Evaluate -a/b: Solving with Values (8,-4) and (-8,4)

Q: Why do both problems give the same answer when the numbers are different?

Great observation! Both $ -\frac{8}{-4} $ and $ -\frac{-8}{4} $ simplify to +2 because the sign patterns create the same result. The key is counting negatives: odd number of negatives = negative result, even number = positive result.

Q: How do I keep track of all the negative signs?

Count the negatives! In $ -\frac{8}{-4} $, you have 2 negatives (outside and denominator), so the result is positive. In $ -\frac{-8}{4} $, you also have 2 negatives (outside and numerator), so it's also positive.

Q: What's the difference between the negative outside and negative inside the fraction?

The negative outside the fraction (like in $ -\frac{a}{b} $) multiplies the entire fraction result. Negatives inside affect just the numerator or denominator. Both types of negatives follow the same multiplication rules!

Q: Can I move the negative sign around in a fraction?

Yes! These are all equivalent: $ -\frac{a}{b} = \frac{-a}{b} = \frac{a}{-b} $. You can move one negative sign to any of these three positions, but the overall value stays the same.

Q: Why does negative times negative equal positive?

Think of it as opposite directions! A negative means 'opposite direction.' When you take the opposite of an opposite, you end up back where you started - that's positive. So (-1) × (-1) = +1.

Fraction Sign Rules with Variable Substitution

$-\frac{a}{b}$

Substitute the following into the expression above and solve.

$b=-4,a=8$
$b=4,a=-8$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Place and Calculate

00:03 Let's start by placing the first option

00:13 Positive divided by negative always equals negative

00:20 Negative divided by negative always equals positive

00:29 This is the solution for option A, now let's calculate option B

00:35 Let's substitute according to the data of option B

00:41 Negative divided by positive always equals negative

00:48 Negative multiplied by negative always equals positive

00:55 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

$-\frac{a}{b}$

Substitute the following into the expression above and solve.

$b=-4,a=8$
$b=4,a=-8$

Step-by-step solution

Let's start with the first option.

Let's substitute the data into the expression:

$-\frac{8}{-4}=$

First, we can see that in the fraction we are dividing a positive number by a negative number, therefore the result will be negative:

$-\times-\frac{8}{4}=$

Now we can see that we have a multiplication between two negative numbers and therefore the result must be positive:

$+\frac{8}{4}=2$

Let's continue with the second option.

Let's substitute the data into the expression:

$-\frac{-8}{4}=$

First, we can see that in the fraction we are dividing a positive number by a negative number, therefore the result will be negative:

$-\times-\frac{8}{4}=$

Now we can see that we have a multiplication between two negative numbers and therefore the result must be positive:

$+\frac{8}{4}=2$

Therefore the final answer is:

$1,2=+2$

Final Answer

$1,2=+2$

Key Points to Remember

Essential concepts to master this topic

Sign Rules: Negative times negative equals positive in fractions
Technique: $-\frac{8}{-4} = -1 \times \frac{8}{-4} = +2$
Check: Both substitutions give +2, confirming correct sign analysis ✓

Common Mistakes

Avoid these frequent errors

Ignoring the negative sign outside the fraction
Don't forget the negative sign in front = wrong answer! Students often focus only on the fraction's numerator and denominator signs, missing that $-\frac{a}{b}$ has an additional negative. Always account for all three signs: the outside negative, numerator sign, and denominator sign.

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 do both problems give the same answer when the numbers are different?

Great observation! Both $-\frac{8}{-4}$ and $-\frac{-8}{4}$ simplify to +2 because the sign patterns create the same result. The key is counting negatives: odd number of negatives = negative result, even number = positive result.

How do I keep track of all the negative signs?

Count the negatives! In $-\frac{8}{-4}$ , you have 2 negatives (outside and denominator), so the result is positive. In $-\frac{-8}{4}$ , you also have 2 negatives (outside and numerator), so it's also positive.

What's the difference between the negative outside and negative inside the fraction?

The negative outside the fraction (like in $-\frac{a}{b}$ ) multiplies the entire fraction result. Negatives inside affect just the numerator or denominator. Both types of negatives follow the same multiplication rules!

Can I move the negative sign around in a fraction?

Yes! These are all equivalent: $-\frac{a}{b} = \frac{-a}{b} = \frac{a}{-b}$ . You can move one negative sign to any of these three positions, but the overall value stays the same.

Why does negative times negative equal positive?

Think of it as opposite directions! A negative means 'opposite direction.' When you take the opposite of an opposite, you end up back where you started - that's positive. So (-1) × (-1) = +1.

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