I have an answer to a question from my book I just don't understand the logic. If John adds 3/5 of the total, Peter adds 2/3 of the remainder and Robert adds 8 which is 1/3 of the remainder you are told to find the total. It states the operation starts 1/3 of (1-(3/5)) why is it a subtraction? Thanks any help!
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Fractions and Operations
- Thread starter lfd217
- Start date
Subtraction?
If the total is divided into 5 parts, John delivers 3 of them (3/5 of the total), leaving 5 - 3 = 2 parts as the "remainder" to be delivered (2/5 of the total), so, (1 -3/5) = (5/5 - 3/5) = 2/5, which can be read as, take the total, divide it into 5 parts and subtract 3 of them to leave 2 of 5 parts (2/5).
So that is where the subtraction comes in.
Of course when the formula says (1/3)(1-3/5) they are saying (1/3)(1-3/5)T, and so 1/3(1-3/5)T = ... etc
I have an answer to a question from my book I just don't understand the logic. If John adds 3/5 of the total, Peter adds 2/3 of the remainder and Robert adds 8 which is 1/3 of the remainder you are told to find the total. It states the operation starts 1/3 of (1-(3/5)) why is it a subtraction? Thanks any help!
If the total is divided into 5 parts, John delivers 3 of them (3/5 of the total), leaving 5 - 3 = 2 parts as the "remainder" to be delivered (2/5 of the total), so, (1 -3/5) = (5/5 - 3/5) = 2/5, which can be read as, take the total, divide it into 5 parts and subtract 3 of them to leave 2 of 5 parts (2/5).
So that is where the subtraction comes in.
Of course when the formula says (1/3)(1-3/5) they are saying (1/3)(1-3/5)T, and so 1/3(1-3/5)T = ... etc
Hi lfd217:
Dale answered your question about the subtraction. I'm going to repeat his answer in a different way.
Here is the given exercise restated:
John, Peter, and Robert find some money on the sidewalk. (Hooray!)
John takes 3/5ths of this money for himself.
From the remaining money, Peter takes 2/3rds and Robert takes 1/3rd.
Robert receives eight dollars.
How much money did John, Peter, and Robert find on the sidewalk?
Note the phrase in red above. It means exactly the same as "2/5ths of the money found on the sidewalk".
If a person does not realize that 2/5ths is what remains, after taking away 3/5ths, then they need to do some arithmetic.
When we do this arithmetic, we use the number 1 to represent the whole amount. Therefore, taking 3/5ths away from the whole is calculated by subtraction from 1:
1 - 3/5
Robert's fraction of the whole is 1/3rd of the 2/5ths. That is, Robert takes (1/3)(1 - 3/5) of the money found on the sidewalk.
(Dale already explained why 1 - 3/5 equals 2/5.)
So, we can say that the fractional amount that Robert takes is (1/3)(2/5) of the money found.
Can you multiply 2/5 by 1/3 ?
Try it, and show us what you get. :cool:
PS: Dale used some algebra notation, when he wrote (1/3)(1-3/5)T. If you're unfamiliar with using letters of the alphabet to represent numbers, don't worry about that "T". You'll learn about this later, in algebra class.
Dale answered your question about the subtraction. I'm going to repeat his answer in a different way.
Here is the given exercise restated:
John, Peter, and Robert find some money on the sidewalk. (Hooray!)
John takes 3/5ths of this money for himself.
From the remaining money, Peter takes 2/3rds and Robert takes 1/3rd.
Robert receives eight dollars.
How much money did John, Peter, and Robert find on the sidewalk?
Note the phrase in red above. It means exactly the same as "2/5ths of the money found on the sidewalk".
If a person does not realize that 2/5ths is what remains, after taking away 3/5ths, then they need to do some arithmetic.
When we do this arithmetic, we use the number 1 to represent the whole amount. Therefore, taking 3/5ths away from the whole is calculated by subtraction from 1:
1 - 3/5
Robert's fraction of the whole is 1/3rd of the 2/5ths. That is, Robert takes (1/3)(1 - 3/5) of the money found on the sidewalk.
(Dale already explained why 1 - 3/5 equals 2/5.)
So, we can say that the fractional amount that Robert takes is (1/3)(2/5) of the money found.
Can you multiply 2/5 by 1/3 ?
Try it, and show us what you get. :cool:
PS: Dale used some algebra notation, when he wrote (1/3)(1-3/5)T. If you're unfamiliar with using letters of the alphabet to represent numbers, don't worry about that "T". You'll learn about this later, in algebra class.
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