Solve the Expression: 7+21÷7×4+3-9 Using Order of Operations

Order of Operations with Mixed Addition Subtraction

7+21:7×4+39= 7+21:7\times4+3-9=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Multiplication and division take precedence over addition and subtraction
00:10 When there are multiple operations at the same level of the order of operations hierarchy, we solve from left to right
00:20 Let's continue with the remaining multiplication operation
00:31 We're left with only addition and subtraction operations
00:34 Addition and subtraction are at the same level of the hierarchy, so we solve from left to right
00:51 That's the solution!

Step-by-step written solution

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1

Understand the problem

7+21:7×4+39= 7+21:7\times4+3-9=

2

Step-by-step solution

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

7+(21:7×4)+39= 7+(21:7\times4)+3-9=

We then proceed to solve the exercise inside of the parentheses from left to right:

21:7=3 21:7=3

3×4=12 3\times4=12

Which results in the following exercise:

7+12+39= 7+12+3-9=

We then finish by solving the exercise from left to right:

7+12=19 7+12=19

19+3=22 19+3=22

229=13 22-9=13

3

Final Answer

13

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Division and multiplication first, then left to right
  • Technique: Group operations: 7+(21÷7×4)+3-9 = 7+12+3-9
  • Check: Final calculation 7+12+3-9 = 19+3-9 = 22-9 = 13 ✓

Common Mistakes

Avoid these frequent errors
  • Solving from left to right without grouping
    Don't solve 7+21÷7×4+3-9 by going 28÷7×4 = 16+3-9 = 10! This ignores order of operations and gives the wrong answer. Always do division and multiplication first: 21÷7=3, then 3×4=12, then solve 7+12+3-9=13.

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 specific rules called order of operations (PEMDAS). Division and multiplication are stronger operations that must be done first, just like how you follow traffic rules even if another path seems shorter!

What does the colon symbol (:) mean in math?

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The colon symbol (:) means division, just like the ÷ symbol. So 21:7 21:7 is the same as 21÷7=3 21÷7 = 3 .

How do I remember to do multiplication and division first?

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Think of PEMDAS: Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). The M and D come before A and S!

Should I put parentheses around the division and multiplication?

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You can add parentheses like 7+(21÷7×4)+39 7+(21÷7×4)+3-9 to help visualize, but they're not required. The order of operations rules automatically handle this grouping.

What if I get a different answer when I check my work?

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Double-check each step! Make sure you did 21÷7=3 21÷7=3 , then 3×4=12 3×4=12 , then 7+12+39=13 7+12+3-9=13 . Go slowly through each calculation.

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