Examples with solutions for Parentheses in advanced 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

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