Solve the Fraction: -864/864 Simplification Challenge

Q: Why is the answer -1 and not 1?

The negative sign in the numerator makes all the difference! When you have a negative number divided by a positive number, the result is always negative. So $ \frac{-864}{864} = -1 $.

Q: How do I know 864 is the greatest common divisor?

Since both the numerator and denominator have the same absolute value (864), the GCD is 864 itself. This means $ \frac{-864}{864} = \frac{-864 ÷ 864}{864 ÷ 864} = \frac{-1}{1} = -1 $.

Q: What if the negative was in the denominator instead?

If you had $ \frac{864}{-864} $, the result would still be -1! A positive divided by a negative also gives a negative result.

Q: Can I cancel out the negative signs?

No! You can only cancel negative signs when both numerator and denominator are negative. Here, only the numerator is negative, so the fraction stays negative.

Q: How do I check if my simplification is correct?

Multiply your simplified answer by the denominator: $ -1 × 864 = -864 $. This should equal your original numerator. Since it does, -1 is correct!

Fraction Simplification with Negative Values

Solve the following problem:

$\frac{-864}{864}=$

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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:

$\frac{-864}{864}=$

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, the number is -864

We will divide the fraction as follows:

$\frac{-864:-864}{864:-864}=\frac{1}{-1}=-1$

Final Answer

$-1$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by positive equals negative result
Technique: Find GCD of 864 and 864, which is 864
Check: Verify $\frac{-864}{864} = -1$ by cross-multiplying: -864 × 1 = 864 × (-1) ✓

Common Mistakes

Avoid these frequent errors

Ignoring the negative sign during simplification
Don't forget the negative sign and write $\frac{-864}{864} = 1$ ! The negative numerator makes the entire fraction negative. Always preserve the sign throughout simplification to get -1, not 1.

Practice Quiz

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Write the fraction shown in the diagram as a number:

FAQ

Everything you need to know about this question

Why is the answer -1 and not 1?

The negative sign in the numerator makes all the difference! When you have a negative number divided by a positive number, the result is always negative. So $\frac{-864}{864} = -1$ .

How do I know 864 is the greatest common divisor?

Since both the numerator and denominator have the same absolute value (864), the GCD is 864 itself. This means $\frac{-864}{864} = \frac{-864 ÷ 864}{864 ÷ 864} = \frac{-1}{1} = -1$ .

What if the negative was in the denominator instead?

If you had $\frac{864}{-864}$ , the result would still be -1! A positive divided by a negative also gives a negative result.

Can I cancel out the negative signs?

No! You can only cancel negative signs when both numerator and denominator are negative. Here, only the numerator is negative, so the fraction stays negative.

How do I check if my simplification is correct?

Multiply your simplified answer by the denominator: $-1 × 864 = -864$ . This should equal your original numerator. Since it does, -1 is correct!

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