# What is add subtract multiply and divide

### Colourful mix

Now you have got to know all the calculation rules for fractions individually. The next step is that you apply the correct rule to a wild set of tasks.

Here you have all the rules at a glance:

Fractions add or subtract you by first using the Main denominator find (the fractions do the same name), which add or subtract the "new numerator" and keep the main denominator:

\$\$3/4+2/5=(3*5)/20+(2*4)/20=(15+8)/20=23/20=1 3/20\$\$

### multiplication

Fractions multiply you by you Numerator times numerator and denominator times denominator calculate:

\$\$2/3*5/4=(2*5)/(3*4)=10/12=5/6\$\$

### division

Two breaks divide you by making the first break with the Multiply the reciprocal of the second fraction :

\$\$3/7:2/5=3/7*5/2=15/14=1 1/14\$\$

Find / use the same name as main denominator: You expand or shorten both fractions so that they have the same denominator (Main denominator) to have.

### Shorten

You can make calculations with fractions much easier by skillfully shortening them:

\$\$18/3*15/2=(18*15)/(3*2)=9*5=45\$\$

### Mixed numbers

You convert mixed numbers into improper fractions before calculating:

\$\$3 1/4*2 2/3=13/4*8/3=104/12=26/3=8 2/3\$\$

### Math vocabulary

Before it begins! Do you know all the important math vocabulary?

The result of the ADDITION called TOTAL.
The result of the SUBTRACTION called DIFFERENCE.
The result of the MULTIPLICATION called PRODUCT.
The result of the DIVISION called QUOTIENT.

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### Special features of fraction terms

Is in the numerator or denominator of a fraction a sum or differencedo you calculate it first, even if no bracket stands.

Example 1:

\$\$(100+50)/25=150/25=6/1=6\$\$

Example 2:

\$\$6/(8-4)=6/4=3/2\$\$

“Only the stupid cut out of sums”, be careful when cutting !! You make fewer mistakes if you calculate the line calculation first and then shorten !!

### A trick

If you can divide all the summands in the numerator by the same factor and this factor is in the denominator, you can reduce it by the common factor. The example from before:

Example: (abbreviated with \$\$ 25 \$\$)

\$\$(100+50)/25=(4+2)/1=6/1=6\$\$

You could also shorten everything with \$\$ 5 \$\$:

\$\$(100+50)/25=(20+10)/5=30/5=6\$\$

You see, it doesn't matter when you cut how. If you stick to all the rules, the result will always be the same.

### Another tip

If there is a fraction in an invoice that you can still shorten, you can first shorten it and then do the math.

Example: (shortened with 2)

\$\$8/12+5/6=4/6+5/6=9/6=3/2\$\$

You could also abbreviate with 4:

\$\$8/12+5/6=2/3+5/6\$\$

The main denominator is then \$\$ 6 \$\$. So that's not so clever.

Behind this is the distributive law:
\$\$100+50=25*(4+2)\$\$
Then you have a product and can shorten it.

### Skilful calculation with line calculation

With a long term, it often helps if you first change the term.

2 important points:

1. In line calculation, you put fractions together with a common denominator.

Example:

\$\$+3/5\$\$ \$\$+1/5=\$\$ \$\$+3/5+1/5=\$\$ \$\$+4/5=\$\$ \$\$+4/5=1 4/5\$\$

2. If you have a term with \$\$ + \$\$ and \$\$ - \$\$, you use the arithmetic symbol in front the break together with the break.

Example:

\$\$2/3+4/7\$\$ \$\$+3/7=2/3\$\$ \$\$+4/7+3/7=1/3+7/7=1/3+1=1 1/3\$\$

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### Skillful calculation with point calculation

You can also calculate advantageously when calculating points.

First, write down all the factors on a fraction line. Make sure to use the reciprocal when dividing.

Example:

\$\$6/5*15/3:2/9*4/3:6=(6*15*9*4*1)/(5*3*2*3*6)\$\$

In the next step, you can then concentrate fully on shortening.

\$\$(6*15*9*4)/(5*3*2*3*6)=(3*2)/1=6\$\$

##### tip

Take a pencil, cross out the abbreviated numbers and write the new value over it. This will make it easy for you to shorten it several times.

### Be careful when shortening:

You can only abbreviate numerators with denominators.
Never shorten just within the numerator or denominator!