# Equations with Fractions

## Practise solving linear equations that contain fractions in this multi-level, self-marking exercise.

##### Menu  Level 1Level 2Level 3Level 4Level 5Exam-StyleHelpMore Algebra

This is level 5: miscellaneous. Answers that are not whole numbers should be entered as fractions using the '/' symbol. You will be awarded a trophy if you get at least 7 correct and you do this activity online.

 1 $$2y-5=\frac{2y+10}{6}$$ y= 2 $$\frac{x+2}{5}=\frac{x+4}{7}$$ x= 3 $$\frac{x-2}{5}+\frac{x}{3}=\frac{x}{2}$$ x= 4 $$\frac{x-4}{3}=\frac{x-11}{10}$$ x= 5 $$\frac{2x+3}{5}-\frac{4x+9}{11}=0$$ x= 6 $$\frac13 = \frac{2}{x}-\frac16$$ x= 7 $$\frac{4}{x+3}=\frac{5}{3x-5}$$ x= 8 $$\frac{11n+6}{5n-2}=3$$ n= 9 $$\frac{x+6}{10}-\frac{x+1}{4}=2$$ x=
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This is Equations with Fractions level 5. You can also try:
Level 1 Level 2 Level 3 Level 4

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

## Transum.org

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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#### Digital Darts

An online darts game for one or two players requiring skill, strategy and mental arithmetic. It provides an enjoyable way to practise adding and subtracting two and three digit numbers.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

## Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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Scan the QR code below to visit the online version of this activity.

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## Description of Levels

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Equations - Basic equations that do not contain fractions.

Level 1 - Equations with fractions :: one step solutions

Level 2 - Equations with fractions :: two step solutions

Level 3 - Equations with fractions :: three step solutions

Level 4 - Equations with fractions :: four step solutions

Level 5 - Equations with fractions :: miscellaneous

Old Equations - Fractions have been appearing in equations for a very long time.

Algebraic Fractions - A mixture of algebraic fraction calculations and simplifications.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More Algebra including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Example

$$\frac{x-3}{3}=\frac{x+3}{5}$$

Multiply both sides by the LCM of 3 and 5 which is 15.

$$5(x-3)=3(x+3)$$ $$5x-15=3x+9$$

$$5x=3x+24$$
$$2x=24$$ $$x=12$$