# Questions tagged [ratio]

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

699 questions
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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)...
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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. ...
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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 ...
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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. ...
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### What is the name for one side of a ratio?

Basic example: "If you are asked to put a ratio in the simplest form, make sure that you have found the smallest factor that goes into both [?]." I've tried searching for ratio diagrams in Google, ...
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### Ratios as Fractions

I’m having trouble understanding how fractions relate to ratios. A ratio like 3:5 isn’t directly related to the fraction 3/5, is it? I see how that ratio could be expressed in terms of the two ...
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### How is the Radius of Convergence of a Series determined?

Consider $$\sum_{n=0}^{\infty}\frac{(-1)^nx^n}{(n+1)^2}$$ which by the ratio test the ratio of two consecutive terms converges to $|x|$ as $n\rightarrow \infty$ and has a radius of convergence equal ...
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### Get numbers from ratios

How to get numbers from ratios? For example: The number of students in a school is 17500. The ratio between boys and girls is 4:3. How many boys and girls are there? Not only for this example, but ...
Let $ABCDE$ be a convex pentagon wiht $CD=DE$ and $\angle{BCD}=\angle{DEA} = 90^{\circ}$. Point $F$ lies on $AB$ such that $\frac{AF}{AE}=\frac{BF}{BC}$. Prove that $\angle{FCE} = \angle{ADE}$ and $\... 1answer 74 views ### How does this line came? :) Today I started to learn algebra with my own. And the first chapter which I'm learning is Ratio. I'm kind of confuse in an example, in all the lines starting with (*). Until first three lines of ... 1answer 113 views ### Three Circle trying to prove the ratio of two length are the same$\bigcirc Q, \bigcirc P$is tangent with$\bigcirc O$at point$A, B$.$\bigcirc Q, \bigcirc P$intersect at$C,D$. Line$AD$is intersects$\bigcirc O$in$E$. Line$DB$is intersects$\bigcirc O$in ... 1answer 69 views ### How is$40$related to$60$? My problem with math is how I talk about it, the words of math. I know math is a language but I don’t translate it very well. For example, if you have$40$units and I have$60$units, from my ... 2answers 544 views ### How fast is the water level rising? A pyramid-shaped vat has square cross-section and stands on its tip. The dimensions at the top are$2\text{ m}\times2\text{ m}$,and the depth is$5\text{ m}$. If water is flowing into the vat at$3\...
If p,q and r are three distinct real numbers such that $(pq+1):(qr+1):(rp+1)$ is $q:r:p$,then prove that $|pqr|=1$.