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Add and subtract fractions of the same name

You add Fractions of the same denominator by adding only theirs counter add.

The denominator stick with it unchanged.

Example:

$$1/7 + 3/7= (1+3)/7= 4/7$$

You subtract Fractions of the same denominator by adding only theirs counter subtract.

The denominator stick with it unchanged.

Example:

$$3/7- 1/7= (3-1)/7= 2/7$$

Add fractions of a different name

Breaks with differentDenominators you can only add up if you bring the fractions to a common denominator first.

For this you need the fractions shorten or expand.

Shortening means:

Numerator and denominator by the same number to divide.

Example:

Reduce $$ 4/12 $$ with $$ 2 $$: $$ (4: 2) / (12: 2) = 2/6 $$

To expand means:

Numerator and denominator with the same number multiply.

Example:

Expand $$ 2/3 $$ with $$ 4 $$: $$ (2 * 4) / (3 * 4) = 8/12 $$


If you have one for all fractions Main denominatorfound you can then use the fractions allnormaladd.

The common denominator is also called Main denominator.

Form the main denominator by shortening it

Example 1:

$$1/4+ 4/8$$

Shorten the 2nd fraction with 2. This means that both fractions have the common denominator 4.

$$1/4+ 4/8=1/4+ (4 : 2)/(8 : 2)= 1/4+ 2/4$$

Now add both fractions as normal.

$$1/4+ 2/4=(1+2)/4 = 3/4 $$

Example 2:

$$2/8 + 6/12$$

Shorten the 1st fraction with 2 and the 2nd fraction with 3. This brings both fractions to the main denominator 4.

$$2/8 + 6/12= (2 : 2)/(8 : 2) + (6 : 3)/(12 : 3)= 1/4+ 2/4$$

Now add both fractions as normal.

$$1/4+ 2/4= (1+2)/4= 3/4$$

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Form the main denominator by expanding

Example 1:

$$1/4+ 1/8$$

Extend the 1st fraction with 2. So both fractions have the common denominator 8.

$$1/4+ 1/8=(1 * 2)/(4 * 2)+ 1/8 = 2/8+ 1/8$$

Now add both fractions as normal.

$$2/8+ 1/8 = (2+1)/8 = 3/8 $$

Example 2:

$$1/2+ 1/3$$

Expand the 1st fraction with 3 and the 2nd fraction with 2. This brings both fractions to the main denominator 6.

$$1/2+ 1/3= (1 * 3)/(2 * 3) + (1 * 2)/(3 * 2) = 3/6+ 2/6$$

Now add both fractions as normal.

$$ 3/6+ 2/6= (3+2)/6= 5/6$$

Subtract unlike fractions

Subtracting is the same as adding: First find a common denominator (= main denominator).

Form the main denominator by shortening it

Example 1:

$$3/4- 4/8$$

Shorten the 2nd fraction with 2. This means that both fractions have the common denominator 4.

$$3/4- 4/8= 3/4- (4 : 2)/(8 : 2) = 3/4- 2/4$$

Now subtract both fractions as normal.

$$3/4- 2/4= (3-2)/4 = 1/4 $$

Example 2:

$$6/8 - 3/12$$

Shorten the 1st fraction with 2 and the 2nd fraction with 3. This brings both fractions to the main denominator 4.

$$6/8 - 3/12= (6 : 2)/(8 : 2)- (3 : 3)/(12 : 3)= 3/4 - 1/4$$

Now subtract both fractions as normal.

$$3/4 - 1/4= (3-1)/4= 2/4$$

Form the main denominator by expanding

Example 1:

$$1/4- 1/8$$

Extend the 1st fraction with 2. So both fractions have the common denominator 8.

$$1/4- 1/8= (1 * 2)/(4 * 2)- 1/8 =2/8- 1/8$$

Now subtract both fractions as normal.

$$2/8- 1/8= (2-1)/8 = 1/8 $$

Example 2:

$$1/2 - 1/3$$

Expand the 1st fraction with 3 and the 2nd fraction with 2. This brings both fractions to the main denominator 6.

$$1/2 - 1/3= (1 * 3)/(2 * 3)- (1 * 2)/(3 * 2) =3/6- 2/6$$

Now subtract both fractions as normal.

$$ 3/6- 2/6= (3-2)/6= 1/6$$

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Addition and subtraction of mixed numbers

Mixednumbers add or subtract by first entering fakeFractionsconvert. Then check to see if the fractions have the same or different denominators.

Convert mixed numbers to fractions

A mixed number always consists of a whole number and a fraction.

Example: $$2 3/4$$

You can turn a mixed number into one fakefractureconvert. The fraction is called spurious because the numerator is then greater than the denominator.

You convert the mixed number to an improper fraction by using the wholenumber with the denominatormultiply and then the counter to add. The denominator remains equal.

Example:

$$2 3/4 = (2 *4 + 3)/4= 11/4$$

Convert fractions to mixed numbers

If you have an improper fraction, check how often denominatorinthecounterfits. You get a whole number and a remainder. You write down the remainder as a fraction with the given denominator for the whole number.

Example:

$$17/3$$

The 3 fits into the 17. The remainder is 2. So the mixed number is:

$$5 2/3$$

Calculating with mixed numbers with the same denominators

Example 1:

$$1 2/3 + 2 2/3$$

Convert the mixed numbers to improper fractions.

$$1 2/3 + 2 2/3 = (1 * 3 + 2)/3 + (2 * 3 + 2)/3 = 5/3 + 8/3 $$

Add up the improper fractions the same way you add normal fractions.

$$5/3 + 8/3 = 13/3$$

Convert the improper fraction back to a mixed number.

$$13/3=4 1/3$$

Example 2:

$$3 1/3 - 2 2/3 $$

Convert the mixed numbers to improper fractions.

$$3 1/3 - 2 2/3 = (3 * 3 + 1)/3 - (2 * 3 + 2)/3 = 10/3 - 8/3$$

Subtract the improper fractions the same way you subtract normal fractions.

$$10/3 - 8/3 = 2/3$$

Calculating with mixed numbers with different denominators

Example 1:

$$1 2/3 + 2 2/5$$

Convert the mixed numbers to improper fractions.

$$1 2/3 + 2 2/5 = (1 * 3 + 2)/3 + (2 * 5 + 2)/5 = 5/3 + 12/5$$

Bring the improper fractions down to a common denominator.

$$5/3 + 12/5 = (5 * 5)/(3 * 5)+ (12 * 3)/(5 * 3) = 25/15 + 36/15$$

Add up the improper fractions the same way you add normal fractions.

$$25/15 + 36/15 = 61/15$$

Convert the improper fraction back to a mixed number and abbreviate as much as possible.

$$61/15=4 1/15$$

Example 2:

$$4 2/5 - 2 2/3$$

Convert the mixed numbers to improper fractions.

$$4 2/5 - 2 2/3 = (4 * 5 + 2)/5 - (2 * 3 + 2)/3 = 22/5 - 8/3$$

Bring the improper fractions down to a common denominator.

$$22/5 - 8/3 = (22 * 3)/(5 * 3)- (8 * 5)/(3 * 5) = 66/15 - 40/15$$

Subtract the improper fractions the same way you subtract normal fractions.

$$66/15 - 40/15 = 26/15$$

Convert the improper fraction back to a mixed number.

$$26/15=1 11/15$$

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Fractions in the formula editor

In kapiert.de you enter fractions with the formula editor. That's how it's done: