# Addition, subtraction, multiplication and division - Examples, Exercises and Solutions

## 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

## examples with solutions for addition, subtraction, multiplication and division

### Exercise #1

$3+4-1+40=$

### Step-by-Step Solution

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

$3+4=7$

$7-1=6$

$6+40=46$

$46$

### Exercise #2

$-7+5+2+1=$

### Step-by-Step Solution

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

$-7+5=-2$

$-2+2=0$

$0+1=1$

$1$

### Exercise #3

$9+3-1=$

### 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

And this is the solution!

$11$

### Exercise #4

$3+2-1=$

### 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 #5

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

## examples with solutions for addition, subtraction, multiplication and division

### Exercise #1

$100+5-100+5$

### Step-by-Step Solution

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

10

### Exercise #2

$3+10-2:4+1=$

### Step-by-Step Solution

According to the order of arithmetic operations, multiplication and division precede addition and subtraction,

Therefore, let's start first with the division operation:

$3+10-(2:4)+1=3+10-\frac{1}{2}+1$

Now, as all remaining operations are at the same level (addition and subtraction),

let's start solving from left to right:

$3+10-\frac{1}{2}+1=13-\frac{1}{2}+1$

$13-\frac{1}{2}+1=12\frac{1}{2}+1=13\frac{1}{2}$

$13\frac{1}{2}$

### Exercise #3

$20:4+3\times2=$

### Step-by-Step Solution

According to the order of operations, we place the multiplication and division exercise within parentheses:

$(20:4)+(3\times2)=$

Now we solve the exercises within parentheses:

$20:4=5$

$3\times2=6$

And we obtain the exercise:

$5+6=11$

11

### Exercise #4

$15:5+4\times3=$

### Step-by-Step Solution

According to the order of operations, we put the multiplication and division exercise in parentheses:

$(15:5)+(4\times3)=$

Now we solve the parentheses:

$15:5=3$

$4\times3=12$

And we get the exercise:

$3+12=15$

15

### Exercise #5

$1+2\times3-7:4=$

### Step-by-Step Solution

According to the rules for the order of arithmetic operations, we will enclose multiplication and division exercises in parentheses:

$1+(2\times3)-(7:4)=$

Now we solve the exercises within parentheses:

$2\times3=6$

$7:4=\frac{7}{4}$

We obtain:

$1+6-\frac{7}{4}=$

We solve the exercise from left to right:

$1+6=7$

$7-\frac{7}{4}=$

We break down the numerator of the fraction with a sum exercise:

$7-(\frac{4+3}{4})$

$7-(\frac{4}{4}+\frac{3}{4})$

$7-(1+\frac{3}{4})$

$7-1\frac{3}{4}=5\frac{1}{4}$

$5\frac{1}{4}$

## examples with solutions for addition, subtraction, multiplication and division

### Exercise #1

Complete the exercise:

$2+3-15:3\times4+6=$

### Step-by-Step Solution

According to the rules of the order of arithmetic operations, we first place multiplication and division exercises in parentheses:

$2+3-(15:3\times4)+6=$

We solve the exercise in parentheses from left to right:

$15:3=5$

$5\times4=20$

Now we obtain the exercise:

$2+3-20+6=$

We solve the exercise from left to right:

$2+3=5$

$5-20=-15$

$-15+6=-9$

-9

### Exercise #2

Complete the exercise:

$2-6:2+5\times2=$

### Step-by-Step Solution

According to the rules of the order of arithmetic operations, we first place multiplication and division exercises in parentheses:

$2-(6:2)+(5\times2)=$

Now, we solve the exercise in parentheses:

$6:2=3$

$5\times2=10$

Now we obtain the exercise:

$2-3+10=$

We solve the exercise from left to right:

$2-3=-1$

$-1+10=9$

9

### Exercise #3

Complete the exercise:

$5-30:2\times3+10=$

### Step-by-Step Solution

According to the rules of the order of arithmetic operations, we first place multiplication and division exercises in parentheses:

$5-(30:2\times3)+10=$

We solve the exercise in parentheses from left to right:

$30:2=15$

$15\times3=45$

Now we obtain the exercise:

$5-45+10=$

We solve the exercise from left to right:

$5-45=-40$

$-40+10=-30$

-30

### Exercise #4

Complete the exercise:

$4-5\times7+3=$

### Step-by-Step Solution

According to the rules of the order of arithmetic operations, we first solve the multiplication exercises.

We place them in parentheses to avoid confusion during the solution:

$4-(5\times7)+3=$

Now we solve the multiplication exercises:

$4-35+3=$

We solve the rest of the exercise from left to right:

$4-35=-31$

$-31+3=-28$

-28

### Exercise #5

$2-5\times3+4=$

### Step-by-Step Solution

According to the rules of the order of arithmetic operations, we will first enclose the multiplication exercise in parentheses:

$2-(5\times3)+4=$

We solve the exercise in parentheses:

$5\times3=15$

We obtain:

$2-15+4=$

We solve the exercise from left to right:

$2-15=-13$

$-13+4=-9$