## 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.

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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:

Which of the following 2 methods is the correct way to solve this problem?

5 − 2 = 3

3 + 3 = 6

Mia has 6 pens now.

2 + 3 = 5

5 − 5 = 0

Mia has no pens now.

**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.

**Method 2: (do addition first)**

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.

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

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.

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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:

Which of the following 2 methods is the correct way to solve this problem?

2 × 3 = 6

12 ÷ 6 = 2

Emily bought 2 eggs.

12 ÷ 2 = 6

6 × 3 = 18

Emily bought 18 eggs.

**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.

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

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:

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.

3 × 10 = 30

5 + 30 = 35

Peter has 35 apples now.

**5 + 3 × 10**Which of the following 2 methods is the correct way to solve this problem?

**Method 1: (do addition first)**

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.

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

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

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:

Which of the following 2 methods is the correct way to solve this problem?

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.

**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.

**Method 2: (do addition first)**

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:

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

48 ÷ (2 × 3) + 1 − 8 = 1