## A fraction as a divisor

A fraction is actually a division exercise! A result obtained from a division exercise is called a quotient and if it is incomplete, it will appear in the form of a fraction.

It is important to remember the rules:

**The fraction line** - symbolizes the division operation.

**The numerator** - symbolizes the number that is being divided (the divided number) - what must be equally divided among all (for example, cakes, pizzas, etc.)

**The denominator** - symbolizes the number that divides the numerator. (for example, the number of people that should be divided among)

### How do we go from a division exercise to a fraction?

A division exercise can be converted into a fraction easily and quickly according to the above rules.

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### Let's look at an exercise

Convert the division exercise $4:2=$ into a fraction

**Solution:**

In the numerator - put the number being divided: $4$

Let's not forget the fraction line that will mark the division operation.

In the denominator - put the number that divides the numerator: $2$

We get: $4 \over 2$

Obviously, we can simplify it and we get $2$ (it was asked how many times the denominator fits into the numerator)

**Another exercise:**

Convert the division exercise $10:3=$ into a fraction

**Solution:**

In the numerator - put the number being divided: $10$

Let's not forget the fraction line that will mark the division operation.

In the denominator -> put the number that divides the numerator-> $3$

We get: $10 \over 3$

We can convert it into a mixed fraction and we get $3 \frac{1}{3}$

### Reminder: How to convert an equivalent fraction into a mixed number?

We will be asked how many times the denominator fits into the numerator without remainder

in our exercise $3$ fits into $10$: $3$ times - this will be the number of whole numbers.

The denominator - will remain the same: $3$

In the numerator - we will subtract the original numerator minus the result of the product between the number of whole numbers we obtained multiplied by the denominator. That is: $10-(3 \times 3)=1$

The final result: $1$ will appear in the numerator.

Do you know what the answer is?

### Now, let's see while we practice how to view the fraction as a division quotient.

#### Here is a question

In the kitchen, there are $6$ delicious chocolate cookies.

Roberto, Mariana, and Lionel want to share them equally.

How many cookies will each one get?

**Solution:**

To find out how many cookies each one will get, we will have to do a division exercise.

We will write down the number of cookies divided by the number of people and get the result.

That is:

$6:3=2$

We could write the exercise as a fraction as we learned before and get:

$\frac{6}{3}=2$

each one will get $2$ cookies.

#### Another question

Bernard, Oscar, Nicholas, Ernest, and Gabriel are playing in the courtyard.

Suddenly, the teacher brings them $6$ pizzas and asks them to share equally.

How many pizzas will each child receive?

**Solution:**

To answer, we will need to write a division exercise: the number of pizzas to be divided, divided by the number of children in the courtyard.

That is:

$6:5=$

Pay attention! It's time to turn the exercise into a fraction to know exactly how many pizzas each child received.

We will invert and get $\frac{6}{5}=$

Now, we will convert the similar fraction into a mixed number and get $1 \frac{1}{5}$.

Each child received one whole pizza and another fifth of a pizza. Or in summary $1 \frac{1}{5}$ pizzas.

#### Another exercise

$3$ Good friends celebrated a birthday in the garden.

On the table –> $4$ Cakes.

The children were asked to distribute the cakes equally.

**Solution:**

This time, we will write the division exercise directly as a fraction to save us a step.

In the numerator - the number that needs to be divided: $4$ Cakes.

In the denominator - the number by which the cakes are divided: $3$ -> the number of children celebrating.

** We will obtain:**

$\frac{4}{3}$

(The fraction expresses the division exercise for us $4:3=$)

We will convert it into a mixed number and obtain: $1 \frac{1}{3}$

Each child received $1 \frac{1}{3}$ cake.

##### Bonus section

What would happen if there were only $2$ cakes on the table? How much would each child get then?

**Solution:**

If there were $2$ cakes on the table we would get:

$2 \over 3$

It is impossible to reduce it or convert it into a mixed number and that is exactly the answer.

All the children would have received $2 \over 3$ cake.

## Examples and exercises with solutions of fraction as divisor

### Exercise #1

Without calculating, determine whether the quotient in the division exercise is smaller than 1 or not:

$2:1$

### Video Solution

### Step-by-Step Solution

We know that every fraction 1 equals the number itself.

We also know that 2 is greater than 1.

Similarly, if we convert the expression to a fraction:

2/1

We can see that the numerator is greater than the denominator. As long as the numerator is greater than the denominator, the number is greater than 1.

### Answer

### Exercise #2

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$5:6=$

### Video Solution

### Step-by-Step Solution

Note that the numerator is smaller than the denominator:

5 < 6

As a result, we can claim that:

\frac{5}{6} < 1

Therefore, the quotient in the division problem is indeed less than 1

### Answer

### Exercise #3

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$7:11$

### Video Solution

### Step-by-Step Solution

Note that the numerator is smaller than the denominator:

7 < 11

As a result, we can claim that:

\frac{7}{11}<1

Therefore, the quotient in the division problem is indeed less than 1

### Answer

### Exercise #4

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$1:2=$

### Video Solution

### Step-by-Step Solution

Note that the numerator is smaller than the denominator:

1 < 2

As a result, we can claim that:

\frac{1}{2}<1

Therefore, the fraction in the division problem is indeed less than 1

### Answer

### Exercise #5

Without calculating, determine whether the quotient in the following division is less than 1 or not:

$11:8$

### Video Solution

### Step-by-Step Solution

Note that the numerator is smaller than the denominator:

11 > 8

As a result, we can claim that:

\frac{11}{8} > 1

Therefore, the quotient in the division problem is not less than 1

### Answer