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Questions and Answers
How did Egyptian scribes handle subtraction in their mathematical calculations?
What was the unique feature of the Egyptian algorithm for addition and subtraction mentioned in the text?
How did Egyptian scribes approach multiplication according to the text?
What did Egyptian scribes do when the next doubling would cause the first element of the pair to exceed the desired number?
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What marks a significant difference between Egyptian mathematics and the hieratic system in terms of addition and subtraction?
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Why did Egyptian scribes stop the multiplication process when the first element of the pair exceeded a certain value?
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What did Egyptian scribes do after determining the powers of 2 that add to a number in multiplication?
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What was significant about the Egyptian algorithm for addition and subtraction compared to that in the hieratic system?
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What could be inferred about Egyptian scribes from their approach to multiplication based on the text?
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How did Egyptian scribes determine which multipliers to use in multiplication based on the text?
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What was a notable limitation of the hieratic system when compared to how Egyptian scribes handled mathematical operations?
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Study Notes
Egyptian Numerals
- Egyptian numerals were written with smaller digits on the left.
- The hieratic system had specific symbols for numbers 1 to 9, multiples of 10 from 10 to 90, and multiples of 100 from 100 to 900.
- Examples of hieratic symbols: 7 = , 30 = , 3 = , 40 = , 200 = .
Writing Numbers
- To write a number, symbols were combined; for example, 37 was written as .
- The Egyptians had a zero symbol, but it was not used in mathematical papyri.
Computation Algorithms
- Addition and subtraction were simple: combine units, tens, hundreds, and so on, replacing groups of ten with the next symbol.
- For example, adding 783 and 275: + = .
Division and Fractions
- Division was the inverse of multiplication; for example, 156 ÷ 12 was solved by finding the sum of powers of 2 that equals 156.
- Fractions were represented as unit fractions (1/n) or "parts," with the exception of 2/3.
- The fraction 1/n was represented by the symbol for n with a symbol above it.
Multiplication
- The Egyptian algorithm for multiplication was based on a continual doubling process.
- To multiply a and b, a scribe would write down the pair 1, b, double each number, and stop when the next doubling would exceed a.
- The powers of 2 that add to a were determined, and the corresponding multiples of b were added to get the answer.
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Description
Explore the Egyptian numerals used on the Naqada tablets around 3000 BCE and the hieratic system, a ciphered numerical system used in ancient Egypt. Learn how numbers were represented symbolically and how larger numbers were constructed in the hieratic system.
