Solve for the Missing Number in 12×3-4+?=27: Order of Operations

Order of Operations with Missing Terms

12×3−4+?=27 12\times3-4+?=27

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Step-by-step video solution

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00:01 Multiplication comes before addition and subtraction
00:24 Subtract 32 from both sides of the equation to isolate the unknown

Step-by-step written solution

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1

Understand the problem

12×3−4+?=27 12\times3-4+?=27

2

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:

36−4+?=27 36-4+?=27

We reduce:

32+?=27 32+?=27

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

?=27−32 ?=27-32

?=−5 ?=-5

3

Final Answer

−5 -5

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Multiply first, then subtract and add from left to right
  • Technique: Calculate 12×3=36 12\times3=36 first, then solve 36−4+?=27 36-4+?=27
  • Check: Substitute -5: 12×3−4+(−5)=36−4−5=27 12\times3-4+(-5)=36-4-5=27 ✓

Common Mistakes

Avoid these frequent errors
  • Adding and subtracting before multiplying
    Don't solve left to right without following PEMDAS = wrong answer! If you calculate 12×3-4 as 12×(3-4), you get 12×(-1)=-12, making the equation impossible to solve. Always multiply first, then work left to right with addition and subtraction.

Practice Quiz

Test your knowledge with interactive questions

\( 8 + 3 \times 2 = \)

FAQ

Everything you need to know about this question

Why can't I just work from left to right like in reading?

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Math has a special order called PEMDAS that ensures everyone gets the same answer! Multiplication always comes before addition and subtraction, no matter where it appears in the expression.

How do I know when to use parentheses in my work?

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You can add parentheses around multiplication to help visualize: (12×3)−4+?=27 (12\times3)-4+?=27 . This reminds you to multiply first before doing anything else!

What if I get a negative number as the missing value?

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Negative answers are completely normal! In this problem, we need -5 to make the equation balance. Always trust your math, even with negative results.

How can I double-check my work?

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Substitute your answer back into the original equation: 12×3−4+(−5) 12\times3-4+(-5) . Calculate step by step: 36−4−5=27 36-4-5=27 . If you get 27, you're correct!

Why did 32 change to -32 when moved to the other side?

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When you move a number across the equals sign, it changes sign! So 32+?=27 32+?=27 becomes ?=27−32 ?=27-32 . This is like 'undoing' the addition.

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