The first thing we should do is add up the total number of apprentices in each of the three trades. What we can do now is put each of the apprentice totals into both a ratio and a fraction of the whole. If percentages are based on , then we have to translate the ratio and the fraction into forms based on In other words, we have to make it so that the number on the right in the ratio is and the denominator in the fraction is For this, we have to go back to our work with fractions.
We have 97 apprentices out of a total of Our goal here is to get this fraction down to a point where the denominator is We are essentially reducing the fraction.
Luckily for us, going from down to is quite easy. We just divide the denominator by 3, and then also divide the numerator by 3. What we end up with is the fact that Once we find out the number of carpentry students per students, we automatically have our percentage.
Step 1 : Put the numbers into an equation that we can work with. In this case, put the numbers into a fraction. Now calculate the percentage of plumbing apprentices.
Check the video to see if your answer is correct. The next step actually makes the whole process of finding percentages easier. In this section, we skip that whole procedure and just take the numbers we have and work with them as they are. We could go back to our old ways and get to a fraction with a denominator of , or we could simply divide the 57 by the Now take the 0. This moves the decimal point 2 spots to the right and leaves us with a whole number. Using the same method we just used with the carpentry apprentices, find the percentage of plumbing students in the trades college.
Step 2 : Work this out in your head. Just kidding: grab your calculator and plug the numbers in. Log in Social login does not work in incognito and private browsers. Please log in with your username or email to continue. No account yet? Create an account. Edit this Article. We use cookies to make wikiHow great. By using our site, you agree to our cookie policy. Cookie Settings. Learn why people trust wikiHow. Download Article Explore this Article parts. Practice Problems.
Related Articles. Article Summary. Part 1. Be aware of how ratios are used. Ratios are used in both academic settings and in the real world to compare multiple amounts or quantities to each other. The simplest ratios compare only two values, but ratios comparing three or more values are also possible. In any situations in which two or more distinct numbers or quantities are being compared, ratios are applicable.
By describing quantities in relation to each other, they explain how chemical formulas can be duplicated or recipes in the kitchen expanded. After you get to understand them, you will use ratios for the rest of your life. Get to know what a ratio means. 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. They would find the staff turnover ratio by comparing the number of employees who left to the total number of staff. You can use ratios to determine the rate that products are being returned. This ratio can give you insight into products that are faulty or don't meet customer expectations.
It can also help determine patterns of returns and what items need to be redesigned or discontinued. To find the product return ratio, compare the number of items that were returned over a period of time to the total sales over that same time. Here's an example of using a ratio in the workplace:. You want to find out the ratio of employees who are not meeting their KPIs.
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.
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