# 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 \$\$.

1. 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\$\$

2. 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 \$\$.

3. 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:

1. Convert the mixed number to an improper fraction.
2. Divide as usual. As soon as possible.
3. 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 \$\$.

1. 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\$\$

2. Divide as usual. As soon as possible.

\$\$17/3 : 4 = 17/(3·4) = 17/12\$\$

You cannot cut any further here.

3. 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:

1. Write the improper fraction as a division with \$\$: \$\$. Do the math.
Or: Determine how often the denominator fits into the numerator.
2. 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 \$\$.

1. Convert the mixed number to an improper fraction.

\$\$5 1/4 = 21/4\$\$

2. Divide as usual. As soon as possible.

\$\$21/4 : 3 = 21/(4·3)\$\$

Abbreviation with 3: \$\$ 21 / (4 3) = 7/4 \$\$

3. 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 \$\$