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4.07 Order of operations


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Stories can help us to understand the operations that need to happen, in order to solve a problem. Have a look at this story, to remember how to write a number sentence to represent the story.


Example 1

There were 11 flowers in Dave’s garden. 4 more flowers grew, then Dave picked 8 flowers to put in a vase.

Which expression matches the word problem for the number of flowers left in the garden?

Worked Solution
Create a strategy

The phrase "The flowers grew" means that the flowers will be added, and the phrase "the flowers were picked" means that the flowers will be taken away.

Apply the idea

Dave's garden started with 11 flowers and 4 more flowers grew. This is same as: 11+4.

Dave picked 8 flowers. This is same as: -8.

So the number sentce is 11+4-8. The correct answer is option A.

Idea summary

Identifying the clues helps us work out how to write out our number problem. We can also look for pieces of information that may not be useful, and ignore those.

Order of operations with and without parentheses

This video shows us how the order of operations is used in everyday problems.

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Example 2

Write the number sentence described as:

The sum of 4 and 6 is multiplied by 2.

Worked Solution
Create a strategy

The word "sum" means add.

Apply the idea

The sum of 4 and 6 means we are adding 4 and 6 together: 4+6

Since we need to multiply the whole sum by 2, we can use brackets to group the sum together, and then multiply it by 2:

(4+6)\times 2

Idea summary

Another word that is sometimes used for parentheses is brackets.

If we need to multiply or divide multiple numbers by the same amount, that is when we should use parentheses.

The rules of the order of operations

This video explains what the rules are when it comes to the order of operations.

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Example 3

Evaluate 44\div4-7+17.

Worked Solution
Create a strategy

We need to workout the division before the addition and subtraction.

Apply the idea
\displaystyle 44\div4-7+17\displaystyle =\displaystyle 11-7+17Divide 44 by 4
\displaystyle =\displaystyle 4+17Subtract 7 from 11
\displaystyle =\displaystyle 21Add 17
Idea summary

The order of operations:

  1. Solve anything inside grouping symbols (parentheses/brackets).
  2. Solve any multiplication or division, including powers, working from left to right.
  3. Solve any addition or subtraction, working from left to right.



selects and applies appropriate strategies for addition and subtraction with counting numbers of any size


selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

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