Proportional Relationships: Understanding This Algebraic Concept

propotional relationshipsIn mathematics you will constantly find yourself dealing with the relationship between two equations. A proportional relationship has the specific aspect of being a multiple of an equation. There are different types of math problems used for proportional relationships, and proportional relationships are used constantly in applications in everyday life.

For a person studying mathematics, finding the proportional relationship between two numbers is used to discover the potential price of a product or the distance between two objects. It’s a simple concept to learn and understand, and it only requires knowledge of division and basic multiplication to apply. In fact, anyone who has an understanding of algebra can perform math problems that deal with proportional relationships.

Of course, algebra isn’t always easy. In fact, some concepts in algebra courses can be difficult and takes an incredibly large amount of time to learn. If you want to find a new and simpler way to learn algebra, check out the Udemy course Algebra I Made Easy.

Definition of Proportional

In order to perform proportional relationship problems, the two quantities must have the same ratio. For example, if a person had 2 apples and they were sold for $5 then a proportional relationship would be having a second bag filled with 4 apples that were sold for $10.

The set up for this would be 2:5 = 4:10. Notice the proportions in the relationship between the two ratios. It stays the same no matter what the numbers are. For every 2 apples the cost is 5$. If there are 4 apples, then the cost would be $10. If there were 200 apples, then the cost would be $500. It doesn’t matter what the numbers are as long as the ratio of 2:5 remains the same.

One of the best ways to tell if two equations are proportional is to simplify them to their lowest numbers. Look at the two ratios 3:6 and 8:16. Despite these numbers appearing to be very different, they are actually proportional. Break down the two ratios into their simplest forms and you will see for yourself.

When you simplify 3:6, by dividing 3 into both 3 and 6, you get 1:2. Doing the same thing to 8:16, where you divide 8 into both 8 and 16 to simplify the ratio to its smallest form, and you also get 1:2. The ratio in both of these numbers is 1:2, which means that they are proportional.

Using the same example as before, whenever you have 3 apples that $6 you will have 8 apples that equal $16.

Sometimes the most difficult thing about concepts like proportional relationships is that the textbooks present it in a way that’s confusing. There are simpler ways to learn about mathematic concepts like this. Try the Udemy course Algebra I: Straight to the Point.

Proportional Relationship Equations

When searching for the ration of a particular equation, you may find moments where you are unable to instantly find out what the corresponding numbers may be. In order to figure out the number needed for a proportional relationship to work, you must use a specific type of equation.

For example, say you have 5 bananas and you sold them for $25, but you wanted to find out how much you could sell 8 bananas for. Well you already have one ratio 5:25, but what is the corresponding ratio when 8 is switched with 5. In order to do a problem like this, you must do something called cross multiplication.

You can find tons of algebra tutorials on Udemy that teach you about cross multiplication, and it’s a simple concept of multiplying across different math equations. Take the problem above.

You can set it up like so 5:25 = 8:X. Now the point of the cross multiplying is to find what x equals. To do this you must move every number to one side of the equal sign so that X is left standing alone.

Multiply 25 by 8 and 5 by x. Notice how they make a criss cross. Remember that the key to cross multiplying is multiplying the numerator by the divider in the other equation. You should get 200 = 5x. The final step in the problem is dividing 200 by 5 in order to remove it from the x. The end result is 40 = x, which means that in a ratio of 5: 25 there is an equivalent of 8:40.

Learning More 

You can go deeper and learn more about proportional relationships. The Udemy course on Beginning Algebra can help you build a strong foundation for concepts such as this. You can also try the Topics in Algebra: Graphing Udemy course, which teaches you how to chart and graph proportional equations and see the relationship between them.