Solve the Expression: 30+6-5+7-17 Step by Step

Integer Operations with Left-to-Right Processing

30+65+717= 30+6-5+7-17=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's use the commutative law to rearrange these numbers in a way that's easier to work with.
00:16 Remember, addition and subtraction are solved left to right, as they have the same level in operation order.
00:33 And there you have it! This is our solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

30+65+717= 30+6-5+7-17=

2

Step-by-step solution

Insofar as the exercise only involves addition and subtraction operations, we will solve it from left to right:

30+6=36 30+6=36

365=31 36-5=31

31+7=38 31+7=38

3817=21 38-17=21

3

Final Answer

21 21

Key Points to Remember

Essential concepts to master this topic
  • Order Rule: Addition and subtraction operations work left to right
  • Technique: Calculate step by step: 30+6=36, then 36-5=31
  • Check: Verify final answer by adding positives and subtracting negatives: 30+6+7-5-17=21 ✓

Common Mistakes

Avoid these frequent errors
  • Trying to combine all positive or negative terms first
    Don't group 30+6+7=43 and 5+17=22, then subtract = wrong order! This ignores the left-to-right sequence and gives 43-22=21 by luck, but fails with other problems. Always work strictly from left to right with addition and subtraction.

Practice Quiz

Test your knowledge with interactive questions

\( 8 - 2 + 6 = \)

FAQ

Everything you need to know about this question

Why can't I just add all the positive numbers and subtract all the negative numbers?

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While that might work sometimes by coincidence, it's mathematically incorrect! The order matters in mixed addition and subtraction. Always follow the left-to-right rule to get reliable results.

What if I get confused with all the signs?

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Take it one step at a time! Write down each calculation: 30+6=36, then 36-5=31, then 31+7=38, finally 38-17=21. This prevents sign errors.

Is there a faster way to solve this?

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You can rewrite as 30+6+7517 30+6+7-5-17 and group: (30+6+7)(5+17)=4322=21 (30+6+7)-(5+17) = 43-22 = 21 . But be very careful with the signs when regrouping!

How do I check my work without redoing the whole problem?

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Use a different method! Try: positive terms (30+6+7=43) minus negative terms (5+17=22) equals 43-22=21. If you get the same answer, you're correct!

What's the most important thing to remember?

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When you see only addition and subtraction, work from left to right like reading a book. Don't jump around or try to be clever with grouping unless you're very confident with signs!

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