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

• kay
In summary, negative fractions are values less than zero while positive fractions are values greater than zero. They can be simplified in the same way, but when dividing a negative number by a negative number, the result becomes positive. Negative fractions can represent debts, losses, or temperatures below zero and are used in physics and mathematics. It is not possible for a fraction with both negative numerator and denominator to be greater than one.
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.

fireflies
kay said:
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.
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.

fireflies
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.

fireflies
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.

N
Mentallic said:
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.
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

And -2<-1

Yeah, I mistook. The converse relation for negative sides

kay said:
Shoudn't the fraction -2/-1 be less than one?
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.

berkeman

## 1. What is the difference between negative fractions and positive fractions?

Negative fractions represent values that are less than zero, while positive fractions represent values that are greater than zero. They have different signs and are located on opposite sides of the number line.

## 2. Can negative fractions be simplified like positive fractions?

Yes, negative fractions can be simplified in the same way as positive fractions. The negative sign can be moved to the numerator or denominator, depending on the simplification rules.

## 3. Why does dividing a negative number by a negative number result in a positive fraction?

This is because when dividing two negative numbers, the negative signs cancel out and the result becomes positive. For example, -2 divided by -1 is equal to 2.

## 4. How does the concept of negative fractions apply to real life situations?

Negative fractions can be used to represent debts, losses, or temperatures below zero. They are also used in physics and mathematics to represent quantities that have a direction or magnitude.

## 5. Is it possible for the fraction -2/-1 to be greater than one?

No, it is not possible for a fraction to be greater than one when both the numerator and denominator are negative. This is because the result of the division will always be a positive number, which is less than one.

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