# How to Calculate a Cash Trade Account

## How do you calculate ratios? - Steps explained simply

### Video: How to Calculate Ratios - Steps explained simply

This text will show you the possibilities for **calculation****of****mathematical****Circumstances** 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:

**Keywords indicating relationships:**

- ... the relationship between ... and ... is ...
- ... 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

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

- ... one
**fracture**write: $ \ frac {4} {1} $ - ...With
**Colon**separate: $ 4: 1 $ - ...with a
**Dash**Separate: $ 4/1 $ - ... or with the
**word****to**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:

**task**: Are in a school class **25** Student. Thereof **15** **Student male**and **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 **bigger****value** always **in the counter** stands, i.e. above the fraction line and the **smaller ones****value****in the****denominator**, 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

**Conditions****scale,** 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:

**task**: Are in a school class **25** Student. Thereof**15** **Student male**and**10 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 **Subtask****a)**

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 **both****Terms** $ four $. That makes:

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

The solution for sub-task a) is that**12 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 the Exercises! We wish you a lot of fun and success!*

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