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 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Order of Operations

When an expression contains more than one operation, we must decide which operation to carry out first. To do so, we use the following procedure.

Procedure

To Use the Order of Operations to Simplify an Expression

Step 1 Perform operations inside grouping symbols (such as parentheses), starting with the innermost set of grouping symbols.

Step 2 Simplify exponents, square roots, and absolute values.

Step 3 Multiply or divide, working in order from left to right.

Step 4 Add or subtract, working in order from left to right.

The grouping symbols referred to in Step 1 include the following:

 Symol Name Example ( ) parentheses 6 Ã· (2 + 1) = 6 Ã· 3 = 2 [ ] brackets 12 - [8 - (4 - 1)] = 12 - [8 - 3] = 12 - 5 = 7 fraction bar |  | absolute value 3 Â· |1 - 5 | = 3 Â· |-4| = 3 Â· 4 = 12 radical symbol

Example 1

Find 5 - 62 Ã· 2 - (9 - 5) Â· 3

 Solution 5 - 62 Ã· 2 - (9 - 5) Â· 3 Step 1 Perform operations inside grouping symbols. = 5 - 62 Ã· 2 - 4 Â· 3 Step 2 Simplify exponents, square roots, and absolute values. = 5 - 36 Ã· 2 - 4 Â· 3 Step 3 Multiply or divide, working in order from left to right. = 5 - 18 - 12 Step 4 Add or subtract, working in order from left to right. = -25
So, the result is -25.

Example 2

Find:

 Solution Step 1 Perform operations inside grouping symbols. Step 2 Simplify exponents, square roots,and absolute values. = 3 + 16 Ã· 2 Step 3 Multiply or divide, working in order from left to right. = 3 + 8 Step 4 Add or subtract, working in order from left to right. = 11
Thus, the result is 11.

Example 3

Find 20 Ã· 2 [1 - (8 - 12)]

 Solution 20 Ã· 2 [1 - (8 - 12)] Step 1 Perform operations inside grouping symbols, starting with the innermost grouping symbol. First, simplify (8 - 12). Now simplify [1 - (-4)]. = 20 Ã· 2[1- (-4)]= 20 Ã· 2[5] = 20 Ã· 2 Â· 5 Step 2 Simplify exponents, square roots, and absolute values. There are none to simplify. Step 3 Multiply or divide, working in order from left to right. First, simplify 20 Ã· 2. Now simplify 10 Â· 5. = 10 Â· 5 = 50
Therefore, the result is 50.