What Is the Order of Operations in Math?

If you have an expression where all the operations are the same (example: only addition, only subtraction, only multiplication, or only division) then the correct way to solve it would be from left to right. But for expressions with multiple operations, we need to follow the order of operations.

The order of operations is the rule that tells us the sequence in which we should solve an expression with multiple operations.

A way to remember that order is BEMDAS. Each letter in BEMDAS stands for a mathematical operation. 

Order of Operations Steps:

Brackets

The first step is to solve the operation within brackets. Brackets are used to group things together. Work out all groupings from inside to out.

Exponents

Work out the exponential expressions after the parentheses.

Multiplication and Division

Next, moving from left to right, multiply and/or divide, whichever comes first.

Addition and Subtraction

Lastly, moving from left to right, add and/or subtract, whichever comes first.

What does lowest term ratio mean?

Just like fractions, ratios can be simplified.

We can simplify ratios by finding common factors of the numbers involved and dividing them all by the common factors.

The ratios are in lowest terms (or simplest form) when there are no more common factors except 1.

Look at the example below:

The ratio of rabbits to cats is 4 to 2 or 4:2.

Because these two numbers have a common factor of 2, they can both be divided by 2 to give a simpler ratio.

So 4 : 2 = (4 ÷ 2) : (2 ÷ 2) = 2 : 1

There are now no common factors apart from 1, so we cannot simplify the ratio further.

So the ratio of rabbits to cats in lowest terms is 2:1. This means that there are 2 rabbits for every cat.

Today we work with a partner to make spinner games.

Work with a partner to design their own two-player game. You need to design both the spinner and write the rules for their game. This could be linked to your interests or culture. 

• Decide who will be player A and player B.

• Spin both spinners and add the two numbers together.

• If the sum is even, player A gets one point. If the sum is odd, player B gets one point.

• The first player to score 20 points wins.

• Before playing the game, predict what you think will happen and write this down.

• 
   

1. Increase $200 by 50%

2. Increase $300 by 50%

3. Increase $160 by 10%

4. Increase $540 by 100%

5. Increase $180 by 25%

6. Increase $2000 by 60%

7. Increase $500 by 30%

8. Increase $1000 by 1%

9. Increase $280 by 25%

10. Increase $860 by 70%

11. Increase $750 by 30%

12. Increase $960 by 15%

Work out the discounted price of each item

e.g. 30% of $200

• 200 ÷10 = 20        First, we divide the amount by 10 (to find 10 percent) 

• 20 x 3 = 60 Next, we multiply 20 (10% of 200) by 3 (30 is 3 times bigger than 10)

• So 30% of 200 is $60

Solve the following percentages of the dollar amounts: 

1. 20% of $200

2. 30% of $500

3. 75% 0f $400

4. 60% of $250 

5. 70% of $90

6. 40% of $55

7. 25% 0f $600

8. 60% of $70

9. 30% of $55

10. 15% of $800

11. 90% of $120 

12. 35% of $250

 Introduction to Percentages %

The term ‘per cent’ means ‘out of a hundred’. In mathematics, percentages are used like fractions and decimals, as ways to describe parts of a whole.  When you are using percentages, the whole is considered to be made up of a hundred equal parts. The symbol % is used to show that a number is a percentage, and less commonly the abbreviation ‘pct’ may be used.

You will see percentages almost everywhere: in shops, on the internet, in advertisements and in the media. Being able to understand what percentages mean is a key skill that will potentially save you time and money and will also make you more employable.

The Meaning of Percentages

Percentage is a term from Latin, meaning ‘out of one hundred’.

You can therefore consider each ‘whole’ as broken up into 100 equal parts, each one of which is a single percent.