# What is two thirds times 3

Why is?

A fraction of .....

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?

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

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?

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.

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?

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. | |

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?

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.

180 : 4 = 45

so there are 45 bears.

Then three times as much:

3 · 45 = 135

Answer: You get 135 from the guys.

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.

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.

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

Then only the desired number or all.

you have to calculate:

Always calculate first

**ONE**Fraction! (, ...)Then only the desired number or all.

If a lawn is 24 m

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

→ 24 m

^{2}big, then how big is the entire lawn?We know three quarters, so we have to divide by 3 to find ONE quarter:

→ 24 m

^{2}: 3 = 8 m^{2} Aha. And the whole area? Well, of course, the whole lawn consists of FOUR quarters. So take 4 times:

→ 8 m

The lawn is 32 m

→ 8 m

^{2}4 = 32 m^{2}The lawn is 32 m

^{2}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.

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.

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