All Operations in the Order of Operations: Complete the missing numbers

What is the missing number?

$23-12\times(-6)+?\colon7=102$

First, we solve the multiplication exercise:

$12\times(-6)=-72$

Now we get:

$23-(-72)+x\colon7=102$

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:

$23+72+x\colon7=102$

We reduce:

$95+x:7=102$

We move the sections:

$x:7=102-95$

$x:7=7$

$\frac{x}{7}=7$

Multiply by 7:

$x=7\times7=49$

49

$12+?+3-1=29$

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:

$12+3-1=$

$15-1=14$

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

Let's verify:

$29-14=15$

$15$

$9+?+3=25$

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:

$9+3=12$

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

Let's verify:

$25-12=13$

$13$

$7+?+2=20$

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:

$7+2=9$

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

Let's verify:

$20-9=11$

$11$

$7-?+4+2\times18=29$

First, we place the multiplication exercise in parentheses:

$7-?+4+(2\times18)=29$

We solve the exercise in parentheses:

$2\times18=36$

Now we obtain the exercise:

$7-?+4+36=29$

We reduce the addition exercise:

$36+4=40$

Now we obtain the exercise:

$7-?+40=29$

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:

$40+7-?=29$

We reduce:

$47-?=29$

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

$-?=29-47$

$-?=-18$

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

$?=18$

$18$

$17-?+4=5$

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:

$17+4-?=5$

We reduce:

$21-?=5$

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

$21=?+5$

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

$16=\text{?}$

$16$

$9+?-3=25$

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:

$9-3=6$

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

Let's verify:

$25-6=19$

$19$$$

$-5\times-7+?=48-11$

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

$(-5\times-7)+?=48-11$

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

$-5\times-7=35$

$48-11=37$

Now we get the problem:

$35+?=37$

We move the term and change the sign accordingly:

$?=37-35$

$?=2$

$2$

$12\times3-4\times?=12$

According to the laws of Arithmetic operations:

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

We then solve the multiplication:

$12\times3=36$

Which should result in the following calculation:

$36-4\times?=12$

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

$-4\times?=12-36$

We complete the subtraction exercise:

$12-36=-24$

Resulting in the following calculation:

$-4\times?=-24$

Finally we divide by negative 4:

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

$?=6$

$6$

$12\times3-4+?=27$

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

$(12\times3)-4+?=27$

We solve the exercise in parentheses:

$12\times3=36$

We obtain the exercise:

$36-4+?=27$

We reduce:

$32+?=27$

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

$?=27-32$

$?=-5$

$-5$

$8\times7-3+?=60$

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

$(8\times7)-3+?=60$

$8\times7=56$

Now we obtain the exercise:

$56-3+?=60$

We reduce the subtraction exercise:

$56-3=53$

We obtain the exercise:

$53+?=60$

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

$?=60-53$

$?=7$

$7$