Questions tagged [fractions]

Questions on fractions, i.e. expressions (not values) of the form $\frac ab$, including arithmetic with fractions. Not to be confused with the tag (rational-numbers): fractions denote rational numbers, but the same rational number may be written in different ways as a fraction.

A fraction is simply an expression $\frac{a}{b}$, where $a$ and $b$ are typically integers (where $b\neq 0$). This tag may be used, when $a$ and $b$ are more general expressions or algebraic objects; however, consider adding a more specific tag also:

Fractions are distinct from rational numbers because they are a representation: $\frac 34$ and $\frac{30}{40}$ are different fractions that happen to represent the same rational number.

For arithmetic with fractions, this tag is appropriate along with .

2981 questions
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Certain Fraction between Fractions

Is there always a fraction $\frac{r}{s}$ with $\frac{p}{q}<\frac{r}{s}<\frac{p+1}{q}$ and $s
user255536
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Find non-repeating decimal between two fractions

I have two fractions which, when evaluated, may or may not be non-terminating (they go on forever). They're both between 1 and 0. I need to find the shortest decimal number that lies between these fractions which terminates. Anyone have an idea? I'm…
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Writing a percent as a decimal and a fraction

I am having a problem understanding some manipulations with recurring decimals. The exercise is Write each of the following as a decimal and a fraction: (iii) $66\frac{2}{3}$% (iv) $16\frac{2}{3}$% For (iii), I write a decimal $66\frac{2}{3}\% =…
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Why does $1/0.5$ equal $2$?

I would like to know, in $1/0.5 =2$ why does $1/0.5$ yield $2$. I want to know a conceptual explanation, not merely a method how to get the answer. If you are able to explain this in example using image that would be super helpful! My…
Kijimu7
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Why is the reciprocal used in fraction division?

I don't know if this is a basic question or whatever, but I can't seem to find an answer. As far as I understand the reciprocal of a number the inverse of that number, that still doesn't clarify why it is needed. For many years I've only ever done…
Argus
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Zero/Zero questions and perhaps faulty logic

So I only have an Algebra II level understanding of math seeing as I am still in high school and am still missing some fundamentals seeing as I didn't pay attention in math until this year. However when recalling something my algebra teacher had…
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"Canceling out" in division doesn't always work the same way does it?

I've been working on Nested Fractions at the Khan Academy. Recently I was doing a routine problem and came to the correct conclusion but I realized I didn't understand why I wouldn't keep dividing. Here's what I begin with. I'm supposed to reduce it…
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Negative fractions - what's the difference?

What's the difference between the following fractions: $ \frac{-4}{-5}$ $ \frac{4}{-5}$ $ \frac{-4}{5}$ $ - \frac{4}{5}$
mal
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Will 0.99999999 eventually become equal to 1?

I am currently learning about fractions, and there is something that I am finding it hard to make sense of. When a fraction it added to the right of the decimal point, the number becomes slightly bigger right? So for example if I add enough…
Steve
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The steps of simplifying a fraction?

So I'm in an Adult Education class for my GED and I'm trying hard to study on my Math which is the only subject I have trouble with. I only have "barely" a 6th grade education to Math so I'm having a lot of trouble totally understanding it all. I'm…
devine
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Fraction Word Problems:

"Kathy had $10 and gave half of it to her brother. She then gave a third of the remaining amount to a friend. How much money will Kathy have left?" Apparently, you have to multiply the second part first then you subtract and it makes no sense to me…
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Difference between $D(x^2)$ and $D(x)^2$?

Could someone clarify whether this is correct? If $$D(x) = \frac{5x + 8}{x - 15},$$ would $$D(x^2) = \frac{5x^2 + 8}{x^2 - 15},$$ and $$D(x)^2 = \frac{5x + 8}{x - 15}\times\frac{5x + 8}{x - 15}?$$ Clarification appreciated!
user818871
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How can I convert this negative fraction to a positive one?

This question may be very simple, but I get confused on things like it. If I have a fraction like this: $-\frac{x}{-2}$ How can I convert this negative fraction to a positive one? It does not matter if the numerator or denominator is negative of…
user60161
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Simplify and find the domain

Simplify the following expression and find its domain $$\frac{3a + 6b}{a-b}:\frac{a+2b}{2ab-2b^2}.$$ A. $6b\ \text{for}\ a \neq b\land a \neq -2b$ B. $6b\ \text{for}\ a \neq b\land (b \neq 0 \lor a \neq b)$ C. $6b\ \text{for}\ a \neq b\land (b \neq…
Dia
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Expressing in rationals

I have this question to express it in a specific form Express $\dfrac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$ in the form $a \sqrt{2} + b \sqrt{3} + c \sqrt{7} + d \sqrt{42}$, for some rationals $a,b,c$ and $d$. So the solution that I have and am…
JackyBoi
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