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 1.
Let's practice and see all the possible cases we might encounter:
Join Over 30,000 Students Excelling in Math!
Endless Practice, Expert Guidance - Elevate Your Math Skills Today
Simple Fraction Division Exercises โ> Fraction Divided by Fraction
Here is an exercise:
54โ:23โ=
Solution:
We will change the division operation to a multiplication and swap the numerator and denominator in the second fraction.
We will obtain:
32โร54โ=
We will solve the exercise as it is done in fraction multiplication - Numerator by numerator and denominator by denominator.
We will obtain:
158โ
Now let's move on to a slightly more complex example:
Division of a Fraction by a Mixed Number
64โ:521โ=
Solution:
Upon examining the exercise, we will realize that there is a mixed number -> 521โ
We will convert it to a fraction:
211โ
Pay attention! After obtaining another fraction, the exercise looks as follows:
64โ:211โ=
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:
64โร211โ=
Upon solving we will obtain:
โโ334โ=668โ
Do you know what the answer is?
Division of an integer by a fraction
Here is an exercise:
3:21โ=
Solution:
First, we will convert the whole number to a fraction: 3=13โ
Let's copy the new exercise:
13โ:21โ=
We will operate according to the rules of fraction division, we will obtain:
12โร13โ=
16โ=6
Word Problems with Division of Fractions
Sometimes you will come across word problems from which you must extract the appropriate division exercise.
For example
A seamstress has 30 meters of fabric. The seamstress uses 143โ 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 30 meters of fabric, we must divide 30 (the amount of fabric she has) by the amount of fabric she uses for each shirt -> 143โ
The division exercise will be: 30:143โ=
We will convert the mixed number to a fraction: ย 143โ=47โ
And the whole number 30 to a fraction: 30=130โ
Let's rewrite the exercise:
130โ:47โ=
Let's convert to multiplication and swap between the numerator and the denominator in the second fraction.
We will obtain:
74โร130โ=
Upon solving, we will obtain:
7120โ=1771โ
The seamstress can make 1771โ shirts with the fabric she has.
Examples and exercises with solutions for fraction division
Exercise #1
Solve the following exercise:
41โ:21โ=?
Video Solution
Step-by-Step Solution
When we approach solving such questions, we need to know the rule of dividing fractions,
When we need to divide a fraction by a fraction, we use the method of multiplying by the reciprocal.
This means we flip the numerator and denominator of the second fraction, and then perform fraction multiplication.
Instead of:
1/4 : 1/2 =
We get:
1/4 * 2/1 =
We'll remember that in fraction multiplication we multiply numerator by numerator and denominator by denominator
1*2 / 4*1 =
2/4 =
We'll reduce the fraction and get:
1/2
Answer
Exercise #2
1ร21โ:2
Video Solution
Step-by-Step Solution
According to the rules of the order of operations, we should first solve the exercise from left to right since there are only multiplication and division operations present:
1ร21โ=21โ
21โ:2=41โ
Answer
Exercise #3
43โ43โโ=?
Video Solution
Step-by-Step Solution
We will use the formula:
aaโ=1
Therefore the answer is 1
Answer
Exercise #4
40.5โ=ย ?
Video Solution
Step-by-Step Solution
First let's convert the decimal fraction into a simple fraction:
40.5โ=421โโ
Then we can convert the division operation into a multiplication operation.
Next, we'll multiply 21โ by the reciprocal of 4 as follows:
21โร41โ
Finally, we solve the problem as follows:
2ร41ร1โ=81โ
Answer
Exercise #5
20.5โ=
Video Solution
Step-by-Step Solution
Let's convert the decimal fraction to a simple fraction:
0.5=105โ
We'll write the division problem as follows:
2105โโ
Let's convert the division problem to a multiplication problem.
We'll multiply 105โ by the reciprocal of 2 as follows:
105โร21โ
We'll solve it this way:
10ร25ร1โ=205โ
We'll reduce both the numerator and denominator by 5 and get:
20:55:5โ=41โ
Answer
Do you think you will be able to solve it?