Egyptian fractions worksheet

Pupils can learn about fractions by doing divisions the Egyptian way!

When all identified resources have been successfully moved, this website will close. We expect this to be in June This unit has a brief look at what is known about Egyptian Fractions. These are unit fractions — fractions whose numerator is one. We look at how fractions can be represented in terms of Egyptian Fractions. Finally we suggest a web site that students might like to use as resource material for a small project. Students also practice adding and subtracting fractions, and looking for patterns.

Egyptian fractions worksheet

One goal of this task is to help students develop comfort and ease with adding fractions with unlike denominators. Another goal is to help them develop fraction number sense by having students decompose fractions. Because the Egyptians represented fractions differently than we do, it can also help students understand that there can be many ways of representing the same number. This helps prepare them for writing algebraic expressions in 6th grade. This task is an instructional task; the teacher may wish to supplement part b of the question in two directions:. In general, however, they used tables in order to break down fractions into sums of unit fractions. One issue which comes up in the solution is that there are apparently many ways to write an Egyptian fraction. This leads to an interesting question: how do you find the "best'' Egyptian fraction representing a given fraction? Here a reasonable interpretation of "best'' would be one which has the smallest number of unit fractions. This problem will be addressed in a second task which falls under the high school algebra standards. Converting to this common denominator we find. Performing subtraction gives. All Egyptian fractions share this same property: there are always endless ways to write an Egyptian fraction.

Egyptian Fractions Age 11 to The ancient Egyptian ideas about fractions are quite surprising.

Or search by topic. Egyptian Fractions printable sheet. Instead they wrote fractions like these as a sum of different unit fractions. You can start by exploring unit fractions at Keep it Simple In this problem we are going to start by considering how the Egyptians might have written fractions with a numerator of 2 i. You might want to check that these are correct. If you can't see how these have been generated, take a look at Keep it Simple.

Or search by topic. This problem follows on from Keep it Simple. You could choose to set the scene briefly by asking students what they know about mathematics throughout history, establishing the idea that some historical maths is distinctly odd to our modern view point. Explain that the ancient Egyptians didn't write fractions with a numerator greater than 1 but expressed every fraction as the sum of different unit fractions. Any that can't be done can be written up on the board for the rest of the class to attempt. Stop the class, and ask them to step back from number crunching and share any discoveries. Listen for any generalisations and record them for discussion. Keep It Simple provides a good introduction to this activity. Students could be directed to The Greedy Algorithm.

Egyptian fractions worksheet

Or search by topic. Egyptian Fractions printable sheet. Instead they wrote fractions like these as a sum of different unit fractions.

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Description of Mathematics. In discussion with the students summarise what has been found in the four lessons so far. Get the students to make a summary of what they have found in this lesson. This problem will be addressed in a second task which falls under the high school algebra standards. In this session we look at how else we could apply the method of finding an Egyptian Fraction representation. This may mean that you will have to carry over the completion of the last exercise until the next lesson. Try some other fractions with a numerator of 2. Can you find a reason why it must work, or a counter-example - the conjecture isn't yet proved. Session 4 In this session we look at how else we could apply the method of finding an Egyptian Fraction representation. How can Egyptian Fractions be applied to other areas of mathematics? Now the method they have been using is called an algorithm. Is there any pattern here? Add and subtract fractions. Creative Commons "Sharealike". Which fractions can be represented by three Egyptian Fractions?

Consider the problem: Share 7 pies equally among 12 kids. Suppose we took this task as a very practical problem. Here are the seven pies:.

And how would you find it? In this session we look at how else we could apply the method of finding an Egyptian Fraction representation. Hold onto this latter idea for a moment and give the students a chance to practice the method that we have shown above. What about four Egyptian Fractions? Find some examples of pairs of numbers such that their sum is a factor of their product. So problem solving is applied to Egyptian Fractions to see what we can find out about them. Site search search. Can you see anything in common between the Egyptian Fraction in the each column? Session 4 In this session we look at how else we could apply the method of finding an Egyptian Fraction representation. Egyptian Fractions printable sheet. Get them to report back to the class.