Calculate fractions Exercises and worksheets online

Calculating and determining fractions - the introduction to fractions

Calculate fractions and determine fractions

We start with fractions. You can find many worksheets online. On this page you can:

recognise individual fractions
colour in many fractions
or colour fractions
and also represent fractions

To do this, you can edit many worksheets online or download them as a PDF and edit them on the tablet computer with a pen or print them out and edit them classically.

The Calculate Fractions exercises are usually calculated in 5th grade or 6th grade .

Fractions explained simply

You have probably eaten a slice of pizza or a slice of cake. The slice of pizza was probably one of maybe 4 or 8 pieces in total. So you have already got to know fractions of a whole.

A fraction is always a part of a whole. E.g. one half = 1 piece of a total of 2. One third = 1 piece of three. Three quarters are three pieces of a total of 4, etc.

How do you write a fraction?

Drei Viertel sind 3 von 4. Man schreibt das so: \(\frac{3}{4}\)

The number of parts that are counted is written on the fraction bar. Therefore, the expression on the fraction bar is called the numerator!
Below the fraction bar are the total parts that are counted. Therefore, the expression below the fraction bar is called the denominator!

Ein Stück Pizza: \(\frac{1}{4}\) und \(\frac{1}{8}\)

\(\frac{1}{4}\Rightarrow numerator = 1, denominator = 4\)

\(\frac{1}{8}\Rightarrow numerator = 1, denominator = 8\)

Fraction =	numerator

	Denominator

Examples for fractions

One third = one piece out of a total of three pieces = \(\frac{1}{3}\)

Four fifths = four parts of five parts = \(\frac{4}{5}\)

One twelfth = one part of twelve parts= \(\frac{1}{12}\)

One eighth = one part of eight parts in total = \(\frac{1}{8}\)

How to calculate a fraction of a size

You divide the total by the number of parts you divide into, i.e. the denominator. Then you multiply the result by the number of parts you are looking at or have, i.e. the numerator.

Examples - this is how you calculate:

\(\frac{3}{12}\) of \(24\)

Divide 24 (the whole) by 12 (the denominator of the fraction), the result is 2:

\(24:12 = 2 \)

Now multiply the result by the numerator of the fraction: 2 times 3 equals 6!

\(2 \cdot 3 = 6 \)

Three twelfths of 24 are therefore 6!

\( \frac{3}{12} \cdot 24 = 6 \)

Maybe you'll understand it better that way:

An example with sizes:

Theorem - How to calculate fractions

When determining a fraction, you not only need to know how many parts you have - this is the numerator of the fraction -, but also how many parts there are in total - this is the denominator of a fraction.

Calculate fractions Exercise - recognise fractions online

Fractions Exercise 1

Draw the correct solution to each fraction!

Exercise 2

Draw the correct solution to each fraction!

Recognise fractions - worksheets for the two online exercises

These worksheets are in German!

Worksheets for the online exercise 📝

Exercise 1 - 1 page for the online task "Recognise fractions" (PDF 🇩🇪)

Exercise 2 - 1 page for the online task "Recognise fractions" (PDF 🇩🇪)

Solutions 👍

📝 Solution Worksheet 1 (PDF, )

📝 Solution Worksheet 2 (PDF, )

online exercise - colouring fractions

Identify fractions and then colour them in. This is difficult to do on the web page. Especially because there are many different solutions. You can still do this exercise directly on the tablet.

Download the fraction worksheets as a PDF to your PC or tablet!

On the tablet, you can solve the task with the pen by colouring in the matching squares.
On the PC, you can print out the sheet and colour it in with a pen.

You can access the solutions via the QR code on the sheet!

Exercise 1

Colouring fractions on paper or in the PDF document online

📝 Worksheet 1 as PDF

Exercise 2

Colouring fractions on paper or in the PDF document online

📝 Worksheet 2 as PDF

Calculate fractions of sizes

Here you can calculate fractions of sizes online.

Times - fractions in a subunit
Fractions of currencies
Convertlengths - fractions

Alternatively, you can find a printable page under each exercise. You can also fill in the PDF documents on a tablet computer and send them to your teacher for checking. You can access the solutions via the QR code on the PDF sheets!

1. exercise

Calculate fractions of times

Exercise 2

Calculate fractions of currencies (money)

Exercise 3

Calculate fractions of lengths

4. exercise

Calculate fractions of weights (masses)

Exercise 5

Simple word problems - If possible, solve the word problems in your head and enter the results in the boxes!

Exercise 6

Calculate with fractions of quantities! Enter the intermediate results and solutions in the boxes!

Exercise 6 - Practical Task

Fold a sheet of paper - and we get fractions

Take a sheet of paper, preferably in DIN A4 format.
Fold the sheet so that the following equal areas are created:
- 3 parts
- 4 parts
- 8 parts
- 16 parts
Are there other ways to divide the sheet neatly into other fractions?

How to learn fractions with these pages

Fractions Exercises -Use worksheets as PDF.

Download and print - work classically and check online.

With new tablet computers with new operating systems, you can already write in the PDF document. Try to click on the file on your tablet and open it directly.

GoodNotes

Import as PDF and work online - that's how it works.

Unfortunately, we cannot offer you a real GoodNotes document for download here. Therefore you have to use the PDF document and import it into GoodNotes. Go to our tutorial to read the detailed instructions!

OneNote

Import as PDF and work online - this is how it works!

Unfortunately, we cannot offer you a real OneNote document for download here. Therefore you have to import the PDF document into oneNote. Go to our tutorial to read the detailed instructions!