Dividing fractions - how do you divide fractions?
How do you divide fractions?
Divide fractions - how to divide fractions?
To do this, we first divide fractions by whole numbers. That is still simple.
Then we divide two fractions. Dividing two fractions is already getting more difficult. But the illustration helps you to understand it better.
Once we have understood the rules of arithmetic, we practise larger arithmetic expressions with fractions, brackets, plus, minus and multiplication signs.
Dividing fractions with whole numbers
Divide fractions by an integer - Rule | Definition
You divide a fraction by a whole number by multiplying the fraction by the reciprocal of the number. To do this, we write the divisor as:
\( \frac{1}{number} \)
If we swap the numerator of a fraction with the denominator of the fraction, the new number is called the reciprocal of the fraction.
The divisor (the number by which we divide) is therefore always multiplied by the denominator. We therefore divide the fraction further!
Example:
\( \frac{3}{4} : 3 = \frac{3}{4} \cdot \frac{1}{3} = \frac{3 \cdot 1}{4 \cdot 3} = \frac{1}{4} \)
divide two fractions
Dividing two fractions - Rule | Definition
In order to understand division correctly, we need to be clear about what division means: dividing by a number means we solve the problem: how many times does the divisor fit into the number.
12 : 2 means: How often does 2 fit into 12. The answer is the solution of the division:
12 : 2 = 6
This is exactly how we divide 2 fractions.
How many times does \( \frac{1}{8} \) fit into \( \frac{3}{4} \)?
The answer is: 6 times. Maths Fritz explains it to you in the picture next to it.
Divide fractions rule:
Two fractions are divided by multiplying the first fraction (dividend) by the reciprocal of the second fraction (divisor).
How often does the divisor fit into the first fraction?
The online exercises will be created very soon!
Dividing fractions tasks - online and as PDF
Dividing fractions Examples and tasks PDF
Two pages of worksheets for the following online exercises. Simply print them out and practise on paper or fill them in on your tablet with a pen.
As a test or class work for an easy introduction to fractions! Are you fit?
Multiplication Fractions with Fractions
The online exercises follow!
to print out
The online exercises will be created very soon!
Here you can still see the exercises on the page Adding and subtracting fractions!
Fractions Exercises - Exercise (1) Fractions with equal denominators
Divide fractions
Enter only the numerator of the fraction in the empty field as the result!
Fractions Division Tasks - Exercise (2)
Enter only the numerator of the fraction in the empty field as the result!
Dividing fractions exercises - mixed tasks
Remember: Multiply by the reciprocal
of the fraction!
So you can add and subtract fractions if they do NOT have the same denominator (are not of the same name).
Fractions with different denominators can only be added or subtracted when the denominators are the same. To do this, you have to reduce and/or expand the fractions until they have the same denominator.
The common denominator (main denominator) results from the smallest common multiple of all denominators involved!
Examples:
(1) \(\frac{1}{3} +\frac{1}{4} = \frac{1\cdot 4}{3 \cdot 4} + \frac{1 \cdot 3}{4 \cdot 3} = \frac{4}{12} +\frac{3}{12} = \frac{7}{12} \)
(2) \(\frac{2}{9} +\frac{1}{6} = \frac{2\cdot 2}{9 \cdot 2} + \frac{1 \cdot 3}{6 \cdot 3} = \frac{4}{18} +\frac{3}{18} = \frac{7}{18} \)
You can also find more theory about fractions on Wikipedia!
Normally you do this in fractions grade 5.
Exercise (2) - Find the same denominator of 2 fractions and then add the fractions.
Add the missing numbers to the numerator of the fraction. Look carefully. The common denominator of the fractions is already there!
Exercise (3) - Write down the task and then work it out!
Add the missing numbers to the numerator and denominator of the fraction.
printable
Divide fractions worksheets
The tasks from the exercises type (III) as PDF for printing:
Exercise (4) - Dividing fractions
These fractions tasks with solutions tasks are only available as worksheets PDF for printing. Here is an example of how the tasks look:
Fractions Colouring
to print out
Crossword - Division of fractions
Divide fractions - The crossword topic!
