Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [ratio]

For questions concerning the ratio of a certain quantity to another.

In mathematics, a ratio is a relationship between two quantities indicating how many times the first number contains the second. For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, $8:6$, which is equivalent to the ratio $4:3$). The numbers compared in a ratio can be any quantities of a comparable kind, such as objects, persons, lengths, or spoonfuls. A ratio is written "$a$ to $b$" or $a:b$, or sometimes expressed arithmetically as a quotient of the two.

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Is there a size of rectangle that retains its ratio when it's folded in half?

A hypothetical (and maybe practical) question has been nagging at me. If you had a piece of paper with dimensions 4 and 3 (4:3), folding it in half along the long side (once) would result in 2 inches and 3 inches (2:3), which wouldn't retain its…
Pyraminx
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Evaluating $\left.\int_0^{\pi/2}\sqrt{1+\frac1{\sqrt{1+\tan^nx}}}\text dx \middle/\int_0^{\pi/2}\sqrt{1-\frac1{\sqrt{1+\tan^nx}}}\text dx\right.$

Evaluate the integral ratio$$\dfrac{I_1}{I_2}=\dfrac{\displaystyle \int_{0}^{\frac{\pi}{2}} \sqrt{1+\frac{1}{\sqrt{1+\tan^nx}}} \mathrm{d}x}{\displaystyle \int_{0}^{\frac{\pi}{2}} \sqrt{1-\frac{1}{\sqrt{1+\tan^nx}}} \mathrm{d}x}$$ Using…
V.G
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How is $\sin 90° = 1$ possible?

How can two angles of a triangle be equal to $90°$? If two angles were $90°$, this would mean that the two sides would be parallel and the angle of the third side would be equal to 0. Thus, there would be only two vertices and this wouldn't be a…
Sarvesh Thiruppathi
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Dividing a rectangle into 4 parts in the ratio 1:2:3:4, with only 2 lines

I have a rectangle made up of 30 identical squares (5 tall and 6 wide). By only drawing two lines on the rectangle, split the rectangle into 4 parts where the areas are in the ratio 1:2:3:4. How would one go around doing this? I tried for a solid…
Kevin fu
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Finding all possible proofs

I'm now working on a geometry problem I'll have to explain in front of my class this week (I'm in the $10^{th}$ grade). I've found so far some proofs, which might, nevertheless, be a bit complicated for my classmates (since they've barely worked…
Dr. Mathva
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How did they get this equation comparing three ratios?

I was reading from an old maths textbook. It was giving some examples on how to solve ratios. I stumbled upon this example and felt perplexed after reading only part of it. We're given this equation. $$\frac{x}{l(mb+nc-la)} = \frac{y}{m(nc+la-mb)} =…
ssharma
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Rates and Ratio work problem

I've encountered this problem It takes $60$ minutes for $7$ people to paint $5$ walls. How many minutes does it take $10$ people to paint $10$ walls. The answer to this one is $84$ minutes. However, How did it come up to this answer? can someone…
KyelJmD
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Ratio. Number of sheep and chickens

At a farm, the ratio of the number of chickens to the number of sheep was 5:2. After the farmer sold 15 chickens, there was an equal number of chickens and sheep. How many chickens and sheep were there at the farm in the end? My work: Number of…
RukaiPlusPlus
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Is there a mathematical description of three-part ratios?

Rational numbers have many interpretations, but one of the simplest is as a ratio of one number to another. The fraction $1/2$ can be interpreted as the ratio 1:2 (i.e. one apple for every two oranges). Rational numbers are also considered an…
MathTrain
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Ratio of two binomial distributions

How to estimate $$ E\left[\frac{X}{X+Y}\right] $$ for two independent random variables $X\sim Bin(n,p)$ and $Y\sim Bin(m,p)$ ? Are there any connection with $\frac{n}{n+m}$ e.g., $1-\varepsilon\leq E\left[\frac{X}{X+Y}\right]/\frac{n}{n+m}\leq…
hiratat
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Are ratios with zero defined?

Are ratios like $4:0$ or $0:4:0$ defined? I saw such ratios being used to describe the phenotype ratio in a mono-hybrid cross – tall plants:short plants $=0:4$.
Suzie Waters
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How much smaller is the set of ratios than the set of ordered pairs?

For integers $a, b$ with $0 < a < N$ and $0 < b < N$ for some integer $N$, let $\{(a, b)\}$ be the set of all their ordered pairs and let $\{\frac{a}{b}\}$ be the set of all their ratios. Clearly, $|\{\frac{a}{b}\}| < |\{(a, b)\}|$ (the number of…
jamaicanworm
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Is this a correct/good way to think interpret differentials for the beginning calculus student?

I was reading the answers to this question, and I came across the following answer which seems intuitive, but too good to be true: Typically, the $\frac{dy}{dx}$ notation is used to denote the derivative, which is defined as the limit we all know…
Ovi
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What are the methods of dividing numbers to get weird values like $16\over 17$ without a calculator?

I tried estimating it to somewhere near $16\over 20$, but it's a far stretch from getting the actual $16\over 17$. How can one do so? Conventionally, I think for numbers such as $50\over 17$, or for any large numbers, we have methods to do division…
mathworker123
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Avoid dividing by zero with just variables and basic operators

I am working on stats for a sports team, and one of the stats I have the ratio of Shots and Shots on Target (Which I call SOTP). So, for instance, if a player has 2 shots, and one's on target, their SOTP ratio is 1/2 or 50%. Now I have a problem…
davidsbro
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