# A fraction can be an integer

### Multiply fractions by natural numbers

You can add and subtract fractions (\$\$ + \$\$ and \$\$ - \$\$). You guessed it, then there is the point calculation! Here comes the multiplication first.

And how does that work - multiply a fraction? The best way to imagine it is figuratively:

Example 1:   \$\$1/4*3\$\$ Example 2:   \$\$2/5*4\$\$ A fraction: \$\$ (counter) / (N e n n e r) \$\$

### The rule

If you write down your results again and mark them in color, you can see the rule for multiplying a fraction and number yourself:  You multiply a fraction by an integer by multiplying the numerator of the fraction by the number and keeping the denominator.
Example: ### Simplify results

Did you notice anything in the example of \$\$ 2/5 * 4 = 8/5 \$\$?
Exactly, you can simplify this result!

Here again the picture: The result consists of a whole plus \$\$ 3/5 \$\$.

So: \$\$ 1 3/5 \$\$.

If the numerator is greater than the denominator as a result of a multiplication, you can convert the fraction to a mixed number.

Example: \$\$ 4/3 * 5 = (4 * 5) / 3 = 20/3 = 6 2/3 \$\$

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### Simplify by shortening

Do you remember? The value of a fraction doesn't change when you go through the numerator and denominator same Dividing number. This is shortening and is now of benefit to you: If you multiply fractions, you can make the calculation much easier by skillfully shortening them.

Example:

\$\$13/15*5=(13*5)/15=65/15=4 5/15\$\$

So far so good. But isn't the task a lot easier when you cut it first?

\$\$ 13/15 * 5 = (13 * 5) / 15stackrel (abbreviated with 5) = (13 * 1) / 3 = 13/3 = 4 1/3 \$\$

Something else comes out? Remember that you can also reduce \$\$ 4 5/15 \$\$ by 5: \$\$ 4 5/15 = 4 1/3 \$\$.

And? Which way was easier for you to calculate? Both ways are correct! You decide how you prefer to calculate.

If you multiply fractions and skilfully shorten them, the calculation can be simplified.

### Mixed numbers

How do you calculate \$\$ 2 3/5 * 3 \$\$?

Don't worry, this is easier than you think. It's just one more step. :-)

First, convert the mixed number to an improper fraction:

\$\$2 3/5=((2*5)+3)/5=(10+3)/5=13/5\$\$

And you can already apply the rule:

\$\$ 13/5 * 3 = (13 * 3) / 5 \$\$ (unfortunately you can NOT shorten it) \$\$ = 39/5 \$\$

And simplify:

\$\$39/5=7 4/5\$\$

When you multiply a mixed number by a natural number, you first convert the mixed number to an improper fraction.

In the case of an improper fraction, the numerator (above) is greater than the denominator (below).

### Further examples

\$\$4 1/2*6=9/2*6=(9*6)/2=(9*3)/1=27\$\$

\$\$3*4 2/6=3*26/6=(3*26)/6=(1*26)/2=26/2=13\$\$

It can be worthwhile to shorten several times.

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### Zoom in or out?

If you multiply a number by a fraction with a value greater than 1, the number increases:

\$\$3*4/3=(3*4)/3=4/1=4\$\$

If you multiply a number by a fraction with a value less than 1, the number will decrease:

\$\$5*3/5=(5*3)/5=3/1=3\$\$

The value of a fraction is based on the ratio of numerator and denominator:
If the numerator is GREATER than the denominator, the value is greater than 1.
If the numerator is less than the denominator, the value is less than 1.