Solve the Expression: 7+3×7-3×4+5 Using Order of Operations

Order of Operations with Mixed Addition-Subtraction

Complete the exercise:

7+3×73×4+5= 7+3\times7-3\times4+5=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Remember, multiplication takes priority over addition and subtraction.
00:24 Now, for addition and subtraction, solve them from left to right.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the exercise:

7+3×73×4+5= 7+3\times7-3\times4+5=

2

Step-by-step solution

According to the rules of the order of arithmetic operations, we must first place multiplication and division exercises within parentheses:

7+(3×7)(3×4)+5= 7+(3\times7)-(3\times4)+5=

We then proceed to solve the exercise inside of the parentheses:

3×7=21 3\times7=21

3×4=12 3\times4=12

We obtain the following exercise:

7+2112+5= 7+21-12+5=

Lastly we solve the exercise from left to right:

21+7=28 21+7=28

2812=16 28-12=16

16+5=21 16+5=21

3

Final Answer

21

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always multiply first, then add and subtract from left to right
  • Technique: Calculate 3×7=21 3\times7=21 and 3×4=12 3\times4=12 before adding/subtracting
  • Check: Final calculation should be 7+2112+5=21 7+21-12+5=21

Common Mistakes

Avoid these frequent errors
  • Solving from left to right without doing multiplication first
    Don't calculate 7+3=10, then 10×7=70! This ignores PEMDAS and gives completely wrong results like 253 instead of 21. Always complete ALL multiplications before any addition or 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 a special order called PEMDAS that's different from reading! If we solved left to right, the same expression could have multiple answers, which would make math impossible to use reliably.

What if I forget to do multiplication first?

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You'll get a completely wrong answer! For example, doing 7+3=10 7+3=10 first would eventually give you 253 instead of the correct answer 21. Always look for multiplication signs first.

How do I remember the order of operations?

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Use the acronym PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). Some people remember it as "Please Excuse My Dear Aunt Sally."

Do I need parentheses around the multiplication?

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Not required, but it can help! Writing 7+(3×7)(3×4)+5 7+(3\times7)-(3\times4)+5 makes it clearer which operations to do first, especially when you're learning.

What if I get a negative number during the calculation?

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That's normal! In this problem, when you calculate 2812=16 28-12=16 , you get a positive result, but negative intermediate results are fine too. Just keep following the order carefully.

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