# What is 3 1 6 3 7

### 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 **different****Denominators** 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 denominator****found** you can then use the fractions **all****normal****add**.

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. So 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

**Mixed****numbers** add or subtract by first converting them into **fake****Fractions****convert**. 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 **fake****fracture****convert**. 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 **whole****number** with the **denominator****multiply** 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 **denominator****in****the****counter****fits**. 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.

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

*kapiert.de*can do more:

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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:

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