# What is 1 3 divided by 3

### Divide fractions by a natural number

Not only can you multiply fractions, you can also divide them. That's when you have to share your pieces of cake with others ... :-)

Mathematically, you then divide a fraction by a natural number.

Natural numbers ($$ NN $$) are 0, 1, 2, 3, ... These are the numbers you use to count: candy bars, holidays, videos, etc.

To divide fractions by a natural number:

As a summary:

You divide fractions by a natural number by using the **denominator** with the **natural number** multiply and keep the counter.

Example:

$$3/8 : 5 = 3/(8·5) =$$ $$3/40$$

### Shortening makes it easier

Often you can shorten it. When dividing, there are 2 ways when you cut.

Example: $$ 4/7: 2 $$

**Possibility Number 1**:

Multiply the denominator (in this exercise: $$ 7 $$) by the natural number (in this exercise: $$ 2 $$).

$$4/7 : 2 = 4/(7·2)$$

You can shorten it here:

In the numerator is the 4, which you can divide by 2; in the denominator is the 2, which you can also divide by 2.

$$4/7 : 2=4/(7·2) =$$ **$$2/7$$****Possibility 2**:

You first calculate the result and then shorten it.

$$4/7 : 2 = 4/(7·2) = 4/14$$

You see because of the divisibility rules that 4 and 14 are divisible by 2. You cut with 2 and also get **$$2/7$$**.

$$4/7 : 2 = 4/(7·2) = 4/14=2/7$$

You can choose the path that you prefer. But shortening is a must! :)

**Shorten** means that you divide a number from the numerator and a number from the denominator by the same number.

### Divide mixed numbers

**Example 1:** Breakage as a result

Calculate $$ 1 3/5: 2 $$.

- Convert the mixed number to an improper fraction.

That's how it's done:

Multiply the whole (here: $$ 1 $$) by the denominator (here: $$ 5 $$): $$ 1 · 5 = $$**$$5$$**

Add the previous counter (here: $$ 3 $$): $$ 5 + 3 = 8 $$

Keep the denominator (here: $$ 5 $$).

$$1 3/5 =8/5$$ - Divide as usual. As soon as possible.

Multiply the denominator (here: $$ 5 $$) by the natural number (here: $$ 2 $$)

$$8/5 : 2 = 8/(5·2) $$

Abbreviation with 2: The result is $$ 4/5 $$. - If possible, convert the result back to a mixed number.

$$ 4/5 $$ is a real fraction. You can't convert that into a mixed number.

Everything in one calculation: $$ 1 3/5: 2 = 8/5: 2 = 8 / (5 · 2) = 4/5 $$

To divide a mixed number by a natural number:

- Convert the mixed number to an improper fraction.
- Divide as usual. As soon as possible.
- If possible, convert the result back to a mixed number.

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### Divide mixed numbers

**Example 2:** Mixed number as a result

Calculate: $$ 5 2/3: 4 $$.

Convert the mixed number to an improper fraction.

That's how it's done:

Multiply the whole (5) by the denominator (3): $$ 5 · 3 = 15 $$.

Add the previous numerator (2), i.e. $$ 15 + 2 = 17 $$.

Keep the denominator (3).

$$5 2/3 =17/3$$Divide as usual. As soon as possible.

$$17/3 : 4 = 17/(3·4) = 17/12$$

You cannot cut any further here.- If possible, convert the result back to a mixed number.

$$17/12 =1 5/12$$

All in one calculation: $$ 5 2/3: 4 = 17 / (3 4) = 17/12 = 1 5/12 $$

To convert a fraction to a mixed number:

- Write the improper fraction as a division with $$: $$. Do the math.

Or: Determine how often the denominator fits into the numerator. - Write the rest as a real fraction.

### All good things come in threes

**Example 3:** With abbreviations and mixed numbers as the result

Calculate $$ 5 1/4: 3 $$.

Convert the mixed number to an improper fraction.

$$5 1/4 = 21/4$$Divide as usual. As soon as possible.

$$21/4 : 3 = 21/(4·3)$$

Abbreviation with 3: $$ 21 / (4 3) = 7/4 $$- If possible, convert the result back to a mixed number.

$$7/4 = 1 3/4$$

Everything in one calculation: $$ 5 1/4: 3 = 21 / (4 3) = 7/4 = 1 3/4 $$

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