Study Guide and Notes: Order of Operations



Study Guide and Notes: Order of Operations

If your class were given the following problem to simplify, would everyone get the same answer? 30 - 12 ÷ 2 + 4 · 3 - 5

Some possible answers may be 34, 16, 4, or 31.

We can arrive at a variety of answers because there is confusion as to which operations should be done in what order. Sometimes symbols of inclusion (parentheses or brackets) are used to group the numbers together in a specific arrangement to help. To avoid confusion and to assure that we all get the same answer, we use the order of operations shown below:

Example #1. 30 - 12 ÷ 2 + 4 · 3 - 5 =

Since there are no parentheses or exponents, using

“pemdas” we would begin by doing multiplication

and division in order left to right. Leave all other

operations alone. Let’s group what we need to do.

30 - (12 ÷ 2) + (4 · 3) - 5 = 30 – 6 + 12 – 5

Next we will do the addition and subtraction in order

left to right. The steps are underlined in order.

30 – 6 + 12 – 5 =

24 + 12 - 5 =

36 – 5 = 31

Evaluate each expression. Check with a calculator .

1. 12 ÷ 4 + 2 2. 62 ÷ (3 + 9) + 2(5+3) 3. [pic]

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|1. 3² + 5 · 6 |2. 2³ + 6 x 3 ÷ 2 |

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|3. (7 + 8)² - 6 |4. 4 + 3 · 6 - 2² |

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After solving each problem and showing your work, you are to pick one of the problems and explain in at least three sentences on how you derived at your answer.

Order of Operations Homework

Apply the order or operations to each problem solving situation.

1. Javier has plans to take his younger siblings and his grandparents to a matinee at the local movie theater. The full adult price for tickets is $9.00, the price for a child’s ticket is $7.50, and the discounted price for a senior citizen ticket is $5.25. Javier counts as an adult, his two siblings count as children, and his two grandparents receive the senior citizen discount. Represent and evaluate this situation using a single number sentence.

2. Jasmine owned 120 acres of land that she divided evenly between herself and her 3 siblings. After she divided the land she purchased 11 more acres and then sold 5 acres. Represent and evaluate this situation using a single number sentence.

3. Yvonne is taking two of her sisters to the movies, three of her younger cousins to the bowling alley, and her aunt to the skating rink. Movie tickets cost $9.50 each, admission to the bowling alley is $3.25, and admission to the skating rink is $5.75 per person. Assume that Yvonne is attending each of these venues as well. Represent and evaluate this situation using a single number sentence.

In your math book Pgs. 12-13 #10-28 even

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Order of Operations ( PEMDAS is a special acronym to help you remember)

1. Simplify expressions inside grouping symbols. (parentheses)

2. Simplify or evaluate any terms raised to powers. (exponents)

3. Do multiplication and division operations in order as you come to them from left

to right. (multiply, divide)

4. Finally, do all addition and subtraction operations in order as you come to them

from left to right. (add, subtract)

* Notice the words in the parentheses at the end of the lines make “pemdas”.

Example #2.

(8 + 4) ÷ ( 10 – 6) + 52

We begin with parentheses: 12 ÷ 4 + 52

Next evaluate the exponent term 12 ÷ 4 + 25

Now do multiplication and division in order 3 + 25

Finally, add and subtract in order 28

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