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

Exercise #1

Fill in the missing number:

? ⁣:(6)+[2(9473)]=153 ?\colon(-6)+\lbrack-2(94-73)\rbrack=-153

Video Solution

Step-by-Step Solution

We begin by solving the innermost parentheses:

9473=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

x6=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+8×37=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+247=26 x\colon4+24-7=26

We then place the subtraction exercise in parentheses:

x ⁣:4+(247)=26 x\colon4+(24-7)=26

We solve the subtraction exercise:

x ⁣:4+17=26 x\colon4+17=26

We swap sections:

x ⁣:4=2617 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?

5×17112?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)112x14=27.5 (5\times17)-112-\frac{x}{14}=-27.5

We solve the multiplication exercise and then subtract:

85112x14=27.5 85-112-\frac{x}{14}=-27.5

27x14=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:

(4522)×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=82442 ?\times3=82-442

?×3=360 ?\times3=-360

We divide by 3

?=120 ?=-120

Answer

?=120 ?=-120