What is two thirds times 3

Why is?
We have understood what is meant by a fraction such as or and can now count on the fractions.

a bag with 120 gummy bears - how many are that?

from a 60 m high tower, how high is that?
 
   
In this lesson you will learn:
1.How to calculate a fraction of a certain amount.
2.Conversely, how to determine the total amount from a fraction.
 A fraction of .....
You and your boyfriend swept the stairwell together. As a reward, you will receive a bag of gummy bears. (In maths, gummy bears are also used in the 10th grade!; O {) And because you have worked a lot more, you get it. The question arises:

How much is 180?
 


      






Action:
Divide by the denominator to find how much ONE part is.
Multiply with the counter to calculate how many ..... parts are.





   
Fractions are also arithmetic instructions:

Times 3 divided by 4.





To find out, first think about how many bears there are in ONE quarter. To do this, divide the number by 4:

180 : 4 = 45

so there are 45 bears.
 
Then three times as much:

3 · 45 = 135

Answer: You get 135 from the guys.
 
Second example:

A climber wants to climb a 60 m high tower of a castle. Afterwards, however, he has to give up exhausted. How high did he get?

The question arises: how many are from 60 m?
 
We first divide by the denominator, i.e. by 3, to calculate what a third is:

60 m: 3 = 20 m

Now we multiply by the numerator, i.e. 2, to find out how many TWO thirds are:
20 m x 2 = 40 m

The climber came 40 m.
 
Third example:

How much is 70 liters of water?

→ 70 l: 5 = 14 l
→ 14 l 3 = 42 l

Answer: It is 42 liters.
 
From a fraction to a whole
Sometimes the question arises the other way around: you know how much a fraction is, but you want to find out how much the whole was.
 









Action:
Divide by the numerator to calculate how much ONE part is.
Multiply by the denominator to find out how many ALL parts are.






No matter in which direction
you have to calculate:

Always calculate first
ONE Fraction! (, ...)
Then only the desired number or all.
If a lawn is 24 m2 big, then how big is the entire lawn?

We know three quarters, so we have to divide by 3 to find ONE quarter:

→ 24 m2 : 3 = 8 m2
 
Aha. And the whole area? Well, of course, the whole lawn consists of FOUR quarters. So take 4 times:

→ 8 m2 4 = 32 m2

The lawn is 32 m2 large.
 

Second example:

Assume that 320 students take the bus in a school, which corresponds to a proportion of. How many students does the school have in total?
 
Again, we first calculate how much ONE seventh is. To do this, we have to divide the number of five sevenths by 5:

320 students: 5 = 64 students

Then ALL are, so SEVEN sevenths:

64 students 7 = 448 students

The school has 448 students.
 

Third example:

a lot of flour weighs 300 grams. How much flour is it in total?

→ 300 g: 4 = 75 g
→ 75 g 6 = 450 g

The whole flour weighs 450 grams.