Examples with solutions for All Operations in the Order of Operations: Small Numbers

Exercise #1

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 #2

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

Exercise #3

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 #4

113:4= 11-3:4=

Video Solution

Step-by-Step Solution

According to the order of operations rules, we must first solve the division problem, and subsequently the subtraction problem:

3:4=34 3:4=\frac{3}{4}

1134=1014 11-\frac{3}{4}=10\frac{1}{4}

Answer

1014 10\frac{1}{4}

Exercise #5

Complete the exercise:

2+3×63×7+1= 2+3\times6-3\times7+1=

Video Solution

Step-by-Step Solution

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

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

2+(3×6)(3×7)+1= 2+(3\times6)-(3\times7)+1=

We then solve the multiplication exercises:

2+1821+1= 2+18-21+1=

Lastly we solve the rest of the exercise from left to right:

2+18=20 2+18=20

2021=1 20-21=-1

1+1=0 -1+1=0

Answer

0

Exercise #6

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 must first solve the multiplication exercises.

We place them inside of parentheses to avoid confusion during the solution:

4(5×7)+3= 4-(5\times7)+3=

We then solve the multiplication exercises:

435+3= 4-35+3=

Lastly we solve the rest of the exercise from left to right:

435=31 4-35=-31

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

Answer

28 -28

Exercise #7

8:2(2+2)= 8:2(2+2)=

Video Solution

Step-by-Step Solution

Let's start with the part inside the parentheses. 

2+2=4 2+2=4
Then we will solve the exercise from left to right 

8:2=4 8:2=4
4×(4)=16 4 × (4)=16

The answer: 16 16

Answer

16

Exercise #8

Solve the following problem using the order of operations:

253×4+4×2= 25-3\times4+4\times2=

Video Solution

Step-by-Step Solution

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

We will put them in parentheses so that we don't get confused later in the solution:

25(3×4)+(4×2)= 25-(3\times4)+(4\times2)=

Let's solve the multiplication exercises:

3×4=12 3\times4=12

4×2=8 4\times2=8

We get:

2512+8= 25-12+8=

Let's solve the exercise from left to right:

2512=13 25-12=13

13+8=21 13+8=21

Answer

21 21

Exercise #9

1+2×37:4= 1+2\times3-7:4=

Video Solution

Step-by-Step Solution

According to the rules of the order of arithmetic operations, we must first enclose both the multiplication and division exercises inside of parentheses:

1+(2×3)(7:4)= 1+(2\times3)-(7:4)=

We then solve the exercises within the parentheses:

2×3=6 2\times3=6

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

We obtain the following:

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

We continue by solving the exercise from left to right:

1+6=7 1+6=7

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

Lastly we break down the numerator of the fraction with a sum exercise as seen below:

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}

Exercise #10

7(5)+8.5+(13)=? -7-(-5)+8.5+(-13)=\text{?}

Video Solution

Step-by-Step Solution

Let's begin by expanding the parentheses. Make sure to pay attention to the minus and plus signs, which change accordingly:

(5)=5 -(-5)=5

8.5+(13)=8.513 8.5+(-13)=8.5-13

We should obtain the following:

7+5+8.513= -7+5+8.5-13=

Now let's solve the exercise from left to right:

2+8.513= -2+8.5-13=

6.513=6.5 6.5-13=-6.5

Answer

6.5 -6.5

Exercise #11

7.5+(9.5)+5+(13.5)=? 7.5+(-9.5)+5+(-13.5)=\text{?}

Video Solution

Step-by-Step Solution

Let's begin by expanding the parentheses whilst paying attention to the minus and plus signs, which change accordingly:

+(9.5)=9.5 +(-9.5)=-9.5

+(13)=13 +(-13)=-13

We should obtain the following:

7.59.5+513.5= 7.5-9.5+5-13.5=

Now let's solve the exercise from left to right:

2+513.5= -2+5-13.5=

313.5=10.5 3-13.5=-10.5

Answer

10.5 -10.5