# Shoudn't the fraction -2/-1 be less than one?

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1. Jun 20, 2015

### kay

Because technically, the numerator is smaller than the denominator as −2<−1

I know it's an extremely stupid question.

I mean I know that I can just multiply −1 to the numerator and the denominator and I'll get 2/1 which is greater than one.

But what exactly is happening here?

A number that is supposed to be less than one is coming out to be greater than one;double, to be precise.

2. Jun 20, 2015

### Mentallic

Starting with

-2<-1

if you divide both sides by the negative number -1, you're supposed to reverse the inequality sign. So

$$-2<-1$$

$$\frac{-2}{-1}>\frac{-1}{-1}=1$$

Also, the numerator being smaller than the denominator isn't the rule for numbers to turn out smaller than 1. The numerator is TWICE the size of the denominator, hence the result should be 2. Fractions are about ratios, not comparisons.

3. Jun 20, 2015

### HallsofIvy

Staff Emeritus
You appear to be using a rule that "a fraction is less than one if the numerator is less than the denominator". That is only true if the denominator is positive.

If n< d then n/d< 1 requires that d be positive.

4. Jun 21, 2015

### Simon Clement

I think you're seeing the negative side of real numbers just as you do the positive sides. What you described goes for the positive side, but conversely for the negative side. The neagative is opposite of the positive. So if small-number-numerator-over-big-number-denominator is a proper fraction on the positive side, then it's an improper fraction on the negative, that is with the same small-number-numerator-over-big-number-denominator arrangement.

5. Jun 23, 2015

### fireflies

N
No, when numerator is smaller than denominator then the fraction is always less than 1. Here, numerator 2>denominator1 so, 2/1 is greater than 1

6. Jun 23, 2015

### fireflies

And -2<-1

Yeah, I mistook. The converse relation for negative sides

7. Jun 23, 2015

### Staff: Mentor

No. Do the division, keeping in mind that when both the numerator and denominator are the same sign, the value of the fraction is positive.
$$\frac{-2}{-1} = 2 > 1$$

If you are using a "rule" that ignores the above property of division, that rule is bogus.