In this post, we’re going to go a little further with **proportional relationship**. Let’s take a look at some different examples of ratio and proportion in everyday life. Before we begin, let’s review both of these concepts in the following link: Ratio and Proportion.

As we’ve mentioned before, it’s all about two ways of relating quantities, numbers or quantities to each other.

### Now, we’re going to consider an example of proportional relationship in our everyday life:

When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we’ll pay. Also, the less money we pay, the less gas we’ll put in our car. This relationship depends on the price of a gallon of gas. *The price is the proportionality ratio that exists between the quantity “gallons of gas” and the quantity “money it takes to fill up.”*

Meanwhile, another car can fill up with a different amount of fuel than ours. The price per gallon stays the same, so the relationship between the gallons put in and the money paid is the same and therefore, filling each car’s tank with gas is proportional because they follow the same proportionality ratio.

Example: “If every gallon of gas costs $2 and I have $30 in my wallet, I’ll be able to put 15 gallons in the tank and if I wanted to put in 20 gallons, I’d have to pay $40”

### Now, let’s make sure that we understood it… Try to solve the next problem:

Example: “Yesterday, I put 10 gallons of gas in my car and I paid $30. A couple hours after, I went back to the gas station with my dad’s car and after filling up the tank, I paid $18. How many gallons of gas did I put in my dad’s car?”

In order to solve this problem, first we’ll have to figure out the proportionality ratio between the gallons I put in my car and the amount I paid.

$30 ÷ 10 gallons = $3/gallon ($ per gallon)

After, once we know that the ratio is $3/gallon, we need to calculate how many gallons we can put in the tank with $18.

$18 ÷ $3/gallon =** 6 gallons**

So then, the second time I went to the gas station, I filled my dad’s car with 6 gallons of gas.

This situation illustrates a clear example of proportional relationships where the quantities of the first fill up are proportional to the ones of the second fill up; the quotient that comes from dividing both of them is the same in both cases: it’s the ratio:

I hope that you can start to see everyday “ratio and proportion” phenomena with the help of this post.

If you want to keep on learning about proportional relationship, ratio and proportion, not to mention other topics, make an account at Smartick and don’t stop learning!

Learn More:

- Proportional Numbers Problems. Ratio and Proportion
- Direct Proportions: What Are They? What Are They Used For?
- Ratio and Proportion: Concept and Some Examples
- Inverse Proportionality: What Is It?
- Proportionality Problems: Learn How to Solve Them

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