Solve the Expression: 9×5×5+7-5+82-2 Using Order of Operations

Order of Operations with Mixed Arithmetic

9⋅5⋅5+7−5+82−2=? 9\cdot5\cdot5+7-5+82-2=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve this expression together.
00:11 Remember, handle multiplication and division before doing addition and subtraction.
00:17 Take your time and solve each multiplication step one at a time.
00:29 Arrange the numbers to make the equation easier to solve.
00:40 First, do all the subtractions, then add everything together.
00:49 And 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

9⋅5⋅5+7−5+82−2=? 9\cdot5\cdot5+7-5+82-2=\text{?}

2

Step-by-step solution

According to the rules for the order of operations, we will isolate the multiplication operations in parentheses:

(9⋅5⋅5)+7−5+82−2= (9\cdot5\cdot5)+7-5+82-2=

We solve the exercise in parentheses from left to right:

9×5=45 9\times5=45

45×5=225 45\times5=225

Now, we obtain the exercise:

225+7−5+82−2= 225+7-5+82-2=

We solve the exercise from left to right

225+7=232 225+7=232

232−5=227 232-5=227

227+82=309 227+82=309

309−2=307 309-2=307

3

Final Answer

307

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Multiply first, then add and subtract from left to right
  • Technique: Calculate 9×5×5=225 9\times5\times5=225 before any addition or subtraction
  • Check: Verify each step: 225+7-5+82-2 = 232-5+82-2 = 307 ✓

Common Mistakes

Avoid these frequent errors
  • Working strictly left to right without considering order of operations
    Don't calculate 9+5=14, then 14×5=70! This ignores multiplication priority and gives 154 instead of 307. Always complete all multiplication operations first, then work left to right for addition and subtraction.

Practice Quiz

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\( 8 + 3 \times 2 = \)

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 a specific order that prevents confusion! Without PEMDAS, the expression 9×5×5+7−5+82−2 9\times5\times5+7-5+82-2 could have many different answers depending on how you read it.

Do I need parentheses around the multiplication?

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No! The multiplication 9×5×5 9\times5\times5 automatically has higher priority than addition and subtraction. Parentheses would be helpful for clarity, but they're not required.

What if I get a different answer than 307?

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Double-check your multiplication first: 9×5=45 9\times5=45 , then 45×5=225 45\times5=225 . Then work left to right: 225+7-5+82-2 step by step.

Is there a shortcut for multiple multiplications?

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Yes! You can group them: 9×5×5=9×25=225 9\times5\times5 = 9\times25 = 225 . Or calculate step by step: 9×5=45 9\times5=45 , then 45×5=225 45\times5=225 .

Why do we add and subtract from left to right?

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Addition and subtraction have equal priority in PEMDAS, so we break the tie by working left to right. This ensures everyone gets the same answer!

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