A fraction as a divisor

🏆Practice fraction as 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.

Remember the rules:
The fraction line - symbolizes the division operation.
The numerator - symbolizes the number that is being divided (the divided number - what needs to be divided equally among all).
The denominator – symbolizes the number that divides the numerator.

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

\( 5:6= \)

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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=4:2= into a fraction

Solution:
In the numerator - put the number being divided: 44
Let's not forget the fraction line that will mark the division operation.
In the denominator - put the number that divides the numerator: 22
We get: 424 \over 2
Obviously, we can simplify it and we get 22 (it was asked how many times the denominator fits into the numerator)

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

Solution:
In the numerator - put the number being divided: 1010
Let's not forget the fraction line that will mark the division operation.
In the denominator -> put the number that divides the numerator-> 33
We get: 10310 \over 3
We can convert it into a mixed fraction and we get 3133 \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 33 fits into 1010: 33 times - this will be the number of whole numbers.
The denominator - will remain the same: 33
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−(3×3)=110-(3 \times 3)=1
The final result: 11 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 66 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=26:3=2
We could write the exercise as a fraction as we learned before and get:
63=2\frac{6}{3}=2
each one will get 22 cookies.


Another question

Bernard, Oscar, Nicholas, Ernest, and Gabriel are playing in the courtyard.
Suddenly, the teacher brings them 66 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=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 65=\frac{6}{5}=
Now, we will convert the similar fraction into a mixed number and get 1151 \frac{1}{5}.
Each child received one whole pizza and another fifth of a pizza. Or in summary 1151 \frac{1}{5} pizzas.


Another exercise

33 Good friends celebrated a birthday in the garden.
On the table –> 44 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: 44 Cakes.
In the denominator - the number by which the cakes are divided: 33 -> the number of children celebrating.
We will obtain:
43\frac{4}{3}
(The fraction expresses the division exercise for us 4:3=4:3=)
We will convert it into a mixed number and obtain: 1131 \frac{1}{3}
Each child received 1131 \frac{1}{3} cake.

Bonus section

What would happen if there were only 22 cakes on the table? How much would each child get then?

Solution:
If there were 22 cakes on the table we would get:
232 \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 232 \over 3 cake.


Examples and exercises with solutions of fraction as divisor

Exercise #1

My numerator is 4 and my denominator is 8.

Which am I?

Video Solution

Step-by-Step Solution

Recall that the numerator is the top number, and the denominator is the bottom number.

Now let's represent it accordingly:

48 \frac{4}{8}

Let's divide the numerator and denominator by 4:

4:48:4=12 \frac{4:4}{8:4}=\frac{1}{2}

Answer

12 \frac{1}{2}

Exercise #2

What fraction results from dividing 8 by 16?

Video Solution

Step-by-Step Solution

Write the exercise translation:

8:16 8:16

Now write it in the form of a simple fraction, remembering that the numerator is above and the denominator is below:

816 \frac{8}{16}

Divide the numerator and denominator by the number that divides both of them, in this case the number is 8:

8:816:8=12 \frac{8:8}{16:8}=\frac{1}{2}

Answer

12 \frac{1}{2}

Exercise #3

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

5:6= 5:6=

Video Solution

Answer

Yes

Exercise #4

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

7:11 7:11

Video Solution

Answer

Yes

Exercise #5

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

11:8 11:8

Video Solution

Answer

No.

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