4.2.3 Further Practice with PEMDAS

Scientific and graphing calculators will follow the PEMDAS code, and the calculator used in this course certainly does. However, be careful, because a typical handheld calculator might not be programmed to perform operations in the correct order, as described earlier in the pizza example.

Calculator symbol The calculator can be accessed in the left-hand side bar under Toolkit.

Activity symbol Activity: PEMDAS on Paper Versus the Calculator

To make sure that you understand PEMDAS, try these calculations in your math notebook without using the calculator. Then, check your answer using the calculator.

(a) open three plus four close multiplication two

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Comment

Remember PEMDAS. Are there parentheses? Then do the calculation inside those first. Next, look for exponents, then multiplication, division, addition, and subtraction.

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Answer

(a) open three plus four close multiplication two

Carry out the calculation in parentheses first: three plus four equals seven. Now multiply by two and the answer is 14.

(b) two plus three squared

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(b) two plus three squared

No parentheses, this time, so start with the exponent: three squared equals nine. Add the two and you get 11.

(c) open two plus three close squared

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(c) open two plus three close squared

This looks like part (b), but this time there are parentheses, so you must do the calculation inside the parentheses first: two plus three equals five. Now square the result, and the answer is 25.

(d) three squared plus four squared

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(d) three squared plus four squared

Work out the exponents first. three squared equals nine  and four squared equals 16. Finally add: nine plus 16 equals 25.

(e) two plus three multiplication four plus five . Take care with this one!

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Answer

It can help to make calculations like this easier to read if you put parentheses around the part that you need to do first.

(e) two plus three multiplication four plus five

This time, you have addition and multiplication, so you must do the multiplication first: three multiplication four equals 12. So now, the calculation is sum with, 3 , summands two plus 12 plus five equals 19.

Using parentheses we would write two plus left parenthesis three multiplication four right parenthesis plus five.

This will give you the same answer but just might make your job easier!

Did you get the same answers using the calculator? You should!

4.2.2 Calculator Exploration: Understanding the Order of Operations

4.2.4 Moving Left to Right