Equations with Fractions

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

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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.

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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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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.

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

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