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
  4. Addition and subtraction

Practice Addition, subtraction, multiplication and division

examples with solutions for addition, subtraction, multiplication and division

Exercise #1

3+41+40= 3+4-1+40=

Video Solution

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 3+4=7

71=6 7-1=6

6+40=46 6+40=46

Answer

46 46

Exercise #2

7+5+2+1= -7+5+2+1=

Video Solution

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 -7+5=-2

2+2=0 -2+2=0

0+1=1 0+1=1

Answer

1 1

Exercise #3

9+31= 9+3-1=

Video Solution

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!

Answer

11 11

Exercise #4

3+21= 3+2-1=

Video Solution

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 3+2=5

51=4 5-1=4

Answer

4

Exercise #5

Solve:

93+42 9-3+4-2

Video Solution

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:

93=6 9-3=6

6+4=10 6+4=10

102=8 10-2=8

Answer

8

examples with solutions for addition, subtraction, multiplication and division

Exercise #1

100+5100+5 100+5-100+5

Video Solution

Step-by-Step Solution

100+5100+5=105100+5=5+5=10 100+5-100+5=105-100+5=5+5=10

Answer

10

Exercise #2

3+102:4+1= 3+10-2:4+1=

Video Solution

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+1012+1 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+1012+1=1312+1 3+10-\frac{1}{2}+1=13-\frac{1}{2}+1

1312+1=1212+1=1312 13-\frac{1}{2}+1=12\frac{1}{2}+1=13\frac{1}{2}

Answer

1312 13\frac{1}{2}

Exercise #3

20:4+3×2= 20:4+3\times2=

Video Solution

Step-by-Step Solution

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

(20:4)+(3×2)= (20:4)+(3\times2)=

Now we solve the exercises within parentheses:

20:4=5 20:4=5

3×2=6 3\times2=6

And we obtain the exercise:

5+6=11 5+6=11

Answer

11

Exercise #4

15:5+4×3= 15:5+4\times3=

Video Solution

Step-by-Step Solution

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

(15:5)+(4×3)= (15:5)+(4\times3)=

Now we solve the parentheses:

15:5=3 15:5=3

4×3=12 4\times3=12

And we get the exercise:

3+12=15 3+12=15

Answer

15

Exercise #5

1+2×37:4= 1+2\times3-7:4=

Video Solution

Step-by-Step Solution

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

1+(2×3)(7:4)= 1+(2\times3)-(7:4)=

Now we solve the exercises within parentheses:

2×3=6 2\times3=6

7:4=74 7:4=\frac{7}{4}

We obtain:

1+674= 1+6-\frac{7}{4}=

We solve the exercise from left to right:

1+6=7 1+6=7

774= 7-\frac{7}{4}=

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

7(4+34) 7-(\frac{4+3}{4})

7(44+34) 7-(\frac{4}{4}+\frac{3}{4})

7(1+34) 7-(1+\frac{3}{4})

7134=514 7-1\frac{3}{4}=5\frac{1}{4}

Answer

514 5\frac{1}{4}

examples with solutions for addition, subtraction, multiplication and division

Exercise #1

Complete the exercise:

2+315:3×4+6= 2+3-15:3\times4+6=

Video Solution

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(15:3×4)+6= 2+3-(15:3\times4)+6=

We solve the exercise in parentheses from left to right:

15:3=5 15:3=5

5×4=20 5\times4=20

Now we obtain the exercise:

2+320+6= 2+3-20+6=

We solve the exercise from left to right:

2+3=5 2+3=5

520=15 5-20=-15

15+6=9 -15+6=-9

Answer

-9

Exercise #2

Complete the exercise:

26:2+5×2= 2-6:2+5\times2=

Video Solution

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)+(5×2)= 2-(6:2)+(5\times2)=

Now, we solve the exercise in parentheses:

6:2=3 6:2=3

5×2=10 5\times2=10

Now we obtain the exercise:

23+10= 2-3+10=

We solve the exercise from left to right:

23=1 2-3=-1

1+10=9 -1+10=9

Answer

9

Exercise #3

Complete the exercise:

530:2×3+10= 5-30:2\times3+10=

Video Solution

Step-by-Step Solution

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

5(30:2×3)+10= 5-(30:2\times3)+10=

We solve the exercise in parentheses from left to right:

30:2=15 30:2=15

15×3=45 15\times3=45

Now we obtain the exercise:

545+10= 5-45+10=

We solve the exercise from left to right:

545=40 5-45=-40

40+10=30 -40+10=-30

Answer

-30

Exercise #4

Complete the exercise:

45×7+3= 4-5\times7+3=

Video Solution

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(5×7)+3= 4-(5\times7)+3=

Now we solve the multiplication exercises:

435+3= 4-35+3=

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

435=31 4-35=-31

31+3=28 -31+3=-28

Answer

-28

Exercise #5

25×3+4= 2-5\times3+4=

Video Solution

Step-by-Step Solution

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

2(5×3)+4= 2-(5\times3)+4=

We solve the exercise in parentheses:

5×3=15 5\times3=15

We obtain:

215+4= 2-15+4=

We solve the exercise from left to right:

215=13 2-15=-13

13+4=9 -13+4=-9

Answer

-9

Topics learned in later sections

  1. Order of Operations: Exponents
  2. Order of Operations: Roots
  3. Order of Operations with Parentheses
  4. Division and Fraction Bars (Vinculum)
  5. The Numbers 0 and 1 in Operations
  6. Neutral Element (Identiy Element)
  7. Multiplicative Inverse
  8. The Order of Operations
  9. Order or Hierarchy of Operations with Fractions