Order of Operations What to do first?????

Presentation 3

When a problem involves more than one operation, we use this order to simplify expressions:

• First, grouping symbols; and you must always simplify expressions with exponents before you can calculate with them.

• Next, multiplication OR division as you come to it reading from left to right.

• Last, addition OR subtraction as you come to it from left to right

Aunt Sally Straightened Out• Please (P stands for parentheses and other

grouping symbols)• Excuse (E stands for exponents)• My Dear (M and D for multiplication and division

as you reach them reading from left to right)• Aunt Sally (A and S for addition and subtraction

as you reach them reading from left to right)

Some people just remember PEMDAS

Parentheses and other Grouping Symbols Change Things.

If there are symbols in the expression that group operations, do those first. For instance, try this problem (the parentheses group (5 + 2). Click on your answer choice. Be sure your sound is on!!

)25(9

6 2

Work these examples on your paper:

4)312(

)46()32(

9 + 4

13

5 – 2

3

Parentheses are not the only grouping symbols!

Try these problems. Choose the correct answer and you will hear the applause. If you don’t hear the applause, you need to try again!

3125

643122

4 8

20 22 38

3125

8

35

symbols) grouping are (radicals 95

22

112

652

first onesinnermost thedo

symbols, nested"" are re when the67122

643122

Absolute value symbols are also grouping symbols as are fractions bars

(which indicate division).Try these:

823312

782

2)53(42

1 32 20

6 1/5 2

Note: the exponent must be applied before one can proceed! We can calculate with 4, but not with 22

1

14312

)86(312

25

10784

284

823312

782

2)53(42

Test Yourself

)4(532

12)4(3)2)(4(8

How did you do?

46

]23[2

]203[2

)4(532

11

164

1212)2)(2(

12)4(3)2)(4(8

If you did not work these correctly, follow your work step by step matching it against these solutions to find your error. Then try again on the next slide.

Try this

64981

)8(1326

2

2(8)

16

25

241

648181

Real Life • This is an important formula. It is referred to by financial professionals as

the Future Value formula.•

• A is the future value (accumulated amount)• m is the amount of a single payment• n is the number of payments per year (same as the number of

compounding periods)• r is the annual rate of interest• t is the time in years

nrnr

mA

nt

11

Note: You will need a calculator to help with the arithmetic! If you don’t have one, you can check on the appropriate slide for values you will need.

The real life problem

Suppose you are 30 years old and can afford to save $100 a month. Your bank is paying an interest rate of 4% compounded quarterly (every 3 months). If you are faithful to put in your $300 each quarter, how much money will you have accumulated by the time you are 50?

First, replace all the variables (except A) with the values from the problem. Check the next slide to be sure you have all the information in the right place in the formula.

n

rn

r

mA

nt

11

A is the future valuem is the amount of a single paymentn is the number of payments per year r is the annual rate of interestt is the time in years

Suppose you are 30 years old and can afford to save $100 a month. Your bank is paying an interest rate of 4% compounded quarterly. If you are faithful to put in your $300 a quarter, how much money will you have accumulated by the time you are 50?

Do you have all the numbers in the right place?

404.

1404.

1300$

204

A

The next step will be to simplify the formula following the order of operations. Where to start? Take care of the innermost grouping symbols first.

Do division and addition in the numerator and simplify the fraction in the denominator.

01.

101.1300$

204

A

Now, multiply the numbers forming the exponent and apply the exponent to it’s base, 1.01.

Some calculators use the ^ key to raise to a power. Others may have an xy key. Try finding 32 (which is 9) as a way of deciding how your calculator works.

Round your answer to the nearest hundredth.

01.

122.2300$A

Now we can do the subtraction in the numerator, then divide by the denominator (remember that the fraction bar is a grouping symbol).

Once we have simplified the fraction, we can multiply by $300.

600,36$

122300$

01.

22.1300$

A

A

A

Not too bad when you consider that the amount of money you contributed was

$300 four times a year for 20 years

which is a total of $24,000.

Car payments

• The formula for calculating a car payment is similar. It is called the present value formula.

P is the cost of the carm is the amount of a single paymentn is the number of payments per year r is the annual rate of interestt is the time in years

nt

nr

nr

Pm

11

Buy a car!

• Suppose you found a great car for only $30,000. You decide that you want it and the dealer says he’ll finance it for 3% and give you 6 years to pay. How much will you need to pay each month?

Place your information in the formula and check the next slide.

612

1203.

11

1203.

000,30

m

What’s the next step?

Calculate within the parentheses and apply the exponent.

84.1

0025.000,30

0025.11

0025.000,30612

m

mIf your calculator does not have a “negative” key you may not be able to apply this exponent.

The last step will be to simplify both numerator and denominator and then divide.

Do you think you can afford this car?

75.468$

16.

75

m

m

Can you afford it? Well, don’t forget about the cost of oil changes, gas, tires, and insurance!

ReviewWhen a problem involves more than one operation, we use this

order to simplify expressions:

• First, grouping symbols; and you must always simplify expressions with exponents before you can calculate with them.

• Next, multiplication OR division as you come to it reading from left to right.

• Last, addition OR subtraction as you come to it from left to right