# Proportionality Equation

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A Proportionality Equation is an Equation that equates two Ratio Statements.

**AKA:**Proportion, Proportion Equation.**Example(s):**- [math]\displaystyle{ 1/2 = 2/4 }[/math].
- [math]\displaystyle{ 3/4 = a/128 }[/math].
- [math]\displaystyle{ a/b = c/d }[/math].
- …

**Counter-Example(s):**- [math]\displaystyle{ 2/4 }[/math], a ratio.

**See:**Direct Proportion, Inverse Proportionality, Proportionality Relation, Frequency Function, Ratio, Common Denominator, Division Quotient, Division Function.

## References

### 2009

- (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=proportion
- S: (n) proportion (the quotient obtained when the magnitude of a part is divided by the magnitude of the whole)
- S: (n) proportion, ratio (the relation between things (or parts of things) with respect to their comparative quantity, magnitude, or degree) "an inordinate proportion of the book is given over to quotations"; "a dry martini has a large proportion of gin"

- http://en.wikipedia.org/wiki/Proportionality_(mathematics)
- In mathematics, two quantities are said to be
**proportional**if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio. - Proportion also refers to the equality of two ratios.
- Given two variables [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math],
*y is***(directly) proportional**to x**(***x and y**vary directly***,****or***x and y are in**direct variation*) if there is a non-zero constant [math]\displaystyle{ k }[/math] such that- y = kx

- In mathematics, two quantities are said to be

### 2008

- Dept. of Eduction, University of Irvine. (2009). “CSET Math Glossary."

### 2007

- http://www.isi.edu/~hobbs/bgt-arithmetic.text
- 3. Measures and Proportions. Sets of rational numbers, and hence sets of nonnegative integers, are very important examples of scales. We will focus on sets in which 0 is the smallest element. If e is the "lt" relation between x and y and s1 is a set of numbers containing 0 but no smaller number, then there is a nonnegative numeric scale s with s1 as its set and e as its partial ordering. … Suppose we have two points x and y on a scale s1 which has a measure. Then the proportion of x to y is the fraction whose numerator and denominator are the numbers the measure maps x and y into, respectively. … In more conventional notation, if m is a measure function mapping s1 into a nonnegative numeric scale, then the proportion f of x to y is given by "f = m(x)/m(y)". … Thus, we can talk about the proportion of one point on a numeric scale to another, via the identity measure.

- http://www.sasked.gov.sk.ca/docs/midlmath/glossary.html
**proportion**: an equality of two ratios; e.g.: 5 : 8 = 10 : 16.

### 2003

- "
*Definition of Ratio.*” http://mathforum.org/library/drmath/view/63884.html- This is as much an English language question as a math question, and that makes it very confusing. Words like this are not used as consistently as you might expect, even among math teachers or mathematicians. Merriam-Webster (m-w.com) says ...
- proportion.
- 3 : the relation of one part to another or to the whole with respect to magnitude, quantity, or degree : RATIO
- 4 : SIZE, DIMENSION
- 5 : a statement of equality between two ratios in which the first of the four terms divided by the second equals the third divided by the fourth (as in 4/2=10/5)

### 2000

- http://www.math.com/school/subject1/lessons/S1U2L3GL.html
- A rate is a ratio that compares two different kinds of numbers, such as miles per hour or dollars per pound. A unit rate compares a quantity to its unit of measure. A unit price is a rate comparing the price of an item to its unit of measure. The rate "miles per hour" gives distance traveled per unit of time. Problems using this type of rate can be solved using a proportion, or a formula.

- Math.com. (2000). “Glossary, http://www.math.com/school/glossary/defs/proportion.html
- proportion: An equation of fractions in the form: a/b = c/d

### 1997

- Ratio and Proportion. http://www.mathleague.com/help/ratio/ratio.htm
- A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. 3/4 = 6/8 is an example of a proportion. When one of the four numbers in a proportion is unknown, cross products may be used to find the unknown number. This is called solving the proportion. Question marks or letters are frequently used in place of the unknown number.