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

103+75= 10-3+7-5=

Video Solution

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:

103=7 10-3=7

7+7=14 7+7=14

145=9 14-5=9

Answer

9

Exercise #2

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 #3

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

Exercise #4

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 #5

10×2:4= 10\times2:4=

Video Solution

Step-by-Step Solution

Division and multiplication are on the same level of order of operations,

therefore, when encountering such a case, we will always solve from left to right.

 

10*2=20

20/4=5

Answer

5

Exercise #6

30:5×2= 30:5\times2=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, the exercise which contains both multiplication and division should be solved from left to right.

30:5=6 30:5=6

6×2=12 6\times2=12

Answer

12

Exercise #7

902+98= 90-2+9-8=

Video Solution

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:

902=88 90-2=88

88+9=97 88+9=97

978=89 97-8=89

Answer

89

Exercise #8

73+847=? 7\cdot3+8-4-7=\text{?}

Video Solution

Step-by-Step Solution

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

We isolate the multiplication exercise in parentheses and solve.

(7×3)=21 (7\times3)=21

Now, the exercise we're left with is: 21+847= 21+8-4-7=

We solve the exercise from left to right. We isolate the next part of the expression with parentheses to avoid confusion(21+8)=29 (21+8)=29

Now, the exercise obtained is: 2947= 29-4-7=

We continue solving from left to right and isolate the next part of the expression in parentheses.

(294)=25 (29-4)=25

Now, the expression obtained is: 257=18 25-7=18

Answer

18

Exercise #9

3+8+4×3= 3+8+4\times3=

Video Solution

Step-by-Step Solution

According to the rules of the order of operations, we first solve the multiplication exercise:

3+8+(4×3)= 3+8+(4\times3)=

4×3=12 4\times3=12

Now, we solve the addition exercise from left to right:

3+8+12= 3+8+12=

11+12=23 11+12=23

Answer

23

Exercise #10

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 #11

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 #12

25×3+4= 2-5\times3+4=

Video Solution

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we begin by enclosing the multiplication exercise inside parentheses:

2(5×3)+4= 2-(5\times3)+4=

We then solve the said exercise inside of the parentheses:

5×3=15 5\times3=15

We obtain the following:

215+4= 2-15+4=

Lastly we solve the exercise from left to right:

215=13 2-15=-13

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

Answer

-9

Exercise #13

2+4×5:2+3= 2+4\times5:2+3=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we first insert the multiplication and division exercises into parentheses:

2+(4×5:2)+3= 2+(4\times5:2)+3=

Now let's solve the expression in parentheses from left to right:

4×5=20 4\times5=20

20:2=10 20:2=10

And we get the expression:

2+10+3= 2+10+3=

Let's solve the expression from left to right:

2+10=12 2+10=12

12+3=15 12+3=15

Answer

15

Exercise #14

2569+73= 25-6-9+7-3=

Video Solution

Step-by-Step Solution

Due to the fact that the exercise only involves addition and subtraction operations, we will solve it from left to right:

256=19 25-6=19

199=10 19-9=10

10+7=17 10+7=17

173=14 17-3=14

Answer

14 14

Exercise #15

1459+7+2= 14-5-9+7+2=

Video Solution

Step-by-Step Solution

Due to the fact that the exercise only involves addition and subtraction operations, we will solve it from left to right:

145=9 14-5=9

99=0 9-9=0

0+7=7 0+7=7

7+2=9 7+2=9

Answer

9 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