Solve -30-(-10): Working with Double Negatives in Subtraction

Q: Why does subtracting a negative become addition?

Think of it as removing a debt! If you owe $10 (negative) and that debt is removed (subtracted), you actually gain $10. So $ -(-10) = +10 $.

Q: How do I remember the double negative rule?

Use the phrase: "Two negatives make a positive!" When you see minus a negative, it always becomes plus a positive.

Q: What if the negative number being subtracted is larger?

Same rule applies! For example: $ -5-(-15) = -5+15 = 10 $. You still change subtraction to addition and make the negative positive.

Double Negatives with Integer Subtraction

$-30-(-10)=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

00:07 Open parentheses

00:10 Find the point (-30) on the axis

00:14 The number is directed, positive

00:17 Movement towards the positive side of the axis is to the right

00:21 Let's take 10 jumps to the right

00:35 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

$-30-(-10)=$

Step-by-step solution

Let's remember the following rule:

$-(-x)=+$

Now let's write the exercise in the appropriate form:

$-30+(10)=$

We'll locate the number negative 30 on the number line.

We'll move 10 steps to the right (since 10 is greater than zero):

We can see that we've arrived at the number negative 20.

Final Answer

$-20$

Key Points to Remember

Essential concepts to master this topic

Rule: Subtracting a negative number equals adding its positive
Technique: Transform $-30-(-10)$ into $-30+10$
Check: Start at -30, move 10 right on number line: -20 ✓

Common Mistakes

Avoid these frequent errors

Treating double negative as multiplication
Don't think -(-10) means -10 times -1 = -10! This ignores the subtraction rule and gives -40. Always remember: subtracting a negative means adding the positive, so -30-(-10) becomes -30+10.

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 $10 (negative) and that debt is removed (subtracted), you actually gain$ 10. So $-(-10) = +10$ .

How do I remember the double negative rule?

Use the phrase: "Two negatives make a positive!" When you see minus a negative, it always becomes plus a positive.

Can I use a number line to solve this?

Absolutely! Start at -30, then since you're adding 10 (not subtracting), move 10 steps to the right. You'll land on -20.

What if the negative number being subtracted is larger?

Same rule applies! For example: $-5-(-15) = -5+15 = 10$ . You still change subtraction to addition and make the negative positive.

Is this the same as adding and subtracting positive numbers?

Not quite! With positive numbers, subtraction means moving left on the number line. But subtracting a negative always means moving right (addition).

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime