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Equations with Fractions

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

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This is level 6: old textbook challenge. 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 10 correct and you do this activity online.

The following questions were written by a person who was born in 1859. His name was Florian Cajori and the questions come from the faded pages of a textbook he published. This exercise makes a nice bonus challenge if you have already managed to complete the previous levels.

Exercise from an old textbook
1

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\(x\)= Correct Wrong

2

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\(y\)= Correct Wrong

3

$$$$

\(v\)= Correct Wrong

4

$$$$

\(n\)= Correct Wrong

5

$$$$

\(r\)= Correct Wrong

6

$$$$

\(x\)= Correct Wrong

7

$$$$

\(r\)= Correct Wrong

8

$$$$

\(y\)= Correct Wrong

9

$$$$

\(y\)= Correct Wrong

10

$$$$

\(t\)= Correct Wrong

11

$$$$

\(x\)= Correct Wrong

12

$$$$

\(s\)= Correct Wrong

13

$$$$

\(t\)= Correct Wrong

14

$$$$

\(s\)= Correct Wrong

15

$$$$

\(x\)= Correct Wrong

16

$$$$

\(x\)= Correct Wrong

17

$$$$

\(w\)= Correct Wrong

18

$$$$

\(z\)= Correct Wrong

Check

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

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.

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

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https://www.Transum.org/go/?Num=879

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.

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Video

Example

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

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

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

Add 15 to both sides

$$5x=3x+24$$

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.

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.

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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.

MathQuill Animation

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