\Textbullet Use Egyptian method to divide 47 by 9.
The Correct Answer and Explanation is:
Solution using Egyptian Division:
We want to compute:47÷947 \div 947÷9
Step 1: Create a table of 9’s multiples
We double 9 repeatedly and list the results alongside powers of 2:
| Power of 2 | Value |
|---|---|
| 1 | 9 |
| 2 | 18 |
| 4 | 36 |
| 8 | 72 ← too large, so ignore this one |
Step 2: Find combinations of values that add to 47
We now look for values in the table that sum up to 47:36+9+2=47(But 2 is not in our table)36 + 9 + 2 = 47 \quad (\text{But 2 is not in our table})36+9+2=47(But 2 is not in our table)
But we can think again:36+9=45(still short by 2)36 + 9 = 45 \quad (\text{still short by 2})36+9=45(still short by 2)
So:479=45+29=459+29=5+29\frac{47}{9} = \frac{45 + 2}{9} = \frac{45}{9} + \frac{2}{9} = 5 + \frac{2}{9}947=945+2=945+92=5+92
Final Answer:
529\boxed{5\frac{2}{9}}592
Explanation (Textbook Style):
The Egyptian method of division is based on repeated doubling and expressing a number as the sum of convenient multiples. Instead of modern long division, the ancient Egyptians used a clever technique involving doubling and subtraction.
To divide 47 by 9, we start by creating a table of multiples of 9 by repeatedly doubling: 9, 18, 36, and so on. This mirrors the powers of 2 (1, 2, 4, 8, …), since Egyptians were familiar with doubling due to their method of multiplication.
Next, we look for combinations of these doubled values that add up to or just below 47. We find that 36 and 9, which are 4 and 1 times 9 respectively, sum to 45. This is close to 47, leaving a remainder of 2.
Now we divide the leftover 2 by 9 to get the fractional part of the answer: 2⁄9.
So, putting it all together:
47 ÷ 9 = 5 (from 45 ÷ 9) plus 2⁄9 leftover.
This gives the final answer as 5 and 2⁄9.
This method demonstrates the ingenuity of Egyptian arithmetic, which relied on addition, subtraction, and doubling instead of multiplication tables or long division.
