When we solve mathematical problems, we could solve them in a number of different ways. However, this could lead to many different answers. The only way to make sure we all get the same answer is to make sure that everyone follows the same method. This is what we call the order of operations.

Solve anything inside grouping symbols (e.g. brackets or parentheses).

Solve any multiplication or division, going from left to right.

Solve any addition and subtraction, working from left to right

What about with decimals?

When our number problems contain decimals, we don't need to change the way we solve them. This means there are no new rules to learn. The most important thing to remember when working with decimals is the place value of the digit we are looking at.

Expressions including multiplication

Now we are ready to work through some examples, using decimals and multiplication in our number problems. You may even want to refresh your memory on the order of operations using whole numbers.

In these examples, we we need to work through two steps to solve our number problem, including tenths and hundredths.

Expressions with more steps

Now let's work through number problems that have more steps, requiring us to really think about the order in which we solve our number problem. We also see what happens if we solve our number problem without following the correct order of operations!

Careful!

We always solve multiplication first, then we solve addition or subtraction, working from left to right.

Examples

QUESTION 1

Find the value of $2.6+0.84\times10$2.6+0.84×10

QUESTION 2

Find the value of $5.1\times6+2.5$5.1×6+2.5, giving your answer as a decimal.

QUESTION 3

Find the value of $1.6\times8-1.6\times7$1.6×8−1.6×7, giving your answer as a decimal.

Outcomes

NA5-3

Understand operations on fractions, decimals, percentages, and integers