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Questions tagged [ratio]

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

85
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8answers
14k views

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 ...
15
votes
4answers
4k views

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 ...
14
votes
3answers
1k views

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 ...
10
votes
3answers
850 views

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. ...
8
votes
6answers
1k views

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 ...
8
votes
1answer
1k views

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)...
8
votes
6answers
3k views

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. ...
7
votes
7answers
618 views

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 ...
7
votes
1answer
56 views

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. ...
6
votes
2answers
3k views

Solving proportions with $3$ ratios,$ x:3:y = -2:3:-4$

Proportion seems simple enough for me. Example is $4:x = 2:5,$ and the answer is $x = 10.$ My problem is how do I solve for proportions with $3$ ratios like $x:3:y = -2:3:-4$ ? Do I write it like $$...
6
votes
4answers
389 views

Ratio of balls in a box

A box contains some identical tennis balls. The ratio of the total volume of the tennis balls to the volume of empty space surrounding them in the box is $1:k$, where $k$ is an integer greater than ...
5
votes
2answers
535 views

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 $=0:4$.
5
votes
1answer
274 views

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\...
4
votes
3answers
160 views

How to combine ratios? If $a:b$ is $2:5$, and $c:d$ is $5:2$, and $d:b$ is $3:2$, what is the ratio $a:c$?

How would I go about solving this math problem? if the ratio of $a:b$ is $2:5$ the ratio of $c:d$ is $5:2$ and the ratio of $d:b$ is $3:2$, what is the ratio of $a:c$? I got $\frac{a}{c} = \frac{2}{...
4
votes
2answers
172 views

Does the sign matter for proportionality?

This question arose from Physics, where the force on an object attached on a spring is proportional to the displacement to the equilibrium (that is, the rest position). Also, if the displacement to ...
4
votes
2answers
112 views

Can a triangle have 3 irrational angles that are not rational multiples of eachother

Consider a triangle where the three angles must sum to a fixed total. I don't care if they sum to $\pi, \frac{\pi}{2}, 360, 180, 1$ or any other number. If every angle is irrational and they add up ...
4
votes
3answers
4k views

Ratio between two numbers is 6:7 and the difference between them is 10. What are the two numbers?

I know the numbers are $60$ and $70$ but I got that by trial and error. Is there some other more logical way to do this problem?
4
votes
2answers
4k views

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 ...
4
votes
2answers
125 views

Time and work. Arithmetic.

$A$, $B$ and $C$ working together completed a job in $10$ days. However, $C$ only worked for the first three days when $\dfrac{37}{100}$ of the job was done. Also, the work done by $A$ in $5$ days ...
4
votes
1answer
48 views

Geometric problem about ratios of line segments: How to transform the limiting case method to a rigorous answer?

In $\triangle ABC$, $D, E, F, G$ are points on the sides of the triangle such that $BD:DE:EC=1:2:3$, $AF:CF=1:1$, and $AG:BG=2:3$. Find the ratio $FH:DH$. My classmate has come up with a brilliant ...
4
votes
4answers
158 views

Find $\log _{24}48$ if $\log_{12}36=k$

Find $\log _{24}48$ if $\log_{12}36=k$ My method: We have $$\frac{\log 36}{\log 12}=k$$ $\implies$ $$\frac{\log 12+\log 3}{\log 12}=k$$ $\implies$ $$\frac{\log3}{2\log 2+\log 3}=k-1$$ So $$\log 3=...
4
votes
2answers
249 views

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, ...
4
votes
3answers
2k views

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 ...
4
votes
2answers
107 views

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 ...
4
votes
1answer
377 views

Is $\frac{1}{(\log n)^{n^p}}$ convergent?

Is $\frac{1}{(\log(n))^{n^p}}$ convergent or divergent? My solution: Use ratio test $\lim_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim_{n \to \infty}|\frac{(\log(n))^{(n)^{p}}}{(\log(n+1))^{(n+1)^{p}}}|...
4
votes
5answers
2k views

Math Behind Creating a “Perfect” Star

I am busy looking to create star paths in my app, and I was wondering how to determine the ratio between the inner radius and the outer radius of the points of a star so that the star has "straight" ...
4
votes
1answer
110 views

Turning an angle into a ratio of squares left/right:squares up/down

I'm a 9th grader in Algebra 1 right now and in my spare time I like programming, I am trying to re-create the game Pong right now but I am having a little problem. I know I am asking a question about ...
4
votes
0answers
76 views

Are my calculations of the pregnancy ratio of the population correct?

So this question is a math question having to do with me calculating the rate of population growth starting from a population of 100,000. I have already gotten the first 3 steps done(sex ratio, ratio ...
4
votes
0answers
64 views

Finding the envelope frequency of a sinusoid (From a musical major triad) [closed]

[Editor 2’s introduction intended to address votes to close because the question wasn’t mathematical.] The trigonometric formula $\sin{(at)}+\sin{(bt)}=2\cos({a-b\over2}t)\sin({a+b\over2}t)$ can be ...
4
votes
0answers
184 views

Ratio of Radius of Circle $B$ to Radius Of Circle $A$ in the form $a + b\sqrt{c}$

The full question is as follows: Suppose $X, Y, Z$ are three different, circles of equal radius which are mutually tangent. Let circle $A$ be the circle tangent to $X, Y$, and $Z$ inside the gap ...
3
votes
5answers
734 views

Ratio of parts of an intersected segment in a rectangle

In rectangle $ABCD$, points $E$ and $F$ lie on sides $BC$ and $CD$ respectively. Point $F$ is the midpoint of $CD$ and $BE=\frac13BC$. Segments $AC$ and $FE$ intersect at point $P$. What is the ratio ...
3
votes
5answers
123 views

Analyze if this series converges: $\sum_{n=0}^{\infty}\frac{n^{2}+1}{n!}$

Analyze if this series converges: $\sum_{n=0}^{\infty}\frac{n^{2}+1}{n!}$ I have used ratio test: $\lim_{n\rightarrow \infty}\left |\frac{a_{n+1}}{a_{n}} \right |< 1$ $\Rightarrow$ $\lim_{n\...
3
votes
2answers
58 views

An interesting result in ratio and proportions

If $$ \frac{a}{b}=\frac{c}{d}=k $$ then $$ \frac{a+c}{b+d}=k $$ Also $$ \frac{a^2}{b^2}=\frac{c^2}{d^2}=k^2 $$ And $$ \left( \frac{a+c}{b+d} \right)^2=k^2 $$ Also $$ \frac{a^2 + c ^2}{b^2+d^2}=k^2 $...
3
votes
4answers
111 views

$AD:DC = BE:EA = 1:2$. Lines $BD$ and $CE$ meet at point $O$. Prove that $\angle AOC = 90^{\circ}$

Points $D$ and $E$ divide sides $AC$ ans $AB$ of an equilateral triengle in the ratio $AD:DC = BE:EA = 1:2$. Lines $BD$ and $CE$ meet at point $O$. Prove that $\angle AOC = 90^{\circ}$ My Work ...
3
votes
3answers
1k views

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 ...
3
votes
2answers
46 views

A is x% more than B

I am taking the AMC10 test, and I don’t want to lose points on silly misunderstandings. When a question says “A is x% greater/less than B”, or things like that sometimes with money, which respect ...
3
votes
3answers
104 views

Suppose $\displaystyle\lim_{n\to\infty} {\frac{a_{n+1}}{a_n}} = \frac{1}{2}$, prove $\displaystyle\lim_{n\to\infty}{a_n}=0$

Suppose $\displaystyle\lim_{n\to\infty} {\frac{a_{n+1}}{a_n}} = \frac{1}{2}$, prove $\displaystyle\lim_{n\to\infty}{a_n}=0$ My start on this was to state the limit in terms of the definition and work ...
3
votes
1answer
71 views

Expressing a decimal percentage as a ratio

Maths newbie here. How would I express a decimal percentage such as 90.3 as a ratio ("one in...")? I've done a search and the explanations aren't too clear at all. I'm about to enrol on to a ...
3
votes
1answer
19 views

If one region is above the $x$-axis, and the other below it, should “the ratio of their areas” use absolute value?

Good morning mathematicians, I apologize for asking such a basic question. When you are to find the ratio of "Area 1" and "Area 2", such that "Area 1" is the area of a region above the x-axis and "...
3
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1answer
109 views

GRE Practice Question Incorrect?

This is a sample GRE question. The answer claims that we cannot make an inference due to insufficient information. Compare the following quantities: Of the 25 people in Fran’s apartment ...
3
votes
1answer
46 views

Percentages increase/Ratios SAT problem

The question goes like this: On Tuesday, a watchmaker made 4 more watches than he made during the previous day. If he made 16% more watches on Tuesday than on Monday, how many watches did he ...
3
votes
2answers
90 views

Equation Involving Ratios

In some of my research, I found multiple equations of this form: $$\frac{ax+b}{cx+d}=k$$ where $a,b,c,d$ are all non-zero integers. Is there a way (that doesn't include factoring or checking within a ...
3
votes
2answers
34 views

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 ...
3
votes
2answers
105 views

Convex pentagon with right angle

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 $\...
3
votes
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 ...
3
votes
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 ...
3
votes
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 ...
3
votes
2answers
539 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\...
3
votes
1answer
34 views

ratio based question

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 $|pqr|=1$.
3
votes
1answer
48 views

Prove that if a fraction is broken up into two the resulting two fractions cannot both have a larger value [duplicate]

I am working on research involving probability tables. I simplified the problem to the following. Say we have the following: $C_1, C_2, C_3, C_4$ $\forall i, C_i > 0$ $x = \frac{C_1 + C_2}{C_1 + ...