Proportional sizes

Proportional sizes

1st example

12

13

11

10

At the end...

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How to do ?

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Is it proportional ?

again...choose x and y

2nd example

Selection of x and y

Number k!

What does "k" means?

Let's define!

table with data

INDEX

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1st exampleThe printer writes 30 pages for 3 minutes. There is an equal amount od text and drawings on each page. 1. How many such pages will be printed for 1 minutes ? 2. How long will it take time for three times as many pages ? 3. How many pages will the printer print if it runs 5 times as long ?

1st example: table with data

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• How many times the size of x increases, so many times the size of y must also increase
• How many times the size od x decreases, so many times the size of y must also decreases

Two sizes, x and y are proportional:

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Let's calculate the proportionality coefficient

In the 1st example, the proportionality coefficient represents the velocity of printing one page.

The quotient of proportional sizes is always equal and is called the proportionality coefficient - k

The size x represents a unit value. In a 1st example it represent how many pages are printed for 1 minutes.

It is more logical to say how many pages are printed for 1 minutes, therefore size y is number of pages and x is the print time.

for 1st example : How many minutes does it take to print 1 page? How many pages are printed for 1 minutes ?

...let's ask ourselves: What is more logical ?

After we establish that two sizes are proportional...

How to choose x and y ?

click on picture to see solution of 2nd example.

It is more logical to say how much sugar is needed for baking 1 cake, therefore the size y is amount od sugar and x is the number of cakes.

What is more logical to say ? How many cakes is needed for 1 dag of sugar ? How much sugar is needed for baking 1 cake ?

Are the number of cakes and amount of sugar proportional quantities ?

If we increase the number of egual cakes to 10, how much sugar is needed ?

2nd example: 125 dag of sugar is needed to bake 5 equal cake.

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In which table the proportional sizes are shown ?

VS

Two ways of solving tasks with proportional sizes

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Start

when you solve the task 3, click here to reveal solution.

When you solve the task 2, click here to reveal the solution.

When you solve the task 1, click here to reveal the solution.

Try to solve tasks!

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Graphical display of proportionality

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P.S. There are inversal proportional in size,... but that is completely different story...maybe next time!

At the end click here and play a game!