MAT 040: Basic Math Learning Unit 3: Handout

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Order of Operations

1. Evaluate all calculations inside grouping symbols like parentheses, brackets, and braces first.

Work from the innermost grouping symbol to the outermost grouping symbol.

2. Evaluate exponents.

3. Evaluate all multiplications and divisions in order from left to right.

4. Evaluate all additions and subtractions in order from left to right.

Example 1

Simplify: Simplify exponent then perform multiplication.

Subtract last.

First simplify the exponent.

Next multiply 5 times 36.

Always multiply before subtracting.

Next subtract.

Answer:

Example 2

Simplify: Perform multiplication and division from

left to right.

Divide first since it comes first on the left.

Next multiply.

Answer:

Example 3

Simplify: Perform addition and subtraction from

left to right.

Subtract first since it comes first on the left.

Next add.

Answer:

MAT 040: Basic Math Learning Unit 3: Handout

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Example 4

Simplify: Perform multiplication and division from

left to right.

Multiply first since it comes first on the left.

Next divide.

Answer:

Example 5

Simplify: A number outside of parentheses

represents multiplication.

Perform calculations inside the

parentheses first.

Multiply before adding.

Multiply 4 and 6.

Next add 3 and 24.

Now multiply by the number outside

the parentheses.

Multiply 7 times 27.

Answer:

Example 6

Simplify:

Start inside the parentheses. Find 2 + 1.

Now perform the remaining calculations.

Perform division before subtraction.

Find 50 divided by 5.

Subtract last.

Answer:

MAT 040: Basic Math Learning Unit 3: Handout

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Example 7

Simplify: –

Always multiply and divide from

left to right first.

Multiply 3 times 8.

Next divide. Find 24 divided by 2.

Subtract last.

Answer:

Example 8

Simplify:

Multiply and divide from

left to right first.

Divide 18 by 3.

Multiply 6 and 3.

Multiply 18 and 3.

Add or subtract from left to right. Add 54 and 9.

Subtract.

Answer:

Grouping Symbols

There are several different grouping symbols.

Braces { }

Brackets [ ]

Parentheses ( )

Always start in the innermost grouping first and work to the outermost grouping symbol.

Inside the grouping symbols follow the order of operations: exponents, multiply and divide left to right,

and finally add and subtract left to right.

Perform operations outside the grouping symbols last.

MAT 040: Basic Math Learning Unit 3: Handout

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Example 9

Simplify: –

– Calculate the innermost grouping first, 6 – 1.

Continue with the innermost grouping, 8 + 5.

Continue inside the braces.

Calculate the exponent first.

Multiply before subtracting, so find 2 times 16.

Continue inside the braces. Find 32 – 13.

Perform the remaining calculations.

Divide before adding.

Add last.

Answer:

Example 10

Simplify:

Start inside the parentheses.

Calculate the exponent.

Continue inside the parentheses.

Multiply 4 times 3.

Inside the parentheses subtract 12 and 8.

The 2 outside the parentheses means multiply.

Always multiply and divide from left to right

before adding or subtracting.

Multiply 2 times 4.

Find 3 divided by 3.

Add and subtract from left to right.

Answer: 6

© Brenda Moore and Indian Hills Community College