7. Ratio and Proportion

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Из курса от партнера University of London

Quantitative Foundations for International Business

156 оценки

University of London

Quantitative Foundations for International Business

156 оценки

Курс 3 из 6 — Specialization International Business Essentials

This course provides the essential mathematics required to succeed in the finance and economics related modules of the Global MBA, including equations, functions, derivatives, and matrices. You can test your understanding with quizzes and worksheets, while more advanced content will be available if you want to push yourself. This course forms part of a specialisation from the University of London designed to help you develop and build the essential business, academic, and cultural skills necessary to succeed in international business, or in further study. If completed successfully, your certificate from this specialisation can also be used as part of the application process for the University of London Global MBA programme, particularly for early career applicants. If you would like more information about the Global MBA, please visit https://mba.london.ac.uk/. This course is endorsed by CMI

Из урока

Equations

Although financial models are theoretical frameworks, we often use mathematical tools to work with these models. Mathematical models usually consist of a set of equations, which are designed to describe the structure of the model, and whose solution determines the importance of variables. This week, we will look at equations, including the basic terminology, and the rules for solving equations requiring more than one operation.

Equations- An Introduction3:33

1. Variables, Constants and Parameters6:14

2. The Real Number System6:08

3. Basic Rules7:34

4. Like Terms3:12

5. Translate Phrases into Mathematics6:22

6. Working with Business Formulas5:30

7. Ratio and Proportion6:25

Equations- Summary2:42

Познакомьтесь с преподавателями

George Kapetanios
Professor of Finance and Econometrics
King's College London

[MUSIC]

A ratio is a quotient of two quantities.

It is normally used to compare the quantities.

The ratio of number a to number b can be written as a to b.

A divided by b or a/b or

are pronounced as a to b or a is to b.

This last way is the most common in mathematics.

The writing a divided by b is more used in business instead.

Let us see an example the ratio of

five hours to two hours is 5 to 2.

If we need to find the ratio of three hours to three days,

first, we need to convert the three days to hours.

24 hours in one day, and

then three days is equal to three times 24,

which is equal to 72 hours.

Therefore, the ratio of three hours to

three days is the quotient of three and

72 that is three to 72.

Another example, we use a ratio between two

numbers in order to compare two amounts.

If two ratios are equal, such as, 3 to 4 and

15 to 20, then we can tell that there is proportion.

We can see that by using the methods of cross products.

And then we have that three times 20 is equal to 60 and

four times 15 is equal to 60 then, there is a proportion.

According to rule of proportion

a to b is equal to c to d if

the cross product a times d and

b times c are equal that is if ad = bc.

For example decide if the following proportions are correct.

3 to 5 and 12 to 20,

3 x 20 = 5 x 12 is that correct?

Yes, because 3 x 20 = 60 and

5 x 12 = 60 as well.

2/3 equal to 9 to 16,

2 times 16 is equal to 9 times 3,

is that correct?

No, because 32 is different than 27

A proportion is composed of two ratios,

therefore, of four numbers.

If we know three of our four numbers,

then any three numbers, what is unknown?

But still we can solve our proportion by finding default unknown number.

We can use alternatively, two methods to solve the proportion.

We can either multiply both sides by

the product of the two denominators, or

use the method of cross products.

Notice, that whatever the method used, we get the same equation.

If we use method one, we need to multiply both sides of

the equation by the product of the two denominators.

Then if we have 3/5 equal

to x to 40 then we have 3/5

x (5 x 40) = x/40

times five times 40 and

we get 120 equal to 5x.

If we use the method two,

we have (3x40)=(5 x X) and

then we get again 120 = 5x.

Now we can solve the equation.

In this case in order to isolate our variable which is x,

on the one side of the equation

in a numbers in all the sides of the equation we need to get rid of five.

We can do it just by applying the operation, which is

the inverse of the multiplication, that is the division.

Therefore, we solve the equation by dividing both sides by five.

And then we have

120/5 = 5x/5

our result is x = 24.

[MUSIC]

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