 We see ratios all around us every day.

From the grocery store, to forecasting into the future, to enlarging or shrinking pictures, a command of ratios can be a powerful math tool. In this lesson, learn how to solve word problems with ratios in them.

### Best services for writing your paper according to Trustpilot

From \$18.00 per page
4,8 / 5
4,80
Writers Experience
4,80
Delivery
4,90
Support
4,70
Price
Recommended Service
From \$13.90 per page
4,6 / 5
4,70
Writers Experience
4,70
Delivery
4,60
Support
4,60
Price
From \$20.00 per page
4,5 / 5
4,80
Writers Experience
4,50
Delivery
4,40
Support
4,10
Price
* All Partners were chosen among 50+ writing services by our Customer Satisfaction Team

## Where Are Ratios?

Ratios are everywhere around us. Try these on for size:

• A 5 oz. bag of gummy bears is \$1.

49. Is it a better deal to get the 144 oz. bag for \$15.99?

• You’ve got 60 homework problems to do and it took you 10 minutes to do eight of them. At that rate, how long will it take?
• Your favorite painting in the museum is 5 feet by 8 feet. How big will the eyes in that painting be on your smart phone’s 4.3-inch screen?

We could go on and on; and while each of these appear to be different problems – dealing with money, time, and size – they are, at their core, the same.

They all involve ratios.Let’s break down ratios a little more and see how they can help us solve these types of problems.

## What Is a Ratio?

A ratio is a comparison between two numbers. To keep it simple, we’ll ignore the units (e.g.

, cost in dollars or weight in ounces) and focus just on the number part for a bit. For example, how does 3 compare to 6? Well, three is half of six. We can write ratios in one of three ways:

1. 3:6
2. 3/6
3. 3 to 6

Because we’ll be using ratios mathematically, we’ll use the format ‘/’ for the rest of the lesson.

## What Is a Proportion?

By itself, a ratio is limited to how useful it is. However, when two ratios are set equal to each other, they are called a proportion. For example, 1/2 is a ratio and 3/6 is also a ratio.

If we write 1/2 = 3/6, we have written a proportion. We can also say that 1/2 is proportional to 3/6. In math, a ratio without a proportion is a little like peanut butter without jelly or bread.

## How Proportions Can Help

In math problems and in real life, if we have a known ratio comparing two quantities, we can use that ratio to predict another ratio, if given one half of that second ratio. In the example 1/2 = 3/?, the known ratio is 1/2. We know both terms of the known ratio. The unknown ratio is 3/?, since we know one term, but not the other (thus, it’s not yet a comparison between two ratios).

We only know one of the two terms in the unknown ratio. However, if we set them as a proportion, we can use that proportion to find the missing number.

## Solving Proportions with an Unknown Ratio

There are a few different methods we can use to solve proportions with an unknown ratio. However, the easiest and most fail-safe method is to cross-multiply and solve the resulting equation. For the last example, we would have: 1 * x = 2 * 31x = 6x = 6 / 1x = 6To check the accuracy of our answer, simply divide the two sides of the equation and compare the decimal that results.

In the example, 1/2 = 0.5 and 3/6 = 0.5.

That was the correct result.

## Solving Ratio Word Problems

To use proportions to solve ratio word problems, we need to follow these steps:

• Identify the known ratio and the unknown ratio.
• Set up the proportion.
• Cross-multiply and solve.
• Check the answer by plugging the result into the unknown ratio.

Your favorite store says it will donate to your soccer team \$3 for every \$50 that anyone wearing a soccer shirt spends at the store. Your team needs at least \$1,200 donated to be able to travel to a tournament. How much money needs to be spent at the store by people wearing soccer shirts?Our known ratio is \$3 donated / \$50 spent, and the unknown ratio is \$1,200 donated / ? spent. The proportion would look like this:

[Image_Link]/cimages/multimages/16/three_50ths_eq_1200_what.

png” alt=”ratio” />

Now let’s do the math.3 * x = 50 * 1,2003x = 60,000x = 60,000 / 3x = \$20,000Checking this, we get:3 / 50 = 1,200 / 20,0000.06 = 0.06This checks out!Your friends and family will need to spend \$20,000 at the store.

No problem, right?Is it really this easy? You betcha! You can use this process to solve any ratio word problem. The trickiest part is often identifying the known ratio and the unknown ratio. Once you’ve done that, make sure you are careful with tracking your calculations accurately, and you should have no trouble with these kinds of problems.

## Lesson Summary

Ratios are found all around us every day and are simply a comparison between two numbers (e.

g., red jellybeans to yellow jellybeans). A proportion is a statement that allows you to find an unknown ratio from a known ratio. In the known ratio, you know both of the numbers.

In the unknown ratio, you only know one of the numbers. To solve for the unknown number, set up a proportion with the known ratio on one side and the unknown ratio on the other, cross multiply, and solve the resulting equation. This method works every single time, so long as you have identified the known and unknown ratios correctly.

chapter is not just one material or product
• -485775-342900COMSATS experience I have picked up at
• Importance of Financial Ratios
• 181102039624000 WOLAITA SODO UNIVERSITY SCHOOL OF GRADUATE STUDIES DETERMINANTS OF FINANCEIAL PERFORMANCE OF MICROFINANCE INSTITUTION IN ETHIOPIA
• We of 14 parts by mass nitrogen
• Watch are proportional, they are also similar
• The as U.S. Treasury bills and commercial
• ALFALAH BANK LIMITED
• Even oranges? There are 3 apples and
• Learn multiply all the numbers in my 