Proportions in mathematics can be viewed from a few perspectives. For instance, the proportionality of two variable values is determined by checking if one of the values is the product of the other value and some constant. In other words, two variable values (numbers or quantities) are proportional if their ratio is a constant, called the coefficient of proportionality or the proportionality constant. This is best explained using the linear equation: y = k*x

If k is a constant quantity, x will always be proportional to y for every possible value. Then k is considered to be the coefficient of proportionality.

Proportion is also the name we use when describing the equality of two ratios. If the ratios in question are equal, we say that they are proportional. For example, we have two ratios here: 5/6 = 15/18

These ratios are proportional because when we multiply both the numerator and the denominator of the ratio 5/6 by 3, we get 15/18 as a result. That is also true for the other way around – if we simplify the second ratio by dividing its numerator and denominator by 3, we get the first ratio as a result. Let us try another example: 2/3 = 8/9

As you can see, this equation is not valid – 8 is the product of 2 times 4 and 9 is the product of 3 times 3. That means that these ratios are not proportional. If we wanted to find the proportional ratio to 2/3 while keeping the denominator of the other ratio, we would have to multiply the numerator 2 with the number 3. So the correct proportion would be: 2/3 = 8/9

Similarity is a form of proportion used to compare sizes of shapes and objects and the same rules apply when solving both similarity and proportion. Knowing your way around similarities is especially useful when working with maps, blueprints and models. In those cases you are often given a ratio. The ratio of 1 : 3 in a model means that 1 cm on the model represents 3 cm on the actual object. The important thing to remember is that for two shapes or...

...Ratio and Proportion
• If 2 numbers are in ratio a: b then consider them as ax and bx (where x is the proportionality constant) and apply ax and bx in the given condition of the problem to proceed for answer
• Ratio can be applied between 2 units if and only if the same physical quantity is compared
• Length : length is correct
• Length : density is wrong
• Ratio can be made only after the units are compared in the same unit
• If two lengths are 1 mile and 1 km respectively then ratio 1:1 is incorrect.
• It should be 1.6:1 = 16:10 = 8:5 being converted to km
• Ratio of a to b = a : b = a / b where a and b are the terms of ratio wherein a = first term = antecedent and b = second term = consequent
• In a problem, to maintain the same ratio, if the antecedent is multiplied / divided by an integer / fraction then the consequent must be multiplied / divided by the same integer / fraction
• Ratio is expressed in lowest terms.
• As every number corresponds to its part in ratio, it is involved so the number of unit differences in the ratio, expressed in lowest terms, corresponds to the actual difference of true figures. Hence similar is with the aggregate values.
• If a number is to be proportionately changed in a given ratio then the antecedent refers to the given number....

...Lesson Guide for Chapter 7: Ratio and Proportion
Write a proportion problem. Design the problem so that the solution is “Leslie would need 16 gal ofgasoline in order to travel 368 mi.”
-Leslie drove from her house to the grocery store last monday the grocery store is 2.875 miles away from her house. She used 1/4 gallon of gas driving to the grocery and back home. At this rate how many gallons of gas would she use to drive to her parents house who lives 368 miles away?
--I am not sure that I understand the question fully but I am going to give it a try:Leslie is planning on visiting her sister who lives 368 miles away. The car that Leslie is planning on driving to visit her sister tank only holds 16 gallon of gas. Leslie’s car gets 23 miles per gallon. How many times will Leslie need to stop to fill up? Crystal
Classical conditioning and operant conditioning are two ways in which learning occurs in some animals, including humans. Provide one example of each type of conditioning from your own life. Explain step-by-step how the conditioning occurred. What would it take to unlearn this behavior? Top of Form
Question 1
1. -------------------------------------------------
You are a pronounced behaviorist. Which statement most closely aligns with your beliefs?
-------------------------------------------------
| | Latent learning occurs without any direct reinforcement. |
| | Operant conditioning uses consequences...

...Solving Proportions
Problem 1
Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?
I think using a simple ratio equation would work here,
let b = bear population
=
cross multiply
2b = 50*100
2b=5000 divide 2 by 5000
5000 =b
2
b=2500 answer
Problem 2
For the second problem in this assignment I am asked to solve this equation for y. The first thing I notice is that it is a single fraction (ratio) on both sides of the equal sign so basically it is a proportion which can be solved by cross multiplying the extremes and means.
y-1 = -3 this problem is a proportion
x+3 4
y-1 (x+3 = -3 (x+3) multiply both sides by x+3 – using the extreme means
x+3 4 property
y-1= -3x+3 add 1 to 3. A number that appears to be a solution but causes 4 0 in a denominator is called an extraneous solutions
y=-3x+4
4 answer
The form of equation I ended up with in problem 10 would be a linear equation. I noticed that the coefficient of x is different than the original problem is that x+3 and in my problem it is -3x/4. I could solve the problem by cross multiply...

...The story opens with the account of a woodcutter who has found a man's body in the woods. The woodcutter reports that man died of a single sword stroke to the chest, and that the trampled leaves around the body showed there had been a violent struggle, but otherwise lacked any significant evidence as to what actually happened. There were no weapons nearby, and no horses—only a single piece of rope, a comb and a lot of blood.
The next account is delivered by a traveling Buddhist priest. He says that he met the man, who was accompanied by a woman on horseback, on the road, around noon the day before the murder. The man was carrying a sword, a bow and a black quiver. All of these, along with the woman's horse, a tall, short-maned palomino, were missing when the woodcutter discovered the body.
The next person to testify is a hōmen (放免, a released prisoner working under contract to the police, similar to a bounty hunter). He has captured an infamous criminal named Tajōmaru. Tajōmaru was injured when thrown from a horse (a tall, short-maned palomino), and he was carrying a bow and a black quiver, which did not belong in his usual arsenal. This proves, he says, that Tajōmaru was the perpetrator. Tajōmaru was not carrying the dead man's sword, however.
The next testimony is from an old woman, who identifies herself as the mother of the missing girl. Her daughter is a beautiful, strong-willed 19-year-old named Masago, married to Kanazawa no Takehiro—a 26-year-old samurai...

...The Golden Ratio: Natures Beautiful Proportion
At first glance of the title, many may wonder: What is the Golden Ratio? There are many names the Golden Ratio has been called including the Golden Angle, the Golden Section, the Divine Proportion, the Golden Cut, the Golden Number et cetera, but what is it and how is it useful for society today? One may have heard of the number π (Pi 3.14159265…) but less common is π’s cousin Φ (Phi 1.61803399…). Both Φ and π are irrational numbers, meaning they are numbers that cannot be expressed as a ratio of two whole numbers as well as the fact that they are never-ending, never-repeating numbers. The Golden Ratio is the ratio of 1:Φ (1.61803399…). The Golden Ratio is a surprising ratio that is based on the research of many composite mathematicians spanning over 2300 years, and it is found in many areas of everyday life including art, architecture, beauty and nature.
Euclid, a Greek mathematician who taught in Alexandria around 300 B.C., was one of the first to discover and record the bases for the Golden Ratio back 2300 years ago. Euclid’s discovery was that if one takes a line and divide it into two unequal sections in such a way that the longer section is the same proportion to the shorter section as the entire line is to the longer section then one will get the...

...
Solving Proportions
MATT222 Intermediate Algebra
A comparison of two numbers is referred to as a ratio, similar to fractions that can be reduced to lowest terms and then converted into a ratio of integers. Ratios allow one to compare sizes of two quantities and unit measurements. Any statement expressing the equality of two ratios is known as a proportion, which is used in numerous formulas in today’s real world settings and applications. Using proportions is an effective way to find solutions by using the extreme means property or cross-multiplying. Extreme means property is simply the end result of the product of the extremes equaling the products of the means. Cross-multiplying is a short cut in proportions providing it is a faster way to solutions rather than multiplying each side of the rational expression equation by the LCD. Applications of rational expressions involving formulas include finding the equation of a line, distance, rate, time, uniform motion, and work problems. Proportions are used on a daily basis without even one realizing it by comparing measurements, unit pricing, driving distances, and calculating populations and wildlife on a daily basis to find a solution.
For example, I will be using the extreme means property to estimate bear population in Keweenaw Peninsula. I was asked to...

...In A Grove
There are different types of points of view in fiction. In the story, “In A Grove” by Ryūnosuke Akutagawa, a high police commissioner investigates a recent murder. The police commissioner gathers different testimonies from six different people. Each one of those testimonies has inconsistencies about the details of the murder. Different points of view were shown in the story.
A woodcutter was first to be questioned. His testimony states that he found the dead body in the woods, about one hundred fifty meters off the Yamashina stage road. The man died by a single sword-stroke to the chest. The body was lying on its back in a bluish silk kimono and a wrinkled head-dress of the Kyoto style. The blood was already dried up. The bamboo blades had fallen which resulted from a violent battle. He did not find a sword and horse but he found a rope at the foot of a cedar and a comb.
The second person to give his testimony was a traveling Buddhist Priest. He says that he saw the dead man with a woman on horse-back, who was his wife, on the road from Sekiyama to Yamashina noon on the day before the murder. He described the woman to be four feet five inches tall, dressed in lilac-colored suit and a scarf hanging from her head. Her horse was a sorrel with a fine mane. He described the man to have been armed with a sword and bow and twenty odd arrows in his quiver.
A policeman was the third to give his testimony. The policeman was the one who...

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