Examples with solutions for All Operations in the Order of Operations: Complete the missing numbers

Exercise #1

7?+4+2×18=29 7-?+4+2\times18=29

Video Solution

Step-by-Step Solution

First, we place the multiplication exercise in parentheses:

7?+4+(2×18)=29 7-?+4+(2\times18)=29

We solve the exercise in parentheses:

2×18=36 2\times18=36

Now we obtain the exercise:

7?+4+36=29 7-?+4+36=29

We reduce the addition exercise:

36+4=40 36+4=40

Now we obtain the exercise:

7?+40=29 7-?+40=29

The question mark is the unknown, therefore we will refer to the exercise as an equation.

We arrange the exercise to isolate the question mark:

40+7?=29 40+7-?=29

We reduce:

47?=29 47-?=29

We move 47 to the other side and change to the correct sign:

?=2947 -?=29-47

?=18 -?=-18

We divide both sides by -1 to change to the correct sign:

?=18 ?=18

Answer

18 18

Exercise #2

What is the missing number?

2312×(6)+? ⁣:7=102 23-12\times(-6)+\red{\boxed{?}}\colon7=102

Video Solution

Step-by-Step Solution

First, we solve the multiplication exercise:

12×(6)=72 12\times(-6)=-72

Now we get:

23(72)+x ⁣:7=102 23-(-72)+x\colon7=102

Let's pay attention to the minus signs, remember that a negative times a negative equals a positive.

We multiply them one by one to be able to open the parentheses:

23+72+x ⁣:7=102 23+72+x\colon7=102

We reduce:

95+x:7=102 95+x:7=102

We move the sections:

x:7=10295 x:7=102-95

x:7=7 x:7=7

x7=7 \frac{x}{7}=7

Multiply by 7:

x=7×7=49 x=7\times7=49

Answer

49

Exercise #3

12+?+31=29 12+?+3-1=29

Video Solution

Step-by-Step Solution

To find out which number is missing, we solve the entire exercise to know which number we will have to add to obtain a result of 29:

12+31= 12+3-1=

151=14 15-1=14

To make 14 equal to 29, we will have to add 15.

Let's verify:

2914=15 29-14=15

Answer

15 15

Exercise #4

12×34+?=27 12\times3-4+?=27

Video Solution

Step-by-Step Solution

According to the rules of operations, we first place the multiplication exercise in parentheses:

(12×3)4+?=27 (12\times3)-4+?=27

We solve the exercise in parentheses:

12×3=36 12\times3=36

We obtain the exercise:

364+?=27 36-4+?=27

We reduce:

32+?=27 32+?=27

We move 32 to the other side and change to the correct sign:

?=2732 ?=27-32

?=5 ?=-5

Answer

5 -5

Exercise #5

17?+4=5 17-?+4=5

Video Solution

Step-by-Step Solution

The question mark is the unknown, so we will refer to the exercise as an equation.

We arrange the exercise to isolate the question mark:

17+4?=5 17+4-?=5

We reduce:

21?=5 21-?=5

We move to thevariable to the other side and change to the correct sign:

21=?+5 21=?+5

We move the 5 to the other side and change to the correct sign: 215=? 21-5=\text{?}

16=? 16=\text{?}

Answer

16 16

Exercise #6

7+?+2=20 7+?+2=20

Video Solution

Step-by-Step Solution

To find out which number is missing, we solve the entire exercise to know which number we will have to add to obtain a result of 20:

7+2=9 7+2=9

To make 9 equal to 20 we will have to add the number 11.

Let's verify:

209=11 20-9=11

Answer

11 11

Exercise #7

8×73+?=60 8\times7-3+?=60

Video Solution

Step-by-Step Solution

According to the rules of operations, we first place the multiplication exercise in parentheses:

(8×7)3+?=60 (8\times7)-3+?=60

8×7=56 8\times7=56

Now we obtain the exercise:

563+?=60 56-3+?=60

We reduce the subtraction exercise:

563=53 56-3=53

We obtain the exercise:

53+?=60 53+?=60

We move 53 to the other side and change to the correct sign:

?=6053 ?=60-53

?=7 ?=7

Answer

7 7

Exercise #8

9+?+3=25 9+?+3=25

Video Solution

Step-by-Step Solution

To find out which number is missing, we solve the entire exercise to know which number we will have to add to obtain a result of 25:

9+3=12 9+3=12

To make 12 equal to 25 we will have to add the number 13.

Let's verify:

2512=13 25-12=13

Answer

13 13

Exercise #9

9+?3=25 9+?-3=25

Video Solution

Step-by-Step Solution

To find out which number is missing, we solve the entire exercise to know which number we will have to add to get a result of 25:

93=6 9-3=6

To make 6 equal to 25 we will have to add 19.

Let's verify:

256=19 25-6=19

Answer

19 19

Exercise #10

12×34×?=12 12\times3-4\times?=12

Video Solution

Step-by-Step Solution

According to the laws of Arithmetic operations:

We must first place the multiplication exercise inside parentheses as shown below:(12×3)4×?=12 (12\times3)-4\times?=12

We then solve the multiplication:

12×3=36 12\times3=36

Which should result in the following calculation:

364×?=12 36-4\times?=12

We then transfer numbers to the other side of the equation and change the signs accordingly:

4×?=1236 -4\times?=12-36

We complete the subtraction exercise:

1236=24 12-36=-24

Resulting in the following calculation:

4×?=24 -4\times?=-24

Finally we divide by negative 4:

?=244 ?=\frac{-24}{-4}

?=6 ?=6

Answer

6 6

Exercise #11

5×7+?=4811 -5\times-7+?=48-11

Video Solution

Step-by-Step Solution

According to the order of operations rules, we first enter the multiplication problem inside the parentheses:

(5×7)+?=4811 (-5\times-7)+?=48-11

We solve the problem inside the parentheses and the subtraction problem:

5×7=35 -5\times-7=35

4811=37 48-11=37

Now we get the problem:

35+?=37 35+?=37

We move the term and change the sign accordingly:

?=3735 ?=37-35

?=2 ?=2

Answer

2 2