The Order of Basic Operations: Addition, Subtraction, and Multiplication

šPractice addition, subtraction, multiplication and division

The Correct Order when Solving Combined Operations

The rules for the order of operations in an addition and subtraction exercise are quite simple.

In exercises with combined operations in which there are also multiplications and divisions, the order of operations is as follows:

1. Parentheses
2. Powers and roots
3. Multiplications and divisions
4. Addition and subtraction

Test yourself on addition, subtraction, multiplication and division!

Solve:

$$9-3+4-2$$

How to Do an Exercise with Several Multiplications and Divisions

In cases when the exercise contains several multiplications and divisions, we solve them in order from left to right.

There are more rules concerning the order of operations when the exercise contains parentheses and powers, which is is covered in the following article:
Order of operations with parentheses and powers

Practical Examples: Addition and Subtraction

As we have learned, the last operations to perform are the additions and subtractions.

1. Parentheses
2. Powers and roots
3. Multiplication and division
4. Addition and subtraction

The order in which the operations are performed is the same even if combined operations with fractions appear. The addition and subtraction of fractions is the last operation to perform and is done in order from left to right.

Solve the following exercises using the order of operations:

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Test your knowledge

Basic Example 1

$100-4+11-20=$

Solve from left to right.

The first part of the exercise is $100-4$, which is equal to $96$.

Next is $96+11$, which equals $107$.

The last part of the exercise is $107-20$, which is equal to $87$.

Therefore, the final result is: $87$.

Basic Example 2

$20-2-3-8=$

Solve from left to right.

The first part of the exercise is $20-2$, which is equal to $18$.

Then, if we solve $18-3$ we get $15$.

Finally, we solve the last part of the exercise: $15-8$ equals $7$.

Therefore, the final result is: $7$.

Do you know what the answer is?

Multiplication and Division Exercises

Basic Example 3

$10\cdot2:4=$

Solve from left to right.

First, we work out $10\cdot2$, which is equal to $20$.

The next part of the exercise is solving $20:4$, which is equal to $5$.

The final result is: $5$.

Basic Example 4

$90:3:2:5=$

Solve from left to right.

The first part of the exercise is solving $90:3$, which equals: $30$.

The next part of the exercise is solving $30:2$, which is equal to $15$.

Finally, we solve $15:5$, which equals $3$.

The final result is therefore: $3$.

Check your understanding

Example 5

$72:2-3:1=$

Solve from left to right (multiplication and division first, then addition and subtraction)

The multiplications and divisions of the exercise:

First, solve $72:2$, which is equal to $36$.

Then, the next part of the exercise is $3:1$, which is equal to $3$.

Giving us: $36-3$.

Now perform the additions and subtractions of the exercise:

Now we perform $36-3$, which is equal to $33$.

Finally, the last part of the exercise is $33:1$, which is equal to $33$.

Therefore, the final result is: $33$.

Example 6

$300:3-20:2+3\cdot4-2-7\cdot3=$

Solve from left to right (multiplication and division first, then addition and subtraction)

The multiplications and divisions of the exercise:

The first part of the exercise is $300:3$, which equals $100$.

Then we solve $20:2$, which equals $10$.

Next, we calculate $3\cdot4$, which equals $12$.

Lastly, we solve $7\cdot3$, which equals $21$.

Giving us: $100-10+12-2-21=$.

The additions and subtractions of the exercise:

Then, we calculate $100-10$, which is equal to $90$.

The next part of the exercise is $90+12$, which is equal to $102$.

After that, we calculate $102-2$, which equals $100$.

The next part of the exercise is $100-21$, which equals $79$.

Finally, we calculate $100-21$, which equals $79$.

Therefore, the final result is: $79$

Do you think you will be able to solve it?

Exercises for Practicing the Order of Operations

1. $90-2+9-8=$
2. $40-3-5-9=$
3. $10\cdot2:4=$
4. $80:4:2:5=$
5. $24:2:4-3:1=$
6. $5\cdot5\cdot2-12:4=$
7. $100:2-10:2+3\cdot4-6-5\cdot2=$

Solutions

After solving the practice exercises, check your answers:

1. R.$89$
2. R.$23$
3. R.$5$
4. R.$2$
5. R.$0$
6. R.$47$
7. R.$41$

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Review Questions

Why multiply before adding?

When we are asked to solve combined calculations where more than one operation appears, we must follow the order of operations. The order of operations dictates that we must must always perform multiplications first and then additions.

Test your knowledge

What is the order in which the mathematical operations are solved?

In general, when solving combined operations we must first solve the parentheses, then the powers and roots, then the multiplications and divisions, and finally the additions and subtractions.

Which is solved first when there are no parentheses, addition or multiplication?

In an operation without parentheses where addition and multiplication appear, we first solve the multiplications and then the additions.

Do you know what the answer is?

What is solved first in combined operations?

When we have combined operations, we must first solve the parentheses before solving the powers and roots.

What is the order of operations?

• Parentheses
• Powers and roots
• Left-to-right multiplication and division
• Addition and subtraction from left to right

Check your understanding

What are the basic operations of mathematics?

The four basic operations are: addition, subtraction, multiplication and division.

Do you think you will be able to solve it?

Examples with solutions for Addition, Subtraction, Multiplication and Division

Exercise #1

Solve:

$9-3+4-2$

Step-by-Step Solution

According to the rules of the order of operations, we will solve the exercise from left to right since it only has addition and subtraction operations:

$9-3=6$

$6+4=10$

$10-2=8$

8

Exercise #2

$3+2-1=$

Step-by-Step Solution

According to the rules of the order of operations, given that the exercise only involves subtraction and addition operations, we solve the exercise from left to right:

$3+2=5$

$5-1=4$

4

Exercise #3

$10-3+7-5=$

Step-by-Step Solution

According to the order of operations rules, we will solve the exercise from left to right since the only operations in it are addition and subtraction:

$10-3=7$

$7+7=14$

$14-5=9$

9

Exercise #4

$9+3-1=$

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we will work to solve the exercise from left to right:

9+3=11

11-1=10

Ā

And this is the solution!

Answer

$11$

Exercise #5

$100+5-100+5$

Step-by-Step Solution

$100+5-100+5=105-100+5=5+5=10$

10

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