4.2.2 Calculator Exploration: Understanding the Order of Operations

Many everyday problems can be solved by doing a little arithmetic. While there will be situations when you might want to work out the calculation quickly in your head or on a piece of paper, using a calculator will often be easier. However, if you do use a calculator, you need to be confident that your answer is correct. This involves understanding what the different keys on your calculator do, using them appropriately, and then checking that your answer is reasonable.

Calculator Exploration: Understanding the Order of Operations

In the following exploration, you will explore the order in which mathematical operations are carried out.

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

Suppose that you have the calculation three plus five multiplication two. Which do you do first, the addition or the multiplication? If you add first, you’ll get three plus five equals eight comma then multiply by two to get 16. If you do the multiplication first, then you get five multiplication two equals 10, and adding three gives 13.

Oh dear, we have different answers depending on which order we do the mathematical operations in! It is important that there are rules to say which order calculations like these should be carried out, and that we all follow the rules so that we get the same answer.

So let’s see what happens when we use the calculator for this.

Activity symbol Activity: Understanding the Order of Operations

Using the calculator, determine the answer to three plus five multiplication two.

Hint

Hint symbol

Comment

You can input the calculation exactly how it appears into the calculator using the buttons or your keyboard. Don’t be tempted to press the equals button part way through, otherwise you will break up the calculation and the order of operation as well.

Solution symbol

Answer

The calculator gives the answer 13.

The calculator has performed the multiplication first. It is programmed to perform the calculations in the correct order.

Remember that to avoid any confusion, a code has been set for the order of mathematical operations, PEMDAS. This stands for

To work out a complicated calculation, follow this code. Work out any parentheses first, then exponents, followed by multiplication and division (from left to right), and finish with addition and subtraction (from left to right).

This tells you how to calculate three plus five multiplication two, which we tried above. There are no parentheses or exponents, but we do have multiplication and addition. Multiplication comes higher in the PEMDAS list so you must do the multiplication first, then the addition.

So, equation sequence three plus five multiplication two equals three plus 10 equals 13.

4.2.1 An Everyday Problem

4.2.3 Further Practice with PEMDAS