Solve Division Problem: 60 Divided by -120

Q: Why is the answer negative when I'm dividing 60 by 120?

The answer is negative because you're dividing by -120, not positive 120. The sign rule says: positive ÷ negative = negative. So $ \frac{60}{-120} = -\frac{1}{2} $.

Q: How do I simplify this fraction?

Find the GCD (Greatest Common Divisor) of 60 and 120. Since both numbers share a factor of 60, divide both by 60: $ \frac{60 ÷ 60}{-120 ÷ 60} = \frac{1}{-2} $.

Q: Is -1/2 the same as 1/-2?

Yes! Both $ -\frac{1}{2} $ and $ \frac{1}{-2} $ represent the same value. It's conventional to write the negative sign in front: $ -\frac{1}{2} $.

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

Multiply your answer by the denominator: $ -\frac{1}{2} \times (-120) = 60 $. If you get the original numerator, your answer is right!

Fraction Division with Negative Numbers

Solve the following:

$\frac{60}{-120}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:06 Let's break down 120 into factors 60 and 2

00:13 Let's reduce what we can

00:20 Positive divided by negative always equals negative

00:26 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following:

$\frac{60}{-120}=$

Step-by-step solution

To solve the problem $\frac{60}{-120}$ , follow these steps:

Step 1: Find the greatest common divisor (GCD) of 60 and 120. The GCD is 60.
Step 2: Simplify the fraction by dividing both the numerator and the denominator by their GCD:

$\frac{60}{-120} = \frac{60 \div 60}{-120 \div 60} = \frac{1}{-2}$

Step 3: When dividing a positive number by a negative number, the result is negative. Thus, $\frac{1}{-2}$ simplifies to $-\frac{1}{2}$ .

Thus, the solution to the problem is $\boxed{-\frac{1}{2}}$ .

Final Answer

$-\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive divided by negative always equals negative
Simplification: Find GCD of 60 and 120, which is 60
Check: $-\frac{1}{2} \times (-120) = 60$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in the final answer
Don't ignore the negative sign and write $\frac{1}{2}$ = wrong answer! When dividing positive by negative, the result must be negative. Always apply the sign rule: positive ÷ negative = negative.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why is the answer negative when I'm dividing 60 by 120?

The answer is negative because you're dividing by -120, not positive 120. The sign rule says: positive ÷ negative = negative. So $\frac{60}{-120} = -\frac{1}{2}$ .

How do I simplify this fraction?

Find the GCD (Greatest Common Divisor) of 60 and 120. Since both numbers share a factor of 60, divide both by 60: $\frac{60 ÷ 60}{-120 ÷ 60} = \frac{1}{-2}$ .

Is -1/2 the same as 1/-2?

Yes! Both $-\frac{1}{2}$ and $\frac{1}{-2}$ represent the same value. It's conventional to write the negative sign in front: $-\frac{1}{2}$ .

How can I check if my answer is correct?

Multiply your answer by the denominator: $-\frac{1}{2} \times (-120) = 60$ . If you get the original numerator, your answer is right!

What if I can't find the GCD easily?

Try dividing by small common factors first. For 60 and 120, both are divisible by 10, then by 6, giving you the same result. Any common factor works - you'll eventually reach the simplest form!

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