Division of Fractions

πŸ†Practice division of fractions

Dividing fractions is easy

We will solve fraction divisions in the following way:
First step
Let's look at the exercise.

  • If there is any mixed number - we will convert it into a fraction
  • If there is any whole number - we will convert it into a fraction

Second step
We will convert the division into multiplication
Also, we will swap the numerator and denominator in the second fraction.
Third step
We will solve by multiplying numerator by numerator and denominator by denominator.

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Test yourself on division of fractions!

einstein

Complete the following exercise:

\( \frac{1}{2}:\frac{1}{2}=\text{?} \)

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How to Divide Fractions

Fraction division is a pleasant and simple topic, especially if you already know how to solve fraction multiplications.
In this article, you will learn how to operate to divide fractions and discover how easy it is to do it with this method.

We will solve fraction divisions in the following way:
First step
Let's look at the exercise.

  • In case there is any mixed number - we will convert it into a fraction
  • In case there is any whole number - we will convert it into a fraction

Second step
We will convert the division into multiplication
Also, we will swap between the numerator and the denominator in the second fraction.
Third step
We will solve by multiplying numerator by numerator and denominator by denominator.


It's worth remembering

How are fractions multiplied?
Numerator by numerator and denominator by denominator.


How is a mixed number converted to a fraction?
Multiply the denominator by the whole number and add the numerator.
Write the result in the numerator. The denominator remains unchanged.


How is a whole number converted to a fraction?
Write the whole number in the numerator
and in the denominator write 11.


Let's practice and see all the possible cases we might encounter:

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Simple Fraction Division Exercises –> Fraction Divided by Fraction

Here is an exercise:

45:32=\frac{4}{5}:\frac{3}{2}=

Solution:
We will change the division operation to a multiplication and swap the numerator and denominator in the second fraction.

We will obtain:

23Γ—45=\frac{2}{3} \times \frac{4}{5}=

We will solve the exercise as it is done in fraction multiplication - Numerator by numerator and denominator by denominator.

We will obtain:
8158 \over 15


Now let's move on to a slightly more complex example:

Division of a Fraction by a Mixed Number

46:512=\frac{4}{6}:5\frac{1}{2}=

Solution:
Upon examining the exercise, we will realize that there is a mixed number -> 5125\frac{1}{2}
We will convert it to a fraction:
112\frac{11}{2}

Pay attention! After obtaining another fraction, the exercise looks as follows:
46:112=\frac{4}{6}:\frac{11}{2}=

Clearly, it remains a division exercise, now we must operate as is done to solve a division exercise:
We will change the division operation to multiplication and swap between the numerator and the denominator in the second fraction.
We will obtain:

46Γ—112=\frac{4}{6} \times \frac{11}{2}=

Upon solving we will obtain:

​​433=866​​\frac{4}{33}=\frac{8}{66}


Do you know what the answer is?

Division of an integer by a fraction

Here is an exercise:
3:12=3:\frac{1}{2}=

Solution:
First, we will convert the whole number to a fraction: 3=313=\frac{3}{1}
Let's copy the new exercise:
31:12=\frac{3}{1}:\frac{1}{2}=
We will operate according to the rules of fraction division, we will obtain:
21Γ—31=\frac{2}{1} \times \frac{3}{1}=
61=6\frac{6}{1}=6


Word Problems with Division of Fractions

Sometimes you will come across word problems from which you must extract the appropriate division exercise.

Check your understanding

For example

A seamstress has 3030 meters of fabric. The seamstress uses 1341\frac{3}{4} m. to sew each shirt.

How many shirts can the seamstress make with the amount of fabric she has?
The solution may include a number that is not an integer.

Solution:
To find out how many shirts the seamstress can make with 3030 meters of fabric, we must divide 3030 (the amount of fabric she has) by the amount of fabric she uses for each shirt -> 1341\frac{3}{4}
The division exercise will be: 30:134=30:1\frac{3}{4}=

We will convert the mixed number to a fraction: Β 134=741\frac{3}{4}=\frac{7}{4}
And the whole number 3030 to a fraction: 30=30130=\frac{30}{1}
Let's rewrite the exercise:
301:74=\frac{30}{1}:\frac{7}{4}=
Let's convert to multiplication and swap between the numerator and the denominator in the second fraction.
We will obtain:
47Γ—301=\frac{4}{7} \times \frac{30}{1}=
Upon solving, we will obtain:
1207=1717\frac{120}{7}=17\frac{1}{7}
The seamstress can make 171717\frac{1}{7} shirts with the fabric she has.


Do you think you will be able to solve it?
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