# Fractions

## Equivalent Fractions

## Video

This video from *Khan Academ*y gives a nice intuition of the idea of equivalent fractions, with pictures.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

## Notes

See pages 4-5 of this guide from MathCentre for more information on equivalent fractions. There are questions at the end of the document with the answers given so you can check your work.

A pdf of this document can be downloaded here.

## Interactive Exercises

The first of these exercises from NUMBAS goes through the method of multiplying above and below to give an equivalent fraction. The second asks you to check some fractions against each other to see which ones are equivalent and which aren't. Lastly, you can test yourself on writing such fractions by filling in missing numerators and denominators on a set of equivalent fractions.

Please click here to view this NUMBAS question in another window.

Please click here to view this NUMBAS question in another window.

Please click here to view this NUMBAS question in another window.

## Simplifying Fractions

## Video

This video from *Khan Academy* shows a few different ways to reduce fractions to their simplest form, along with a visualisation of the idea.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

## Notes

See pages 4-5 of this guide from MathCentre for more information on simplifying fractions, with an example where $\frac{8}{100}$ is reduced to its simplest form.

A pdf of this document can be downloaded here.

## Interactive Exercises

This NUMBAS exercise asks you to take some unreduced fractions and to write them in their simplest form.

Please click here to view this NUMBAS question in another window.

## Adding and Subtracting Fractions

## Videos

This video from *patrickJMT* shows how to find the lowest common denominator, along with how to add and subtract both proper and mixed fractions.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

This video from *Krista King* deals with more examples of adding and subtracting mixed fractions.

Note: All *Krista King* content is available for free at www.youtube.com/c/Integralcalc.

Krista King’s Website: www.kristakingmath.com .

## Notes

See this guide from MathCentre for more information on adding and subtracting fractions. There are questions throughout the document, with answers given on the final page so you can check your work.

A pdf of this document can be downloaded here.

## Interactive Exercises

You can use this exercise from NUMBAS to test what you've learned.

Please click here to view this NUMBAS question in another window.

## Multiplying Fractions and Mixed Numbers

## Videos

This video from *Khan Academy* gives a useful illustrated explanation of the logic behind multiplication of fractions.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

This video from *Khan Academy* shows how to multiply two proper fractions together, as well as how to simplify your result. It also discusses the alternative method of simplifying during calculation.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

## Notes

These notes from MathCentre show with illustrated examples how multiplication of fractions works. See pages 2-5 for the relevant content. You can also test yourself with the exercises given, the answers are at the end of the file so you can check your work.

A pdf of this document can be downloaded here.

## Interactive Exercises

You can test what you’ve learned with this NUMBAS exercise.

Please click here to view this NUMBAS question in another window.

## Dividing Fractions and Mixed Numbers

## Videos

This video from *Khan Academy* gives an intuitive description of how division of fractions works using a representation of fractions on the number line.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

This video from *Krista King* shows you how to divide fractions, and different ways in which the problem is represented. Go to 1:45 for the relevant content.

Note: All *Krista King* content is available for free at www.youtube.com/c/Integralcalc.

Krista King’s Website: www.kristakingmath.com .

This video from *Khan Academy* shows you how to divide mixed fractions by converting them to improper fractions, then how to convert your result back to a mixed fraction. It also discusses simplifying fractions during the calculation.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

## Notes

These notes from MathCentre show with illustrated examples how division of fractions works. See page 5 onwards for the relevant content. You can also test yourself with the exercises given, the answers are at the end of the file so you can check your work.

A pdf of this document can be downloaded here.

## Interactive Exercises

This NUMBAS exercises tests what you’ve learned about dividing fractions, then tests your knowledge of the order of operations with a more complicated example in the final question.

Please click here to view this NUMBAS question in another window.

## Converting between Mixed Numbers and Improper Fractions

## Video

This video from *Krista King* shows how to convert from mixed numbers to improper fractions and vice versa, with a nice visual explanation.

Note: All *Krista King* content is available for free at www.youtube.com/c/Integralcalc.

Krista King’s Website: www.kristakingmath.com .

## Interactive Exercises

This NUMBAS exercise lets you test yourself on converting between mixed and improper fractions.

Please click here to view this NUMBAS question in another window.