Solve -5-(-2): Using Number Line to Subtract Negative Numbers

Q: Why does subtracting a negative become addition?

Think of it as removing a debt! If you owe -2 dollars and that debt is taken away, you actually gain 2 dollars. So -(-2) = +2.

Q: Which direction do I move on the number line?

After converting to addition, move right for positive numbers and left for negative numbers. Since -5+2 means add 2, move 2 steps to the right from -5.

Q: How do I remember the double negative rule?

Use the phrase "two negatives make a positive"! Just like in English: "I don't have no money" actually means "I do have money."

Q: What if I get confused about the direction?

Always rewrite the problem first! Change $ -5-(-2) $ to $ -5+2 $, then use normal addition rules on the number line.

Q: Can I solve this without a number line?

Yes! Once you convert to $ -5+2 $, think: "5 steps back, then 2 steps forward" gives you 3 steps back from zero, which is -3.

Subtracting Negative Numbers with Number Line

$-5-(-2)=$

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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

00:06 Let's open the parentheses

00:11 The number is directed, positive

00:14 Movement towards the positive side of the axis is to the right

00:18 We'll take from point (-5) 2 units towards the positive direction (right)

00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-5-(-2)=$

Step-by-step solution

Let's remember the rule:

$-(-x)=+x$

Therefore, the exercise we received is:

$-5+2=$

We'll locate minus 5 on the number line and move two steps to the right (since 2 is greater than zero):

We can see that we've arrived at the number minus 3.

Final Answer

$-3$

Key Points to Remember

Essential concepts to master this topic

Rule: Subtracting a negative equals adding a positive: -(-x) = +x
Technique: Transform -5-(-2) into -5+2, then move right on number line
Check: Start at -5, move 2 steps right to reach -3 ✓

Common Mistakes

Avoid these frequent errors

Treating double negative as still negative
Don't calculate -5-(-2) as -5-2 = -7! This ignores the negative sign rule and moves left instead of right. Always remember that subtracting a negative number means adding its positive value: -(-2) becomes +2.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why does subtracting a negative become addition?

Think of it as removing a debt! If you owe -2 dollars and that debt is taken away, you actually gain 2 dollars. So -(-2) = +2.

Which direction do I move on the number line?

After converting to addition, move right for positive numbers and left for negative numbers. Since -5+2 means add 2, move 2 steps to the right from -5.

How do I remember the double negative rule?

Use the phrase "two negatives make a positive"! Just like in English: "I don't have no money" actually means "I do have money."

What if I get confused about the direction?

Always rewrite the problem first! Change $-5-(-2)$ to $-5+2$ , then use normal addition rules on the number line.

Can I solve this without a number line?

Yes! Once you convert to $-5+2$ , think: "5 steps back, then 2 steps forward" gives you 3 steps back from zero, which is -3.

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