Transum Software

Fractionagons

Calculate the missing fractions in these partly completed arithmagon puzzles.

Menu Arithmagons Level 1 Level 2 Level 3 Level 4 Level 5 Help More Fractions

Complete the fractionagons so that the fractions in the rectangles are the sums of the fractions at the vertices of the triangles. Use the forward slash / to type a fraction. Give answers in their lowest terms.

\(\frac{1}{8}\)

\(\frac{3}{8}\)

\(\frac{1}{4}\)

Correct Wrong

Correct Wrong

Correct Wrong

+

\(\frac{3}{10}\)

\(\frac{1}{2}\)

\(\frac{1}{10}\)

Correct Wrong

Correct Wrong

Correct Wrong

+

\(\frac{3}{7}\)

Correct Wrong

\(\frac{5}{14}\)

\(\frac{4}{7}\)

Correct Wrong

Correct Wrong

+

\(\frac{1}{3}\)

\(\frac{4}{9}\)

Correct Wrong

Correct Wrong

\(\frac{2}{3}\)

Correct Wrong

+

\(\frac{1}{4}\)

Correct Wrong

Correct Wrong

\(\frac{3}{4}\)

Correct Wrong

\(\frac{3}{8}\)

+

Correct Wrong

Correct Wrong

\(\frac{5}{12}\)

\(\frac{1}{2}\)

\(\frac{7}{12}\)

Correct Wrong

+

Check

This is Fractionagons level 1. You can also try:
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.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 1 August 'Starter of the Day' page by Peter Wright, St Joseph's College:

"Love using the Starter of the Day activities to get the students into Maths mode at the beginning of a lesson. Lots of interesting discussions and questions have arisen out of the activities.
Thanks for such a great resource!"

Comment recorded on the 28 May 'Starter of the Day' page by L Smith, Colwyn Bay:

"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

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Featured Activity

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Playing Card Maths

Imagine you are on a desert island with nothing but a pack of playing cards. Do you have to stop learning mathematics? Of course not! Here are some great ideas for teachers, parents and tutors.

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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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Saturday, June 18, 2022

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© Transum Mathematics :: This activity can be found online at:
www.Transum.org/go/?Num=890

Description of Levels

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Arithmagons - The same sort of puzzle but with numbers not algebra.

Level 1 - Sums of simple fractions

Level 2 - Sums of fractions where one denominator is not a multiple of the other.

Level 3 - Sums of mixed numbers.

Level 4 - Multiplication of fractions.

Level 5 - Multiplication of mixed numbers.

Algebragons - Different topic, same structure.

More Fractions 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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Fractions Video

Mathematical Notation

Use the forward slash / to type a fraction then the right arrow or tab key to end the fraction.

For example: Type 1/2 to get ½.

Fractions should be given in their lowest terms.

All answers are positive.

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.

Log in Sign up

Here are some suggestions for how you may solve the puzzles in which only the three values in the rectangles are given (the last question in levels three and above):

For novice learners

  1. Guess a value for the top circle
  2. From that calculate the values that would be in the bottom two circles
  3. Do these two values sum to the bottom rectangle? If so finish.
  4. If not is their sum too high or too low? Adjust the top circle value accordingly and go back to (2)

Replace 'sum' with 'product' if the operation is multiplication.

For advanced learners

  1. Let x stand for the top circle value
  2. From that find expressions for the bottom two circles
  3. Make an equation from the bottom two circles and the bottom rectangle
  4. Solve that equation.

A great 'trick'

This was found by Ann Roberts, a Transum subscriber, who wrote with this method of solving an arithmagon with 18, 15 and 11 in the rectangles. It also works for fractions.

  1. Add the numbers in the rectangles: 18 + 15 + 11 = 44. This is the same as adding the numbers in the blank circles twice.
  2. Divide this sum by two: 44 ÷ 2 = 22. This is now the same as adding the numbers in the blank circles once.
  3. Finally: 15 is the sum of the bottom white circles so 15 + top white circle = 22

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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