For many of us, mathematical tasks like working out percentages and solving equations caused no end of math anxiety back when we were in high school.
But often, without acknowledging it, we make use of math every day. Whether we’re shopping for bargains, baking, or trying to improve our sporting ability, many of our daily activities and hobbies require some form of math calculation.
One such mathematical task is learning how to calculate ratios. You’re sure to have encountered ratios in math class, but ratios aren’t only used in academic settings. In their simplest form, ratios compare two quantities and are common in everything from news reports to recipes.
But how do you calculate a ratio? Keep reading to find out.
Understanding How to Use Ratios
Before we get into finding ratios and learning how to calculate then, it’s vital that you understand what a ratio means.
As mentioned above, a simple ratio represents two quantities in relation to each other, although ratios can also consist of three or more items. These ratios can be dependent on each other, as they would be in a recipe, or independent, as they would be when describing statistics.
Dependent Ratios
Keeping things simple, a basic pizza dough recipe might call for four cups of flour and two cups of water. The ratio of flour to water is then 2 to 1, or 2 : 1. In this case, if you wanted to make double the amount of dough, you’d have to double up, adding eight cups of flour and four cups of water as well as twice as much of any other ingredients.
Recipes can also list ingredients by parts. For example, to make a basic window cleaning solution, a recipe might call for one part water mixed with one part white vinegar. These ‘parts’ are another way to express ratios that are tied to each other.
As such, your ‘part’ could be any quantity. But, whether you’ve gone for 3 fl oz or a cup, you’ll need to make sure that your proportions, or ratios, are the same to ensure the cleaning solution is effective.
Independent Ratios
You can also use ratios to demonstrate the relation between quantities that aren’t tied to each other as they are in a recipe. For example, if there are five boys and 10 girls in a class, the ratio of boys to girls is 5 to 10, or 5 : 10.
Here, all the ratio does is compares the quantities of these two groups. These two quantities are not tied to each other in any way. If new students entered the class or anyone left, you would need to change the ratio to represent the new proportional difference.
How to Calculate Ratios
Ratios are useful because they allow us to scale amounts down as well as up. And, as these ratios show, it’s often easier to understand and use a ratio when it’s in its simplest form.
Scaling down a ratio is especially useful for things like maps and models. Here, you can convert large numbers down to smaller representations which are still accurate.
When your calculations involve large numbers, it’s a good idea to use a ratio calculator to make sure your equivalent ratios are accurate. But you can also learn how to figure out ratios and calculate them by hand if you don’t have access to this handy tool.
You can simplify ratios in the same way you would simplify a fraction by removing any common factors. To scale a ratio down, divide all the items in the ratio by the largest factor they have in common until no common factors remain.
In the classroom example above of five boys and 10 girls, you can divide both figures by five. This ratio formula then allows us to state that there is one boy for every two girls in the class, or that the girls outnumber the boys by two to one.
Of course, you won’t be able to scale down all ratios. For example, you can’t scale down a ratio of 5 : 57 as these numbers have no common factors.
Converting Ratios for Easier Calculation
Ratios also have many other real-world applications if you know how to make use of them. But sometimes, you may need to change the units of measurement to calculate an accurate and understandable ratio.
For example, the scale of a map might be 3 cm to 15 m. Since whole numbers are easier to work with, the best way to convert these units is to multiply the 15 by 100 to give us this figure in cm, where 3 cm to 15 m becomes 3 : 1500.
We can then scale this down as both three and 1500 are divisible by 3, so the final ratio is 1 : 500. You can then use this simplified ratio to understand the scale distances between various points on the map in a clearer and quicker way.
Other times, parts of the ratio may not be represented as whole numbers. This could be the case when converting different world currencies. For example, $10 is equal to 2.50€, or 10 : 2.5.
To calculate this ratio in a more understandable way, you can multiply both sides of the ratio by two to become 20 : 5. We can then scale down this ratio to 4 : 1 as you can divide both figures by five. From this, it becomes easier to see that there are four dollars to every euro, making it easier for us to convert prices in our heads when traveling.
Your Complete Guide to Calculating Ratios
As this handy guide shows, learning how to calculate ratios can be a really useful skill with many real-world applications.
But, the good news is, calculating ratios is also a lot easier than you might have expected all those years ago when you were struggling through high school math. And, even if you can’t quite get to grips with calculating ratios in your head, there are plenty of handy online tools that can help you out!
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