Solve (-6)+(-7)+13: Evaluating the Sum to Zero

Integer Addition with Number Line Visualization

(6)+(7)+13?0 (-6)+(-7)+13\text{?}0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate sign
00:03 Let's start from point (-6) on the negative side (left) of the axis
00:07 The number is directed and negative
00:10 The negative direction on the axis is left, so we'll take 7 to the left
00:25 The number is directed and positive
00:30 The positive direction on the axis is right, so we'll take 13 to the right
00:49 This is the solution for the left side
00:53 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

(6)+(7)+13?0 (-6)+(-7)+13\text{?}0

2

Step-by-step solution

Let's first solve the equation:

(6)+(7)+13= (-6)+(-7)+13=

We'll need to locate -6 on the number line and then move 7 steps to the left (since -7 is less than zero):

-15-14-13-12-11-10-9-8-7-6-5-4-3

After doing this, we will have reached the number -13.

Now we'll move 13 steps to the right (since 13 is greater than zero):

-15-14-13-12-11-10-9-8-7-6-5-4-3-2-10

After doing this, we will have reached the number 0.

The solution to the equation is:

(6)+(7)+13=0 (-6)+(-7)+13=0

Therefore, the appropriate sign will be:

0=0 0=0

3

Final Answer

= =

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Add from left to right: (-6) + (-7) first, then add 13
  • Number Line Method: Start at -6, move 7 left to -13, then 13 right to 0
  • Verification: Check that -6 + (-7) + 13 = -13 + 13 = 0 ✓

Common Mistakes

Avoid these frequent errors
  • Adding signs incorrectly with negative numbers
    Don't treat (-6) + (-7) as 6 + 7 = 13! This ignores the negative signs and gives +13 instead of -13. Always remember that adding two negative numbers gives a more negative result, so (-6) + (-7) = -13.

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 do I add the negative numbers first?

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You follow the order of operations and work from left to right! Start with (6)+(7)=13 (-6) + (-7) = -13 , then add the positive 13 to get your final answer.

How does the number line help me visualize this?

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The number line shows movement! Starting at -6, moving 7 steps left (because -7 is negative) takes you to -13. Then moving 13 steps right (because +13 is positive) brings you exactly to 0.

What does it mean when the answer equals zero?

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When an expression equals zero, it means the positive and negative parts cancel out perfectly! In this case, the negative parts (-6 and -7) total -13, which exactly balances the positive 13.

Can I group the numbers differently?

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Yes! You could calculate (6)+13+(7) (-6) + 13 + (-7) or 13+(6)+(7) 13 + (-6) + (-7) . The commutative property means addition order doesn't change the final result.

How do I know if my final comparison is correct?

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Calculate the left side completely first: (6)+(7)+13=0 (-6) + (-7) + 13 = 0 . Since 0 = 0 is always true, the correct comparison symbol is = (equals).

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