# Equations with Fractions

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

##### MenuLevel 1Level 2Level 3Level 4Level 5Level 6ExamHelpMore

This is level 1: one step solutions. 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 $$\frac16 x=12$$ $$x$$= 2 $$\frac{y}{9}=11$$ $$y$$= 3 $$8 = \frac{w}{8}$$ $$w$$= 4 $$\frac{4}{9} + a= \frac{8}{9}$$ $$a$$= 5 $$b - \frac{3}{7} = \frac{2}{7}$$ $$b$$= 6 $$\frac{4}{9} = c - \frac{4}{9}$$ $$c$$= 7 $$\frac{m}{3} = \frac{3}{10}$$ $$m$$= 8 $$\frac{1}{8} = \frac{n}{3}$$ $$n$$= 9 $$s - \frac{1}{4} = \frac{2}{3}$$ $$s$$=
Check

This is Equations with Fractions level 1. You can also try:
Level 2 Level 3 Level 4 Level 5 Level 6

## 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.

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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.

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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.

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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

Level 6 - Equations with fractions :: old textbook challenge

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.

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

$$5x=3x+24$$

Subtract 3x from both sides

$$2x=24$$ $$x=12$$

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

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### Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

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