Solve Division Problem: -8 ÷ -12 Step by Step

Q: How do I simplify the fraction after dividing?

Look for the greatest common factor (GCF) in both numbers. Here, -8 = -4×2 and -12 = -4×3, so the GCF is 4. Cancel it out: $ \frac{-8}{-12} = \frac{2}{3} $

Q: Can I convert this to a decimal instead?

Absolutely! $ \frac{2}{3} = 0.666... $ But fractions are often more precise than decimals, so keep the fraction form unless specifically asked for a decimal.

Q: What if I wrote the division as -8 ÷ (-12)?

That's the same thing! Whether you write $ -8 ÷ (-12) $ or $ \frac{-8}{-12} $, both mean dividing -8 by -12, and both equal $ \frac{2}{3} $.

Q: How can I double-check my sign is correct?

Use the multiplication check: Does $ \frac{2}{3} \times (-12) = -8 $? Yes! If your answer were negative, you'd get $ -\frac{2}{3} \times (-12) = +8 $, which is wrong.

Division of Negative Numbers with Simplification

$-8:-12=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem.

00:09 Think of division as putting it into a fraction.

00:18 Now, let's break the number eight into four times two.

00:23 Next, break the number twelve into four times three.

00:27 Now let's simplify the fraction by canceling what we can.

00:32 Remember, a negative divided by a negative gives a positive.

00:41 And there we go, that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-8:-12=$

Step-by-step solution

Let's write the exercise as a fraction:

$\frac{-8}{-12}=$

We'll break down the numerator and denominator into multiplication exercises:

$\frac{-4\times2}{-4\times3}=$

We'll simplify the 4 in the numerator and denominator of the fraction and get:

$\frac{-2}{-3}=$

Let's remember that when we divide a negative number by a negative number, the result will always be positive.

Therefore, the answer is:

$\frac{2}{3}$

Final Answer

$\frac{2}{3}$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Dividing two negative numbers always gives a positive result
Technique: Factor out common terms like -4 from both -8 and -12
Check: Verify $\frac{2}{3} \times (-12) = -8$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative-negative sign rule
Don't think $\frac{-8}{-12} = -\frac{2}{3}$ ! This ignores that dividing two negatives gives a positive result. Always remember: negative ÷ negative = positive, so the answer is $\frac{2}{3}$ .

Practice Quiz

Test your knowledge with interactive questions

$(+10)\times(+3)=$

FAQ

Everything you need to know about this question

Why does dividing two negative numbers give a positive answer?

Think of it this way: if you owe $8 and split that debt among 12 people equally, each person owes a positive amount! The mathematical rule is: negative ÷ negative = positive, just like (-1) × (-1) = +1.

How do I simplify the fraction after dividing?

Look for the greatest common factor (GCF) in both numbers. Here, -8 = -4×2 and -12 = -4×3, so the GCF is 4. Cancel it out: $\frac{-8}{-12} = \frac{2}{3}$

Can I convert this to a decimal instead?

Absolutely! $\frac{2}{3} = 0.666...$ But fractions are often more precise than decimals, so keep the fraction form unless specifically asked for a decimal.

What if I wrote the division as -8 ÷ (-12)?

That's the same thing! Whether you write $-8 ÷ (-12)$ or $\frac{-8}{-12}$ , both mean dividing -8 by -12, and both equal $\frac{2}{3}$ .

How can I double-check my sign is correct?

Use the multiplication check: Does $\frac{2}{3} \times (-12) = -8$ ? Yes! If your answer were negative, you'd get $-\frac{2}{3} \times (-12) = +8$ , which is wrong.

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