Solve: 35 × 9 - 15 - 65 | Multi-Step Arithmetic Problem

Q: Why do I multiply 35 × 9 first instead of subtracting?

The order of operations (PEMDAS) tells us to do multiplication before subtraction. This ensures everyone gets the same answer! Always follow: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Q: Can I subtract 15 and 65 first to get 80, then do 35 × 9 - 80?

Yes! Since both operations after multiplication are subtraction, you can combine them: $ 35 \times 9 - (15 + 65) = 315 - 80 = 235 $. This gives the same correct answer.

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

Mathematics has special rules! If we worked left to right, everyone would get different answers for the same problem. The order of operations ensures consistency - the same problem always has the same solution.

Order of Operations with Multi-Step Subtraction

$35 \times 9 - 15 - 65 =$

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Understand the problem

$35 \times 9 - 15 - 65 =$

Step-by-step solution

First, perform the multiplication: $35 \times 9 = 315$

Next, perform the subtraction: $315 - 15 = 300$

Finally, subtract 65: $300 - 65 = 235$

Final Answer

$235$

Key Points to Remember

Essential concepts to master this topic

PEMDAS Rule: Multiplication before subtraction in order of operations
Left to Right: After multiplication, subtract sequentially: 315 - 15, then - 65
Verification: Check by working backwards: 235 + 65 + 15 = 315 ✓

Common Mistakes

Avoid these frequent errors

Performing subtraction before multiplication
Don't calculate 35 × (9 - 15 - 65) = 35 × (-71) = -2485! This ignores order of operations and gives a completely wrong negative result. Always multiply first, then subtract from left to right.

Practice Quiz

Test your knowledge with interactive questions

$8 + 3 \times 2 =$

FAQ

Everything you need to know about this question

Why do I multiply 35 × 9 first instead of subtracting?

The order of operations (PEMDAS) tells us to do multiplication before subtraction. This ensures everyone gets the same answer! Always follow: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Can I subtract 15 and 65 first to get 80, then do 35 × 9 - 80?

Yes! Since both operations after multiplication are subtraction, you can combine them: $35 \times 9 - (15 + 65) = 315 - 80 = 235$ . This gives the same correct answer.

What if I accidentally get 230 instead of 235?

You likely made an arithmetic error in one of the subtractions. Double-check: $315 - 15 = 300$ , then $300 - 65 = 235$ . Take your time with each step!

How can I check if 235 is really correct?

Work backwards! Start with 235, add back what you subtracted: $235 + 65 = 300$ , then $300 + 15 = 315$ . Finally check: $35 \times 9 = 315$ ✓

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

Mathematics has special rules! If we worked left to right, everyone would get different answers for the same problem. The order of operations ensures consistency - the same problem always has the same solution.

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