Evaluate the Expression: 2+(-4)+(-4) Compared to 6

Integer Addition with Multiple Negative Terms

Using the number line below select the appropriate sign for the following expression:

2+(4)+(4)?6 2+(-4)+(-4)\text{?}6

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Choose the appropriate sign
00:04 Let's start from point (2) on the positive side of the axis
00:07 The number is directed and negative
00:10 The negative direction on the axis is to the left, so we'll take 4 to the left
00:17 The number is directed and negative
00:23 The negative direction on the axis is to the left, so we'll take 4 to the left
00:32 This is the solution for the left side
00:39 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

Using the number line below select the appropriate sign for the following expression:

2+(4)+(4)?6 2+(-4)+(-4)\text{?}6

2

Step-by-step solution

Let's begin by solving the following equation:

2+(4)+(4)= 2+(-4)+(-4)=

We'll locate the number 2 on the number line, and move 4 steps left from zero (since minus 4 is less than zero):

-8-7-6-5-4-3-2-101234

We reach minus 2.

Now let's move 4 steps left again from minus 2 (since minus 4 is less than zero):

-8-7-6-5-4-3-2-101234

We reach minus 6.

Therefore:

2+(4)+(4)=6 2+(-4)+(-4)=-6

So the correct sign will be:

6<6 -6 < 6

3

Final Answer

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Key Points to Remember

Essential concepts to master this topic
  • Addition Rule: When adding negative numbers, move left on number line
  • Technique: From 2, move left 4 units to -2, then left 4 more to -6
  • Check: Verify 2+(4)+(4)=6<6 2 + (-4) + (-4) = -6 < 6 using comparison ✓

Common Mistakes

Avoid these frequent errors
  • Confusing addition of negatives with subtraction
    Don't think 2 + (-4) means 2 - 4 = -2, then subtract 4 more to get 2! This ignores the second negative term completely. Always treat each negative addition as a separate leftward move on the number line.

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 move left when adding negative numbers?

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On a number line, positive numbers are to the right and negative numbers are to the left. Adding a negative number means moving in the negative direction, which is leftward.

How is adding (-4) different from subtracting 4?

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They give the same result, but the thinking is different! Adding (-4) means "add a negative four," while subtracting 4 means "take away four." Both move you 4 units left on the number line.

What if I have more than two negative numbers to add?

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Just keep moving left! Each negative number you add moves you further left on the number line. For example: 5+(2)+(3)+(1) 5 + (-2) + (-3) + (-1) means start at 5, then move left 2, then left 3, then left 1 more.

How do I remember which comparison symbol to use?

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Think of the symbols as hungry mouths that want to eat the bigger number! The open side faces the larger number. Since -6 is smaller than 6, we write 6<6 -6 < 6 .

Can I use parentheses to group the negative numbers first?

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Yes! You could write 2+[(4)+(4)]=2+(8)=6 2 + [(-4) + (-4)] = 2 + (-8) = -6 . This shows that adding two negatives gives you an even more negative result.

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