almostshelby
New member
- Joined
- Oct 15, 2018
- Messages
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How would you show algebraically that this multiplication "trick" does/doesn't work?
Thanks so much for trying to help. I have a really tricky question here, hoping someone can help me with it. My professor asked us to show algebraically if this 'trick' works with all numbers. It involves multiplying two numbers which share the same first digit (e.g. 57 and 53). Take the first number of the first term (5 from 57) and multiply it by the first number of the second term plus one (6 by adding 1 to the 5 in 53), in this example, =30. Then multiply the second number of the first term (7 from 57) by the second number of the second term (3 from 53), in this example, =21. Visually, these two products will accurately represent the correct answer to the original problem. For example, 30 followed by 21 equals the product of 57 x 53 = 3,021.
He stated this would only work for two numbers which begin with the same first digit. How would you go about proving algebraically that this does/doesn't work for all numbers?
Example:
57 x 53 = 3021
Trick:
5 x (5+1) = 30
7 x 3 = 21
Thanks so much for trying to help. I have a really tricky question here, hoping someone can help me with it. My professor asked us to show algebraically if this 'trick' works with all numbers. It involves multiplying two numbers which share the same first digit (e.g. 57 and 53). Take the first number of the first term (5 from 57) and multiply it by the first number of the second term plus one (6 by adding 1 to the 5 in 53), in this example, =30. Then multiply the second number of the first term (7 from 57) by the second number of the second term (3 from 53), in this example, =21. Visually, these two products will accurately represent the correct answer to the original problem. For example, 30 followed by 21 equals the product of 57 x 53 = 3,021.
He stated this would only work for two numbers which begin with the same first digit. How would you go about proving algebraically that this does/doesn't work for all numbers?
Example:
57 x 53 = 3021
Trick:
5 x (5+1) = 30
7 x 3 = 21