Write and Solve Proportions
Introduction
Two equivalent ratios form a proportion when they are put together into a single equation.
When you are determining whether two fractions for a proportion, first see if one numerator and/or denominator is a multiple of the other. The proportion to the right can be shown to be true by multiplying each of the numbers in the first fraction by 5 to change them into the second fraction.
In the second proportion above, there is no number that can be used to change the first fraction into the second. An observant student will notice that both fractions can be reduced. A second way to show two fractions are equal is to reduce them to lowest terms. Reducing each fraction changes them into fourfifths. Since they are equal to each other in lowest terms, the fractions are equal.
Lesson
The easiest ways to determine whether two fractions make a proportion are to:

see if one fraction is a multiple of the other

reduce each fraction to lowest terms and then compare them
When you are faced with smaller fractions like the ones above, those two methods are your best options. However, for larger fractions there is a “catch all” method that can save a lot of time. One thing that all proportions have in common is that cross multiplication always yields the same answer.
Example 1: Use cross multiplication to see if the fractions form a proportion.
Solution:
The cross product is a method that always works, but an observant math student will notice when a simpler method can be used. In part c above, the numerator of 3 can easily be changed into a 9. In instances like this, it is easier to use simple multiplication rather than cross multiplication to see if the fractions are equivalent.
Write and Solve Proportions
When a builder constructs a new building, it is a common practice to make a smaller scale model of the new building before beginning construction. Since the scale model is an exact replica of the building, the size of the scale model is proportional to the size of the building. When figuring its dimensions, proportions can come in very useful.
Example 2: A builder is constructing a new building and has made model with a scale factor of 1 inch = 8 feet. If the scale model is 33 inches tall, then what will be the height of the actual building?
Solution:
Proportions can often be used in word problems such as example 2. The same kind of thinking can be used to find an unknown value in a standalone proportion.
Example 3: Find the missing value in the proportion.
Solution: