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

Exercise #1

Fill in the missing number:

? ⁣:(−6)+[−2(94−73)]=−153 ?\colon(-6)+\lbrack-2(94-73)\rbrack=-153

Video Solution

Step-by-Step Solution

We begin by solving the innermost parentheses:

94−73=21 94-73=21

We obtain the following calculation:

x ⁣:(−6)+[−2(21)]=−153 x\colon(-6)+\lbrack-2(21)\rbrack=-153

Next we focus on the parentheses and multiply:

−2×21=−42 -2\times21=-42

We obtain the following calculation:

x ⁣:(−6)+(−42)=−153 x\colon(-6)+(-42)=-153

Let's consider the multiplication between minus and plus:

x ⁣:(−6)−42=−153 x\colon(-6)-42=-153

We swap sections:

x ⁣:(−6)=−153+42 x\colon(-6)=-153+42

x ⁣:(−6)=−111 x\colon(-6)=-111

x−6=−111 \frac{x}{-6}=-111

Lastly we multiply by minus 6:

x=−111×−6=666 x=-111\times-6=666

Answer

x=666 x=666

Exercise #2

Fill in the missing number:

? ⁣:4+8×3−7=26 ?\colon4+8\times3-7=26

Video Solution

Step-by-Step Solution

First, we place the multiplication exercise inside of parentheses:

x ⁣:4+(8×3)−7=26 x\colon4+(8\times3)-7=26

Next we solve the multiplication exercise:

x ⁣:4+24−7=26 x\colon4+24-7=26

We then place the subtraction exercise in parentheses:

x ⁣:4+(24−7)=26 x\colon4+(24-7)=26

We solve the subtraction exercise:

x ⁣:4+17=26 x\colon4+17=26

We swap sections:

x ⁣:4=26−17 x\colon4=26-17

x4=9 \frac{x}{4}=9

Multiply by 4

x=4×9=36 x=4\times9=36

Answer

?=36 ?=36

Exercise #3

What is the missing number in the equation?

5×17−112−?14=−27.5 5\times17-112-\frac{?}{14}=-27.5

Video Solution

Step-by-Step Solution

We place the multiplication exercise inside of the parenthesis:

(5×17)−112−x14=−27.5 (5\times17)-112-\frac{x}{14}=-27.5

We solve the multiplication exercise and then subtract:

85−112−x14=−27.5 85-112-\frac{x}{14}=-27.5

−27−x14=−27.5 -27-\frac{x}{14}=-27.5

We swap sections:

−x14=−27.5+27 -\frac{x}{14}=-27.5+27

−x14=−12 -\frac{x}{14}=-\frac{1}{2}

We multiply by 14:

−x=−12×14 -x=-\frac{1}{2}\times14

−x=−7 -x=-7

We multiply by -1

x=7 x=7

Answer

7 7

Exercise #4

Calculate the missing number in the equation:

(45−22)×19+25 ⁣:5+?×3=82 (45-22)\times19+25\colon5+?\times3=82

Video Solution

Step-by-Step Solution

We solve the exercise in parentheses:

23×19+25 ⁣:5+?×3=82 23\times19+25\colon5+?\times3=82

We place the multiplication and division exercises inside parentheses:

(23×19)+(25 ⁣:5)+?×3=82 (23\times19)+(25\colon5)+?\times3=82

We solve the exercise in parentheses:

437+5+?×3=82 437+5+?\times3=82

We simplify:

442+?×3=82 442+?\times3=82

We swap sections:

?×3=82−442 ?\times3=82-442

?×3=−360 ?\times3=-360

We divide by 3

?=−120 ?=-120

Answer

?=−120 ?=-120