Solve -27-(-7)+(-6)+2-11: Complete Integer Operations Challenge

Integer Operations with Consecutive Sign Changes

27(7)+(6)+211= -27-(-7)+(-6)+2-11=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Negative times negative always equals positive
00:18 Let's calculate one operation at a time from left to right
00:24 Take 7 jumps to the right (to the positive side) on the axis
00:35 This is the solution to the operation
00:39 Positive times negative always equals negative
00:43 Let's arrange the exercise
00:48 Take 6 jumps to the left (to the negative side) on the axis
01:00 This is the solution to the operation
01:10 Take 2 jumps to the right (to the positive side) on the axis
01:18 This is the solution to the operation
01:30 Take 11 jumps to the left (to the negative side) on the axis
01:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

27(7)+(6)+211= -27-(-7)+(-6)+2-11=

2

Step-by-step solution

First, we solve the multiplication exercise, that is where there is a plus or minus sign before another sign.

27+76+211= -27+7-6+2-11=

Now we solve as a common exercise from left to right:

27+7=20 -27+7=-20

206=26 -20-6=-26

26+2=24 -26+2=-24

2411=35 -24-11=-35

3

Final Answer

35 -35

Key Points to Remember

Essential concepts to master this topic
  • Order: Simplify double negatives before calculating from left to right
  • Technique: -(-7) becomes +7, so -27-(-7) = -27+7 = -20
  • Check: Final calculation: -20-6+2-11 = -35, verify each step ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to change -(-7) to +7
    Don't leave -27-(-7) as -27-7 = -34! This ignores the double negative rule and gives the wrong starting point. Always convert -(-7) to +7 first, making the expression -27+7-6+2-11.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

FAQ

Everything you need to know about this question

Why does -(-7) become +7?

+

When you have two negative signs next to each other, they cancel out and become positive. Think of it as: subtracting a negative is the same as adding a positive!

Do I have to solve from left to right?

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Yes! For addition and subtraction problems like this, always work from left to right to avoid mistakes. Don't try to rearrange or skip around.

How can I avoid making sign errors?

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Write each step clearly: 27+7=20 -27+7=-20 , then 206=26 -20-6=-26 , then 26+2=24 -26+2=-24 , finally 2411=35 -24-11=-35 . Show every calculation!

What if I get confused by all the negative numbers?

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Break it down step by step! First handle the double negative, then tackle one operation at a time. Use a number line if it helps you visualize adding and subtracting.

Is there a shortcut for problems like this?

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The best 'shortcut' is being systematic: handle sign rules first, then calculate left to right. Rushing through these problems usually leads to sign errors!

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