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How do you calculate ratios? - Steps explained simply

Video: How to Calculate Ratios - Steps explained simply

This text will show you the possibilities for calculationofmathematicalCircumstances shown. As a rule, you compare two values ​​with each other and then try to put them into a relationship. You can find more about this in the following text.

What is a relationship?

You will encounter relationships in mathematics, but also in everyday life, for example when you bake a cake or with miniature cars. But what exactly does relationship mean?

For example, if you pass on a pancake recipe without knowing how much will be baked later, you can put the ingredients in a Ratio put. It is said, for example:

$ On \; \ textcolor {green} {200} \; Gram \; Flour \; come \; \ textcolor {blue} {50} \; Milliliter \; Milk. $

Here is a relationship between the Flour and the milk produced. These relationships usually appear in a text and cannot be recognized directly. There are a few key words to look out for here:

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Keywords indicating relationships: 

  1. ... the relationship between ... and ... is ...
  2. ... come to XYZ ABC ...

These Conditions but can also occur in fractions. You could say that relationship between flour and milk is $ \ frac {4} {1} $, or $ 4 \; $ parts to $ \; $ 1 part. Here we have the values $ 200 $ and $ 50 $ shortened enough to get a small fraction, so:

$ \ frac {200} {50} \ rightarrow \ frac {20} {5} \ rightarrow \ frac {4} {1} $

Another way of writing a ratio is to separate the values ​​with a colon. In our example that would be $ 4: $ 1.

4 spellings of relationships

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There are different Spellings to indicate a relationship between two or more values. You can:

  1. ... one fracture write: $ \ frac {4} {1} $
  2. ...With Colon separate: $ 4: 1 $
  3. ...with a Dash Separate: $ 4/1 $
  4. ... or with the wordto connect: $ 4 \; to \; $ 1

But it doesn't always have to be about baking. We can also create relationships of values ​​that are actually not directly related, as in the following example:

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task: Are in a school class 25 Student. Thereof 15 Student maleand 10 students female. Imagine relationship.

In this task we have all the important information fat marked. In the next step we will explain exactly how to proceed:

Step 1: First you should Values, that you gave write out. In this case that would be the 15 boys, the 10 girls and the 25 students as a total.

step 2: Now you should look how you do that relationship to scare. It is important that the biggervalue always in the counter stands, i.e. above the fraction line and the smaller onesvaluein thedenominator, i.e. below the fraction line.

$ \ frac {15 \; Boys} {10 \; Girl} $.

We shorten this fraction:

$ \ frac {3 \; boys} {2 \; girls} $.

step 3: Write out the solution. Here you write down the solution in one of the possible spellings in an answer sentence.

How do you calculate ratios?

Not only can you create relationships, you can also calculate them. There are two different methods of doing this.

Scale ratios

Conditionsscale, means something like adapting circumstances. If you like that relationship If you have $ 3: 1 $ and it is said that you need 4 times the amount, then you proceed as for expanding fractions. You multiply the numerator and denominator by the same number:

$ \ Large {\ frac {3} {1} \ rightarrow \ frac {3 \ times 4} {1 \ times 4} \ rightarrow \ frac {12} {4}} $.

The ratio is thus extended by 4 and a new ratio of $ \ frac {12} {4} $ results.

Determine relationships

It can also happen that a known ratio is to be expanded by an indefinite value. Let's look again at the assignment with the students:

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task: Are in a school class 25 Student. Thereof15 Student maleand10 students female.

a) Adjust the ratio so that exactly 5 fewer students attend the class in the event that the school class consists of 20 students.

b) Change the values ​​so that you only have 6 girls in the class. How many boys and how many students are there in total in the class?

To Subtaska)

The relationship was already calculated above and it was $ \ Large {\ frac {3} {2}} $. So you have at least 3 boys and 2 girls in one class. Now you have to find a value independently, with which you take the fraction times, so that you have a total of 20 students in the class. So in this case you do the math bothTerms $ four $. That makes:

$ \ Large {\ frac {3 \ times 4} {2 \ times 4} \ rightarrow \ frac {12} {8}} $.

The solution for sub-task a) is that12 boys and 8 girls are in class.

To Subtask b)

Here you have to look at what value you calculate the $ 2 \; $ in the ratio, so that you get 6. It's $ 3. Now we expand the fraction and get the solution:

$ \ Large {\ frac {3 \ times 3} {2 \ times 3} \ rightarrow \ frac {9} {6}} $

So the solution is $ 9 \; Boys \;:\; 6 \; Girl $.

To find out more about this topic, have a look at theExercises! We wish you a lot of fun and success!