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1.2 Order of Operations

22

The expression 53 means to use 5 as a factor 3 times.We say that 53 is the third power of 5, where 5 is called the base and 3 is called the exponent.

Here, 53 means 5 5 5 = 125.

The expression 24 means that 2 is used as a factor 4 times; that is, 24 = 2 2 2 2 = 16.

Here, 24 is the fourth power of 2.

Order of Operations

33

Just as we use periods, commas, and other punctuation

marks to help make sentences more readable, we use

grouping symbols in mathematics, such as parentheses

“( )” and brackets “[ ],” to help clarify the meaning of

mathematical expressions.

Parentheses not only give an expression a particular

meaning, they also specify the order to be followed in

evaluating and simplifying expressions.

Order of Operations

44

What is the value of 8 – 3 2?

Is it 10? Is it 2?

Or is it some other number?

It is very important that each mathematical expression have

only one value.

For this to happen, we all must not only perform the exact

same operations in a given mathematical expression or

problem but also perform them in exactly the same order.

Order of Operations

55

The following order of operations is followed by all.

Order of Operations

1. Always do the operations within parentheses or other grouping symbols first.

2. Then evaluate each power, if any. Examples:

4 32 = 4 (3 3) = 4 9 = 36

52 6 = (5 5) 6 = 25 6 = 150

Order of Operations

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3. Next, perform multiplications and divisions in the order in which they appear as you read from left to right. For example,

60 5 4 3 2

= 300 4 3 2

= 75 3 2

= 25 2

= 50

Order of Operations

77

4. Finally, perform additions and subtractions in the order in which they appear as you read from left to right.

Note

If two parentheses or a number and a parenthesis occur next to one another without any sign between them, multiplication is indicated.

By using the above procedure, we find that

8 – 3 2 = 8 – 6 = 2.

Order of Operations

88

Evaluate: 2 + 5(7 + 6).

= 2 + 5(13)

= 2 + 65

= 67

NoteA number next to parentheses indicates multiplication.In Example 1, 5(13) means 5 13.

Adjacent parentheses also indicate multiplication:(5)(13) also means 5 13.

Example 1

Add within parentheses.

Multiply.

Add.

99

If pairs of parentheses are nested (parentheses within

parentheses, or within brackets), work from the innermost

pair of parentheses to the outermost pair.

That is, remove the innermost parentheses first, remove

the next innermost parentheses second, and so on.

2 + 3[2(5-3) +4(4+2) – 3] = 2+ 3[2(2) + 4(6) – 3] =

2 + 3[4 +10 – 3] = 2 + 3[11] = 2 + 33 = 35

Order of Operations

1010

Let’s Break it Down!

http://www.flocabulary.com/pemdas/

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Section 1.2 Discussion Problems

Pg. 13-14

20. (19+8)(4+3) / 21 + (8*15) / (4*3) =

23. 12 * 9 / 18 * 64 / 8 +7 =

29. 28 – 4(2*3) + 4 – (16*8) / (4*4) =

37. 20 + (2*3)squared / 7 * 2 cubed =