## Operations and Order of Operations

#### Introduction

The order in which you do operations will determine the answer that you get. So, to get to the correct answer you must follow the right order of operations.

#### 1.  Mia had 5 pens. She gave 2 to Tracey and received 3 more from Alex. How many pens does she have now?

The number statement for this problem is:
5  −  2  +  3

Which of the following 2 methods is the correct way to solve this problem?
Method 1: (do subtraction first)
5  −  2  =  3
3  +  3  =  6
Mia has 6 pens now.
2  +  3  =  5
5  −  5  =  0
Mia has no pens now.
Let's draw a model diagram to solve this problem.

Mia has 6 pens now.

Therefore, Method 1 is the correct way to solve this problem.

Rule:
Do all addition and/or subtraction from left to right.

#### 2. Joe divided 12 eggs equally into 2 trays. If Emily bought 3 such trays of eggs, how many eggs did she buy?

The number statement for this problem is:
12  ÷  2  ×  3

Which of the following 2 methods is the correct way to solve this problem?
Method 1: (do multiplication first)
2  ×  3  =  6
12  ÷  6  =  2
Emily bought 2 eggs.
Method 2: (do division first)
12  ÷  2  =  6
6  ×  3  =  18
Emily bought 18 eggs.
Let's draw a model diagram to solve this problem.

Emily bought 18 eggs.

Therefore, Method 2 is the correct way to solve this problem.

Rule:
Do all multiplication and/or division from left to right.

#### 3. Peter had 5 apples. He bought another 3 bags of apples containing 10 apples each. How many apples does he have now?

The number statement for this problem is:
5  +  3  ×  10

Which of the following 2 methods is the correct way to solve this problem?
5  +  3  =  8
8  ×  10  =  80
Peter has 80 apples now.
Method 2: (do multiplication first)
3  ×  10  =  30
5  +  30  =  35
Peter has 35 apples now.
Let's draw a model diagram to solve this problem.

Peter has 35 apples now.

Therefore, Method 2 is the correct way to solve this problem.

Rules:

First, do all multiplication and/or division from left to right.
Second, do all addition and/or subtraction from left to right.

#### 4. Su drinks 1 glass of milk in the morning and 1 glass of milk at night. How many glasses of milk does she drink in a week? (1 week = 7 days)

The number statement for this problem is:
1  +  1  ×  7

Which of the following 2 methods is the correct way to solve this problem?
Method 1: (do multiplication first)
1  ×  7  =  7
1  +  7  =  8
Su drinks 8 glasses of milk in a week.
1  +  1  =  2
2  ×  7  =  14
Su drinks 14 glasses of milk in a week.
Let's draw a model diagram to solve this problem.

Su drinks 14 glasses of milk in a week.

Therefore, Method 2 is the correct way to solve this problem.

However, we learnt above that we should first multiply and/or divide from left to right and next add and/or subtract from left to right. So then why isn't Method 1 the correct way to solve this problem?

Well, that's because we did not write the number statement correctly. The correct number statement for the above problem is:
(1  +  1)  ×  7

The standard order of operations is:

Step 1:  Do the operations within brackets.
Step 2:  Do all multiplication and/or division from left to right.
Step 3:  Do all addition and/or subtraction from left to right.

#### 5. Find the value of the following: 48  /  (2  ×  3)  +  1  −  8

Step 1: Do the operations within brackets.
48  ÷  (2  ×  3)  +  1  −  8
=  48  ÷  6  +  1  −  8
Step 2: Do all multiplication and/or division from left to right.
48  ÷  6  +  1  −  8
8  +  1  −  8
Step 3: Do all addition and/or subtraction from left to right.
8  +  1  −  8
9  −  8
=  1
Therefore,
48  ÷  (2  ×  3)  +  1  −  8  =  1