Egyptian Fractions: Ancient Egyptians used unit fractions, such as and to represent all fractions. For example, they might write the number as+ We often think of as + , but the ancient Egyptians would not write it this way because they didn't use the same unit fraction twice. a. Write the Egyptian fraction++as a single fraction. b. Write the fractions and as Egyptian fractions. c. Develop a process for finding an Egyptian fraction if you are given a fraction with a numerator greater than 1. Explain why your process will work for any such fraction. Give at least two examples of applying your process, one with a proper fraction and one with an improper fraction, using different values from any that have been used earlier in the problem. d. Does each fraction have only one way to write it as an Egyptian fraction? If so, explain why. If not, provide at least one example of a fraction that you can write as an Egyptian fraction in more than one way. e. A teacher took her class on a field trip and brought 5 pans of brownies. She wants to split the brownies evenly among the 9 groups of students on the field trip. She would like to find a simple way to split up all the brownies so that each group has an equal share without using a calculator (as she left it at school). Explain how you can use Egyptian fractions to help the teacher find a process to evenly distribute the brownies to the groups. f. Use Egyptian fractions to determine which is larger, 5/9 or 9/14. Explain. g. Describe at least one advantage of Egyptian fractions when compared to our current method of writing fractions. Then describe at least one disadvantage of the Egyptian fraction form when compared to our current form.
Egyptian Fractions: Ancient Egyptians used unit fractions, such as and to represent all fractions. For example, they might write the number as+ We often think of as + , but the ancient Egyptians would not write it this way because they didn't use the same unit fraction twice. a. Write the Egyptian fraction++as a single fraction. b. Write the fractions and as Egyptian fractions. c. Develop a process for finding an Egyptian fraction if you are given a fraction with a numerator greater than 1. Explain why your process will work for any such fraction. Give at least two examples of applying your process, one with a proper fraction and one with an improper fraction, using different values from any that have been used earlier in the problem. d. Does each fraction have only one way to write it as an Egyptian fraction? If so, explain why. If not, provide at least one example of a fraction that you can write as an Egyptian fraction in more than one way. e. A teacher took her class on a field trip and brought 5 pans of brownies. She wants to split the brownies evenly among the 9 groups of students on the field trip. She would like to find a simple way to split up all the brownies so that each group has an equal share without using a calculator (as she left it at school). Explain how you can use Egyptian fractions to help the teacher find a process to evenly distribute the brownies to the groups. f. Use Egyptian fractions to determine which is larger, 5/9 or 9/14. Explain. g. Describe at least one advantage of Egyptian fractions when compared to our current method of writing fractions. Then describe at least one disadvantage of the Egyptian fraction form when compared to our current form.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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PROBLEMS (continued):
2. Egyptian Fractions: Ancient Egyptians used unit fractions, such as and to represent all
fractions. For example, they might write the number as+ We often think of as +
, but the ancient Egyptians would not write it this way because they didn't use the same
unit fraction twice.
a. Write the Egyptian fraction -+÷+÷as a single fraction.
b. Write the fractions and - as Egyptian fractions.
c. Develop a process for finding an Egyptian fraction if you are given a fraction with a
numerator greater than 1. Explain why your process will work for any such fraction.
Give at least two examples of applying your process, one with a proper fraction and
one with an improper fraction, using different values from any that have been used
earlier in the problem.
d. Does each fraction have only one way to write it as an Egyptian fraction? If so,
explain why. If not, provide at least one example of a fraction that you can write as
an Egyptian fraction in more than one way.
e. A teacher took her class on a field trip and brought 5 pans of brownies. She wants to
split the brownies evenly among the 9 groups of students on the field trip. She
would like to find a simple way to split up all the brownies so that each group has an
equal share without using a calculator (as she left it at school). Explain how you can
use Egyptian fractions to help the teacher find a process to evenly distribute the
brownies to the groups.
f. Use Egyptian fractions to determine which is larger, 5/9 or 9/14. Explain.
g. Describe at least one advantage of Egyptian fractions when compared to our current
method of writing fractions. Then describe at least one disadvantage of the Egyptian
fraction form when compared to our current form.
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