Simplify the Negative Fraction: -40/120 Step-by-Step

Q: Why is the answer negative when I'm simplifying a fraction?

The answer is negative because you have -40 in the numerator (negative) and 120 in the denominator (positive). When you divide a negative by a positive, the result is always negative!

Q: Can I move the negative sign to the denominator instead?

Yes! $ \frac{-40}{120} = \frac{40}{-120} = -\frac{40}{120} $ are all equivalent. But it's conventional to write the negative sign in front of the fraction.

Q: What if I divided by a smaller number like 10 instead of 40?

You'd get $ \frac{-4}{12} $, which isn't fully simplified! You can simplify further by dividing by 4 to get $ -\frac{1}{3} $. Always use the largest common factor to simplify in one step.

Q: How do I check if my simplified fraction is correct?

Multiply your answer by the original denominator: $ -\frac{1}{3} \times 120 = -40 $. If you get the original numerator, your simplification is correct!

Fraction Simplification with Negative Numbers

Solve the following problem:

$\frac{-40}{120}=$

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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:

$\frac{-40}{120}=$

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 -40

We will divide the fraction as follows:

$\frac{-40:-40}{120:-40}=\frac{1}{-5}=-\frac{1}{5}$

Final Answer

$-\frac{1}{3}$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by positive equals negative result
Technique: Find GCD of 40 and 120, which is 40
Check: Verify $-\frac{1}{3} \times 120 = -40$ ✓

Common Mistakes

Avoid these frequent errors

Ignoring the negative sign when simplifying
Don't forget the negative sign and write 1/3 instead of -1/3! The negative sign must stay with the simplified fraction because we're dividing a negative by a positive. Always keep track of the sign throughout your simplification.

Practice Quiz

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FAQ

Everything you need to know about this question

Why is the answer negative when I'm simplifying a fraction?

The answer is negative because you have -40 in the numerator (negative) and 120 in the denominator (positive). When you divide a negative by a positive, the result is always negative!

How do I find the greatest common divisor of 40 and 120?

List the factors: 40 = 1, 2, 4, 5, 8, 10, 20, 40 and 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. The largest common factor is 40.

Can I move the negative sign to the denominator instead?

Yes! $\frac{-40}{120} = \frac{40}{-120} = -\frac{40}{120}$ are all equivalent. But it's conventional to write the negative sign in front of the fraction.

What if I divided by a smaller number like 10 instead of 40?

You'd get $\frac{-4}{12}$ , which isn't fully simplified! You can simplify further by dividing by 4 to get $-\frac{1}{3}$ . Always use the largest common factor to simplify in one step.

How do I check if my simplified fraction is correct?

Multiply your answer by the original denominator: $-\frac{1}{3} \times 120 = -40$ . If you get the original numerator, your simplification is correct!

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