Solve the Fraction -9/9: Basic Negative Number Division

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

Because you have a negative numerator (-9) divided by a positive denominator (9). The rule is: negative ÷ positive = negative. Think of it as: "How many 9s go into -9?" The answer is -1.

Q: Can I just cancel out the 9s and get 0?

No! You can't cancel numbers that are being added or subtracted. Here we have $ \frac{-9}{9} $, not $ \frac{9-9}{9} $. The negative is part of the number -9, not subtraction.

Q: What if both the numerator and denominator were negative?

If you had $ \frac{-9}{-9} $, then negative ÷ negative = positive, so the answer would be +1. Remember: same signs give positive, different signs give negative.

Q: How do I know when a fraction is fully simplified?

A fraction is fully simplified when the greatest common divisor (GCD) of the numerator and denominator is 1. Since $ \frac{-1}{1} $ has GCD = 1, it's fully simplified!

Q: Does the negative sign have to stay in the numerator?

No! $ \frac{-9}{9} = \frac{-1}{1} = -1 $ are all equivalent. You can write the negative sign in the numerator, denominator, or in front of the fraction - they all mean the same thing.

Fraction Simplification with Negative Numerators

Solve the following problem:

$\frac{-9}{9}=$

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Step-by-step written solution

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Understand the problem

Solve the following problem:

$\frac{-9}{9}=$

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 -9

We will divide the fraction as follows:

$\frac{-9:-9}{9:-9}=\frac{1}{-1}=-1$

Final Answer

$-1$

Key Points to Remember

Essential concepts to master this topic

Rule: Negative divided by positive always equals negative
Technique: Divide both parts by GCD: $\frac{-9}{9} = \frac{-9÷9}{9÷9} = \frac{-1}{1} = -1$
Check: Verify by multiplication: $-1 × 9 = -9$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring the negative sign during simplification
Don't simplify $\frac{-9}{9}$ to just 1 by forgetting the negative = wrong positive answer! The negative sign in the numerator makes the entire fraction negative. Always keep track of negative signs throughout all steps.

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?

Because you have a negative numerator (-9) divided by a positive denominator (9). The rule is: negative ÷ positive = negative. Think of it as: "How many 9s go into -9?" The answer is -1.

Can I just cancel out the 9s and get 0?

No! You can't cancel numbers that are being added or subtracted. Here we have $\frac{-9}{9}$ , not $\frac{9-9}{9}$ . The negative is part of the number -9, not subtraction.

What if both the numerator and denominator were negative?

If you had $\frac{-9}{-9}$ , then negative ÷ negative = positive, so the answer would be +1. Remember: same signs give positive, different signs give negative.

How do I know when a fraction is fully simplified?

A fraction is fully simplified when the greatest common divisor (GCD) of the numerator and denominator is 1. Since $\frac{-1}{1}$ has GCD = 1, it's fully simplified!

Does the negative sign have to stay in the numerator?

No! $\frac{-9}{9} = \frac{-1}{1} = -1$ are all equivalent. You can write the negative sign in the numerator, denominator, or in front of the fraction - they all mean the same thing.

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