# Fractionagons

## Calculate the missing fractions in these partly completed arithmagon puzzles.

##### MenuArithmagonsLevel 1Level 2Level 3Level 4Level 5HelpMore 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.

 $$\frac{1}{2}$$ $$\frac{1}{3}$$ $$\frac{1}{4}$$ + $$\frac{1}{3}$$ $$\frac{2}{5}$$ $$\frac{3}{7}$$ + $$\frac{1}{9}$$ $$\frac{2}{5}$$ $$\frac{5}{18}$$ + $$\frac{3}{8}$$ $$\frac{3}{10}$$ $$\frac{7}{15}$$ + $$\frac{5}{12}$$ $$\frac{19}{24}$$ $$\frac{19}{24}$$ + $$\frac{1}{3}$$ $$\frac{42}{55}$$ $$\frac{11}{15}$$ +
Check

This is Fractionagons level 2. You can also try:
Level 1 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.

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Saturday, June 18, 2022

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© Transum Mathematics :: This activity can be found online at:
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## 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.

## 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.

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.

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.

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

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