Solve: 13-(-3)+(-4)?12-(-2)-2 | Integer Operations with Multiple Signs

Sign Rules with Double Negatives

Fill in the missing sign (?):

13−(−3)+(−4)?12−(−2)−2 13-(-3)+(-4)?12-(-2)-2

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:10 Let's find the correct sign!
00:14 Remember, a negative times a negative gives a positive.
00:19 Let's open the parentheses.
00:22 Calculate one step at a time, from left to right.
00:26 A positive times a negative gives a negative.
00:30 Open the next set of parentheses.
00:33 Let's continue. Now we have the left side. Let's solve the right side.
00:38 Again, a negative times a negative results in a positive.
00:43 Open the parentheses here too.
00:45 Continue to calculate step by step.
00:49 Here's the result for the right side.
00:52 And that's the solution! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Fill in the missing sign (?):

13−(−3)+(−4)?12−(−2)−2 13-(-3)+(-4)?12-(-2)-2

2

Step-by-step solution

Let's solve the left side first, remembering the following rules:

−(−x)=+x -(-x)=+x

+(−x)=−x +(-x)=-x

Now, let's rewrite the expression in the appropriate form:

13+3−4= 13+3-4=

Let's now solve the expression from left to right:

13+3=16 13+3=16

16−4=12 16-4=12

Next, we will solve the right-hand side, using the laws we covered earlier.

Let's now rewrite the expression in the appropriate form:

12+2−2= 12+2-2=

Now, we can solve the expression from left to right:

12+2=14 12+2=14

14−2=12 14-2=12

Since both sides are equal, the appropriate sign is:

12=12 12=12

3

Final Answer

= =

Key Points to Remember

Essential concepts to master this topic
  • Sign Rules: Double negatives become positive: -(-3) = +3
  • Technique: Simplify each side separately: 13+3-4 = 12, then 12+2-2 = 12
  • Check: Both sides equal 12, so 12 = 12 is correct ✓

Common Mistakes

Avoid these frequent errors
  • Treating subtraction of negatives incorrectly
    Don't change -(-3) to -3 = getting 13-3-4 = 6! This ignores the double negative rule and gives the wrong result. Always remember that subtracting a negative number means adding the positive.

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 -(-3) become +3?

+

Think of it as "the opposite of the opposite". Since -3 is negative, the opposite of -3 is positive 3. So -(-3) = +3!

What's the difference between -(-2) and +(-2)?

+

-(-2) = +2 (subtracting a negative), but +(-2) = -2 (adding a negative). The first operation changes the sign twice!

Do I solve both sides at the same time?

+

No! Solve the left side completely first, then the right side completely. Finally, compare your two results to determine the correct comparison sign.

How do I remember the double negative rule?

+

Remember: "Two negatives make a positive!" Just like in English - saying "I don't have no money" actually means you DO have money.

What if I get confused with all the signs?

+

Take it step by step! First, handle all the parentheses and double negatives. Then rewrite the expression with simpler signs before calculating.

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