How does it work 5 3 12 3 35

The division of fractions

You know what fractions are and you can add, subtract, multiply and divide a fraction by a natural number. Still missing? The division of two fractions!

As a reminder, here are the most important rules again! Then the rule for dividing will be easier for you!

RULE example
A fraction consists of a numerator and a denominator:
$$ (COUNTER) / (NEN NER) $$
You multiply two fractions by multiplying the numerators and denominators, respectively.
Or in short: and
$$1/2*3/4= (1*3)/(2*4)$$ $$=3/8$$
You divide a fraction by a natural number by adding the $$4/5:3=4/((5*3))$$ $$=4/15$$

What does it mean to divide two fractions?

The task: $$ 3/4: 3/8 $$

That means:
How often does the fraction $$ 3/8 $$ fit into the fraction $$ 3/4 $$?

As a picture:

Move the $$ 3/8 $$ pie piece and think about how it fits into the area of ​​$$ 3/4 $$.
Exactly 2 of the $$ 3/8 $$ - cake fit into the $$ 3/4 $$ - cake:


So the calculation is: $$ 3/4: 3/8 = 2 $$

Do you remember? Even when dividing whole numbers, you wondered how often one number fits into another.
$$ 8: 2 = 4 $$ told you that the 2 fits into the 8 exactly 4 times

An example when it doesn't fit that well

The task: $$ 6/9: 3/6 $$

That means: How often does the fraction $$ 3/6 $$ fit into the fraction $$ 6/9 $$?


Imagine it figuratively:


Move the $$ 3/6 $$ block: The block fits in a whole time and in addition to a fraction of $$ 1/3 $$. The $$ 3/6 $$ fit $$ 1 1/3 $$ times into $$ 6/9 $$.


The problem is: $$ 6/9: 3/6 = 1 1/3 = 4/3 $$

kapiert.decan do more:

  • interactive exercises
    and tests
  • individual classwork trainer
  • Learning manager

Do you already find the rule?

Try to derive a rule from the examples:


That of the result is derived from multiplication the one ruptures with that of the other.

That results from the multiplication the one ruptures with that of the other.

In brief the 3rd example: $$ 6/9: 3/6 = 6/9 * 6/3 = (6 * 6) / (9 * 3) = 36/27 $$

You turn the division task into a painting task! To do this, turn the second fraction over. In mathematical terms, that means: You build it Reciprocal of the fraction.

You divide two fractions by multiplying the first fraction by the reciprocal of the second fraction.
Example: $$ 5/3: 7/2 = 5/3 * 2/7 = (5 * 2) / (3 * 7) = 10/21 $$

The reciprocal:
For every break there is a valuable partner: the Sweeping break or Reciprocal. Swap the numerator and denominator and you get the reciprocal value.
The reciprocal of $$ 2/3 $$ is $$ 3/2 $$.

The reciprocal of $$ 5 = 5/1 $$ is $$ 1/5 $$.

Examples, examples

$$2/3:1/2=2/3*2/1=(2*2)/(3*1)=4/3$$

$$5/6:2/7=5/6*7/2=35/12$$

And with shortening

Skilful shortening is always good. :-)

$$11/7:22/35=11/7*35/22=(1*5)/(1*2)=5/2$$

$$24/15:16/25=24/15*25/16=(6*5)/(3*4)=(2*5)/(1*4)=(1*5)/(1*2)=5/2$$

Do not shorten it until you have converted the division problem into the painting problem.

Division of mixed numbers

As with multiplying, mixed numbers are first converted into an improper fraction.

Example:

$$2 1/3:5 2/3=7/3:17/3=7/3*3/17=7/17$$


Example 2: with shortening

$$4 4/5:3 6/10=24/5 : 36/10=24/5*10/36=(2*2)/(1*3)=4/3=1 1/3$$

kapiert.decan do more:

  • interactive exercises
    and tests
  • individual classwork trainer
  • Learning manager

Double fractions

Do you remember: A fraction is nothing more than a division problem.

$$ 1/2 = 1: 2 = 0.5 $$ or $$ 3/4 = 3: 4 = 0.75 $$

You need that with Double fractions. Double fractions? They have a fraction in the numerator and denominator.

Examples:

$$(3/4)/(5/8)=3/4:5/8=3/4*8/5=6/5$$

$$(10/4)/(9/2)=10/4*2/9=10/18=5/9$$

What do you need the division of fractions for?

You need the division when you divide a fraction evenly.

Example:

A bottle contains $$ 3/4 $$ liters of juice. How many glasses ever
Can you fill 150ml ($$ 3/20 $$ liters) with it?

Solution:

$$3/4:3/20=3/4*20/3=5$$


Answer: You can fill exactly 5 glasses.