Mathematics Stack Exchange
Mathematics Stack Exchange

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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How to compare fractions without finding common denominators?

This is the question: Use reasoning other than finding common denominators, cross-multiplying, or converting to decimals to compare each pair of fractions listed below. Which is greater? Give reasoning. 37/52 or 37/64 7/12 or 5/8 I need help…
Ben
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What is the value of $x$ which satisfies: $\frac{17}{85}+\frac{19}{95}+\frac{21}{105}+\frac{23}{115}+\frac{25}{125}+\frac{x}{135}=1$

What is the value of $x$ which satisfies: $\frac{17}{85}+\frac{19}{95}+\frac{21}{105}+\frac{23}{115}+\frac{25}{125}+\frac{x}{135}=1$ I thought $x=27$ because the numerator seems to have a pattern of adding $2$ and adding $10$ on the denominator.…
Caddy Heron
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Evaluate $\frac{3}{4}$ to the power of $-3$

I have gotten to the next stage where you write it as $\frac{1}{\left(\frac 34\right)}$ to the power of $3$, now I am stuck I've got it now, thanks everyone.
rooroo
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Value of a fraction

It it true that is ${a^2+c^2\over b^2+d^2}=1$ for $ad-bc=1$? I tried substituting in $a={1-bc\over d}$ but it is still a mess. (How do you ask Wolfram Alpha a question like this where we ask it to calculate something with an imposed condition?)
Greg D
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Is there a name for the rule $a \div (b \times c) = a \div b \div c$?

Edit, because I should have looked it up before I posted the question: Is there a name for the rule $a \div (b \div c) = a \div b \times c$ ? I ran across this in Liping Ma's book, Knowing and Teaching Mathematics, and I have searched the internet…
Debra P Otto
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Simplification of rational expressions

I have the following expression: $${2\over x-2} + {2 \over{x^2} -5x +6}$$ So I can simplify this as: $${2 \over x -2} + {2 \over (x -3) (x-2)}$$ I make the common denominator to be ${(x-3)(x-2)}$ So I then apply ${(x-3)}$ to the left hand side which…
dagda1
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Simplifying a fraction with a cubed root in the denominator

I have an equation the following equation in my textbook, but I don't understand how it's legal for it to be simplified this way. $${1000\over \pi\sqrt[3]{500\over \pi}^2}=2\sqrt[3]{500\over \pi}$$ I know that an equivalent equation is…
matryoshka
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How to compute $\frac{t^2}{t+1}$ to the form $\frac{1}{t+1} +t -1$

One of my attempts would look like below. $\frac{t^2}{t+1}$ = $\frac{t \times t+1-1}{t+1}$ = 1+ $\frac{t-1}{t+1}$ = $\frac{t-1+1-1}{t+1} + 1$ = $\frac{-2}{t+1} +2$ Also, I put into t an arbitrary number in both equations and have gotten the same…
user275564
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Fractions with Hours and Days

So the question is: The number of hours left in a day on Mars was $\frac{1}{4}$ on the number of hours that had already passed. How many hours were left in the day? Day on Mars: $40$ hours. I did $\frac{1}{4}\times40$ and got $10$. It seems a bit…
John
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Hard problem with fractions

I can't solve the following problem. A person is $x$ years old. Find his age if the following is true. In a group of $x$ people each one started taking pictures of each of the others. At some point we know that more than $\frac{1}{2}$ of the people…
chen h.
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How is it possible that when you divide 1 by 9,899, you get two-digit Fibonacci numbers also being carried, etc.?

When I divided $1$ by $9,899$, I got two-digit Fibonacci numbers also being carried: $0.0001010203050813213455904636\dots$ When I divided $1$ by $89$, I got one-digit Fibonacci numbers at the beginning: $0.0112359\dots$ (there was originally an…
VladInTheTaylor
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Trying to subtract 2 fractional

I'm trying to solve $f(x)=0$ for $x$, but I can't figure it out as I have to get both the denominators to become for instance $8x$, and then only 1 numerator has $x$ in it. How can I solve this? $$ f(x) = \frac{1}{4}-\frac{3}{2x} $$
Erik
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Why is (n+1)/2n = 1/2 + 1/n, and not 1/2 + 1/2n?

If I factor $(n+1)/2n$ by $n$, I get $n(1+1/n)/n(2)$. Simplifying, I end up with $(1 + 1/n) / 2$. This can be rewritten as: $1/2 + (1/n)/2$, which would give me $1/2 + (1/n) \times (1/2) = 1/2 + 1/(2n)$. Why is this wrong? I'm told: $(n+1) / (2n) =…
Sam
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Could this be factored any further?

My friend recently told me that $\frac{-x}{x}$ could not be simplified any further. Is he correct or could it be simplified such that the answer isn't undefined when you x=0?
Joe Torraca
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Using a factor tree to reduce a fraction? Good Idea?

I am trying to figure out how one reduces 180/100 to 9/5 My factor tree for 180 is 90 *2 - 30*3 -5*6 - 2*3 Thus my prime numbers are 2*3*5 = 30 Maybe I have totally forgotten how to reduce a fraction like this, however, what method should I use if…
user137452
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