Solve the Division Problem: -5000 ÷ 500

Q: Why is the answer negative when I'm dividing by a positive number?

The sign rules for division say that negative ÷ positive = negative. Think of it this way: if you have -5000 and divide it into 500 equal groups, each group must be negative too!

Q: How do I remember the sign rules for division?

Use this simple pattern: same signs give positive, different signs give negative. Since -5000 (negative) and 500 (positive) have different signs, the answer is negative.

Q: Can I simplify the fraction before dividing?

Yes! Both numbers are divisible by 500. $ \frac{-5000}{500} = \frac{-5000÷500}{500÷500} = \frac{-10}{1} = -10 $

Q: What's the difference between -5000 ÷ 500 and 5000 ÷ (-500)?

Both give the same answer: -10! In division, it doesn't matter which number carries the negative sign - if only one number is negative, the result is always negative.

Q: How can I check if my answer is right?

Multiply your answer by the divisor: -10 × 500 = -5000 ✓. If you get back to the original dividend, your division is correct!

Integer Division with Negative Numbers

Solve the following problem:

$\frac{-5000}{500}=$

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following problem:

$\frac{-5000}{500}=$

Step-by-step solution

Remember that we are dividing a positive number by a negative number, so the result must be a negative number.

We will divide both the numerator and the denominator by the highest number that both are divisible by.

In this case, that number is 500

We will divide the fraction as follows:

$\frac{-5000:500}{500:500}=\frac{-10}{1}=-10$

Final Answer

$-10$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by positive always gives negative result
Technique: Simplify by dividing both numbers by common factor: 5000÷500=10
Check: Verify -10 × 500 = -5000, confirming our division is correct ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in the final answer
Don't ignore the negative sign and write 10 instead of -10! When dividing a negative by a positive, the result must be negative. Always keep track of the sign throughout your calculation and apply the division sign rules.

Practice Quiz

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Write the fraction shown in the picture, in words:

FAQ

Everything you need to know about this question

Why is the answer negative when I'm dividing by a positive number?

The sign rules for division say that negative ÷ positive = negative. Think of it this way: if you have -5000 and divide it into 500 equal groups, each group must be negative too!

How do I remember the sign rules for division?

Use this simple pattern: same signs give positive, different signs give negative. Since -5000 (negative) and 500 (positive) have different signs, the answer is negative.

Can I simplify the fraction before dividing?

Yes! Both numbers are divisible by 500. $\frac{-5000}{500} = \frac{-5000÷500}{500÷500} = \frac{-10}{1} = -10$

What's the difference between -5000 ÷ 500 and 5000 ÷ (-500)?

Both give the same answer: -10! In division, it doesn't matter which number carries the negative sign - if only one number is negative, the result is always negative.

How can I check if my answer is right?

Multiply your answer by the divisor: -10 × 500 = -5000 ✓. If you get back to the original dividend, your division is correct!

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