 5 + 4 = 9 ⋅ 9 Add
5 and 4.
= 81 Multiply
9 and 9.
Is the answer 49 or
81? The values are different because we multiplied and added in different
orders in the two methods. To find the correct value of the expression, follow
the order of operations.
|
Order of |
1.
Find the values
of expressions inside grouping symbols, such as parentheses ( ), brackets [
], and as indicated by fraction bars. 2.
Do all
multiplications and/or divisions from left to right. 3.
Do all
additions and/or subtractions from left to right |
According to the order of operations, do multiplication and
then
addition. So, the value of the expression in Method 1 is correct. The value
of the expression is 49.
Example
Finance Link
1. As a
16-year old, Trent Eisenberg ran his own consulting company called F1
Computer. Suppose he charged a flat fee of $50, plus $25 per hour. One day
he worked 2 hours for one customer and the next day he worked 3 hours for the
same customer. Find the value of the expression 50 + 25 (2 + 3) to find the total amount of money he earned.
Source: Scholastic
Math
Alternative Solutions :
50 + 25(2 + 3) = 50 + 25(5) Do
the operation in parentheses first.
= 50 + 125 Multiply 25 and 5.
= 175 Add 50 and 125.
Trent earned $175.
In algebra, statements that are
true for any number are called properties. Four properties of equality are listed in the
table below.
|
Property of Equality |
Symbols |
Numbers |
|
Substitution |
If a =
b, then a may be replaced by b |
If 9 + 2 = 11, then 9 + 2 may be replaced by
11. |
|
Reflexive |
a = a |
21 = 21 |
|
Symmetric |
If a =
b, then b = a |
If 10 = 4 + 6, then 4 + 6 = 10 |
|
Transitive |
If a +
b and b = c, then a = c. |
If 3 + 5 = 8 and 8 = 2(4), then 3 + 5 = 2(4). |
When two or more sets of grouping
symbols are used, simplify withinbthe innermost grouping symbols first.
Example
2. Find the value of 5[3 – (6 ÷ 2)] +
14. Identify the properties used.
Alternative Solutions :
5[3 – (6 ÷ 2)] + 14
= 5[3 – 3] + 14 Substitution
Property of Equality
= 5(0)
+ 14 Substitution Property of Equality
= 0
+ 14 Multiplicative
Property of Zero
= 14 Additive Identity
You can also apply the properties
of numbers to find the value of an algebraic expression. This is called evaluating an expression.
Replace the variables with known values and then use the order of operations.
Example
Evaluate each expression if a = 9 and b = 1.
Sumber
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