1TH/vwo §5.1 Calculating in a ratio table

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 1

§5.1 Calculating in a RATIO TABLE

GOAL of this lesson:

HOW TO CALCULATE IN A RATIO TABLE

What is a RATIO?

It's a 'verhouding' in Dutch.

For example: 

you need 200 grams of flour to bake 2 muffins,

so the RATIO is 200 : 2, or better:          100 : 1

Why is 100:1 better than 200:2 ?

Explanation:

Both expressions mean the same.

However a RATIO is always written with:

THE SMALLEST POSSIBLE WHOLE NUMBERS ! 

How to calculate in a ratio table?

example 1 

Look above! It's about the euros earned by working  a number of hours.

Think about how to get the numbers on the dots.

hours	5	15	90
euros	2	...	...

Solution:

We Multiply from LEFT to RIGHT in this case!

So: Multiplying HORIZONTALLY is simplest here:

5 x 3 = 15, so for 15 hours worked you get 2 x 3 = 6 euros

5 x 18 = 90, so for 90 hours worked you get 2 x 18 = 36 euros

hours	5	15	90
euros	2	6	36

Do you prefer to calculate vertically (= top down) or horizontally (= from left tot right), now?       

Think this over. 

You may talk about it 

with your neighbor, too!

Again calculating from left to right is most logical.

The symbols   x  and  :  already help you in this!

Working top down,

from 6 to 192,

is more difficult than

doing it from left to

right!

 example 3:

Sometimes it's obvious that you can 

get the number on the dots BOTH by

multiplying VERTICALLY and

HORIZONTALLY .

Here it clearly doesn't matter!

Doing  x 1.5   or   x 4 are both pretty simple.

example 4:

Let us try to find the missing number!

However, doing this DIRECTLY in one step is not easy.

In the next slide I will show you a handy METHOD.

grams	500	240
euros	750	...

What's up, now?

Well, if we first calculate the price in euros for just one gram,

the rest is quite easy!

Think about the missing numbers.

grams	500	1	240
euros	750	...	...

Explanation:

Now that we know that 1 gram costs 1.5 cents,

we do:

240 x 1.5 = 240 + 120 = 360 cents.

grams	500	1	240
euros	750	1.5	360

The book calls this Method:

'adding a number as an INTERMEDIATE STEP (=tussenstap)'

This intermediate step is mostly the number 1.

However it could also be 10,   50    or any handy number!

It depends on the concrete situation.

grams	500	1	240
euros	750	1.5	360

Two Methods 

are used here!

Both work good,

as you can see.

example 5:

TASK:

Find the easiest way to get the missing numbers.

grams	200	20	220
cents	600	...	...

example 5:

Solution:

Now easiest for sure is ADDING up! No multiplying this time.

That's because 200 + 20= 220

20 grams cost 60 cents

So the price of 220 grams is 600 + 60 = 660 cents

grams	200	20	220
cents	600	60	660

example 6:

Again find the missing numbers.

grams	40	2	38
cents	160	...	...

example 6:

Solution:

This time SUBTRACTING does the trick!

This is because 40 - 2 = 38

First we calculate that 2 grams cost 8 cents.

Then we do       160 - 8 = 152 cents.

grams	40	2	38
cents	160	8	152

Homework time

Now do §5.1 

Always make and work out RATIO TABLES!