How does ratios work

As noted above, ratios demonstrate the quantity of at least two items in relation to each other. So, for example, if a cake contains two cups of flour and one cup of sugar, you would say that the ratio of flour to sugar was 2 to 1. Ratios can be used to show the relation between any quantities, even if one is not directly tied to the other as they would be in a recipe. For example, if there are five girls and ten boys in a class, the ratio of girls to boys is 5 to Neither quantity is dependent on or tied to the other, and would change if anyone left or new students came in.

The ratio merely compares the quantities. Notice the different ways in which ratios are expressed. Ratios can be written out using words or can be represented using mathematical symbols.

Because they are used so commonly and in such a variety of ways, if you find yourself working outside of mathematic or scientific fields, this may the most common form of ratio you will see. Ratios are frequently expressed using a colon. When comparing two numbers in a ratio, you'll use one colon as in 7 : When you're comparing more than two numbers, you'll put a colon between each set of numbers in succession as in 10 : 2 : In our classroom example, we might compare the number of boys to the number of girls with the ratio 5 girls : 10 boys.

We can simply express the ratio as 5 : Ratios are also sometimes expressed using fractional notation. That said, it shouldn't be read out loud the same as a fraction, and you need to keep in mind that the numbers do not represent a portion of a whole. Part 2. Reduce a ratio to its simplest form.

Ratios can be reduced and simplified like fractions by removing any common factors of the terms in the ratio. To reduce a ratio, divide all the terms in the ratio by the common factors they share until no common factor exists. However, when doing this, it's important not to lose sight of the original quantities that led to the ratio in the first place. Divide both sides by 5 the greatest common factor to get 1 girl to 2 boys or 1 : 2.

However, we should keep the original quantities in mind, even when using this reduced ratio. There are not 3 total students in the class, but The reduced ratio just compares the relationship between the number of boys and girls.

There are 2 boys for every girl, not exactly 2 boys and 1 girl. Some ratios cannot be reduced. For example, 3 : 56 cannot be reduced because the two numbers share no common factors - 3 is a prime number, and 56 is not divisible by 3. Use multiplication or division to "scale" ratios.

One common type of problem that employs ratios may involve using ratios to scale up or down the two numbers in proportion to each other. Multiplying or dividing all terms in a ratio by the same number creates a ratio with the same proportions as the original, so, to scale your ratio, multiply or divide through the ratio by the scaling factor.

If the normal ratio of flour to sugar is 2 to 1 2 : 1 , then both numbers must be increased by a factor of three. The appropriate quantities for the recipe are now 6 cups of flour to 3 cups of sugar 6 : 3. The same process can be reversed. Find unknown variables when given two equivalent ratios. Another common type of problem that incorporates ratios asks you to find an unknown variable in one ratio, given the other number in that ratio and a second ratio that is equivalent to the first.

The principle of cross multiplication makes solving these problems fairly simple. Write each ratio in its fractional form, then set the two ratios equal to each other and cross multiply to solve. If we were to maintain this proportion of boys to girls, how many boys would be in a class that contained 20 girls? Part 3. Avoid addition or subtraction in ratio word problems. Many word problems look something like this: "A recipe calls for 4 potatoes and 5 carrots.

To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by So for every 2 inches, meters, whatever of height there should be 3 of width. If we made the flag 40 cm high, it should be 60 cm wide which is still in the ratio Here is a chart showing the number of goals made by five basketball players from the free-throw line, out of shots taken.

Each comparison of goals made to shots taken is expressed as a ratio, a decimal, and a percent. They are all equivalent, which means they are all different ways of saying the same thing.

Which do you prefer to use? All rights reserved. Please read our Privacy Policy. We use ratios to make comparisons between two things. There are employees and five aren't meeting the KPIs. Find jobs.

Company reviews. Find salaries. Upload your resume. Sign in. Career Development. Business uses for ratios. Cash flow and liquidity. Financial risk and return. Stock turnover and sales.

Key performance indicators KPIs. Employee tracking. Product returns. How to calculate a ratio. Determine the purpose of the ratio. You should start by identifying what you want your ratio to show. Each ratio will use different data, and you want to be sure you are using the correct information to give you the details you are looking for. Set up your formula. Ratios compare two numbers, usually by dividing them.