Evaluate the Expression: 5 + (-4) + (-2) Compared to Zero

Integer Addition with Negative Numbers

5+(4)+(2)?0 5+(-4)+(-2)\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 (5) on the positive (right) side of the axis
00:08 The number is directed and negative
00:13 The negative direction on the axis is left, so we'll take 4 to the left
00:22 The number is directed and negative
00:27 The negative direction on the axis is left, so we'll take 2 to the left
00:31 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

5+(4)+(2)?0 5+(-4)+(-2)\text{?}0

2

Step-by-step solution

Let's first solve the following equation:

5+(4)+(2)= 5+(-4)+(-2)=

Now we will locate the number 5 on the number line and move 4 steps to the left (since minus 4 is less than zero):

-8-7-6-5-4-3-2-101234675

This brings us to the number 1.

Now let's move two steps to the left (since minus 2 is less than zero):

-8-7-6-5-4-3-2-101234675

This leaves us on the number -1.

Therefore, the solution to the equation is:

5+(4)+(2)=1 5+(-4)+(-2)=-1

The missing sign is:

1<0 -1<0

3

Final Answer

< <

Key Points to Remember

Essential concepts to master this topic
  • Addition Rule: Adding negatives means moving left on number line
  • Step-by-Step: Start at 5, move 4 left to 1, then 2 more left to -1
  • Verification: Check final position: -1 is left of 0, so -1 < 0 ✓

Common Mistakes

Avoid these frequent errors
  • Treating negative signs as subtraction
    Don't think 5 + (-4) means 5 - 4 = 1, then somehow get confused with the second negative! This misses that we're adding negative values, not subtracting. Always think of negative numbers as directions on the number line - adding negatives means moving left from your starting position.

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 we 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. When you add a negative number, you're 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 conceptually they're different! Adding (-4) means 'add a negative four,' while subtracting 4 means 'take away four.' Both move you 4 steps left on the number line.

Can I just ignore the parentheses around negative numbers?

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Never ignore them! The parentheses show you're adding a negative number. 5+(4) 5 + (-4) is very different from 54 5 - 4 conceptually, even though they equal the same thing.

What if I get confused with multiple negative numbers?

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Take it one step at a time! Start at your first number, then move left for each negative number you're adding. Don't try to do it all at once.

How do I know if my final answer should be compared to zero?

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Look at where you end up on the number line! If you're to the left of zero, your number is less than zero. If you're to the right of zero, it's greater than zero.

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