Solve: 5×5×2-12÷4 Using Order of Operations

Order of Operations with Mixed Calculations

Solve the following problem using the order of operations:

5×5×212:4= 5\times5\times2-12:4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this math problem together.
00:11 Remember! Multiplication and division come first, before addition and subtraction.
00:18 Now, let's tackle one step at a time. Ready?
00:23 First, calculate the multiplication. Take your time!
00:28 Next, move on to the division part. We got this!
00:36 And there you have it! That's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following problem using the order of operations:

5×5×212:4= 5\times5\times2-12:4=

2

Step-by-step solution

According to the order of operations rules, we first enter the multiplication and division exercises into parentheses:

(5×5×2)(12:4)= (5\times5\times2)-(12:4)=

Now let's solve the exercises in parentheses from left to right:

5×5=25 5\times5=25

25×2=50 25\times2=50

12:4=3 12:4=3

We obtain the following exercise:

503=47 50-3=47

3

Final Answer

47 47

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Multiplication and division before addition and subtraction
  • Technique: Calculate 5×5×2=50 5\times5\times2=50 and 12÷4=3 12÷4=3 first
  • Check: Verify final calculation 503=47 50-3=47 matches given answer ✓

Common Mistakes

Avoid these frequent errors
  • Solving from left to right without following PEMDAS
    Don't solve 5×5×2-12÷4 as ((5×5×2)-12)÷4 = 38÷4 = 9.5! This ignores order of operations and gives completely wrong results. Always complete all multiplication and division first, then handle 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 solve from left to right like reading?

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Mathematics has specific rules that ensure everyone gets the same answer! The order of operations (PEMDAS) prevents confusion. Without these rules, 5×5×212÷4 5×5×2-12÷4 could have multiple different answers.

Do I need parentheses around the multiplication and division parts?

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You don't need to write them, but adding parentheses like (5×5×2)(12÷4) (5×5×2)-(12÷4) can help you visualize which operations to do first!

What if I have multiple multiplications in a row like 5×5×2?

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Work from left to right: first 5×5=25 5×5=25 , then 25×2=50 25×2=50 . When operations have the same priority level, go left to right.

How do I remember the order of operations?

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Use the acronym PEMDAS:

  • Parentheses
  • Exponents
  • Multiplication and Division (left to right)
  • Addition and Ssubtraction (left to right)

What's the difference between ÷ and : symbols?

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Both ÷ and : mean division! The colon (:) is commonly used in some countries instead of the division sign. So 12:4 12:4 and 12÷4 12÷4 both equal 3.

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