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...

...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...

...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...

...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...

...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...

...
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...

...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...

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