SOLUTION: the smallest fraction which, when added to 2/5*15/21*7/10*3/8 given a whole number is: 36/37,37/40 how to solve it?

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Question 770473: the smallest fraction which, when added to 2/5*15/21*7/10*3/8 given a whole number is: 36/37,37/40 how to solve it?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F5%22%22%2A%22%2215%2F21%22%22%2A%22%227%2F10%22%22%2A%22%223%2F8

Factor all numbers into primes:

2%2F5%22%22%2A%22%223%2A5%2F%283%2A7%29%22%22%2A%22%227%2F%282%2A5%29%22%22%2A%22%223%2F%282%2A2%2A2%29

Cancel a pair of 2's

cross%282%29%2F5%22%22%2A%22%223%2A5%2F%283%2A7%29%22%22%2A%22%227%2F%28cross%282%29%2A5%29%22%22%2A%22%223%2F%282%2A2%2A2%29


1%2F5%22%22%2A%22%223%2A5%2F%283%2A7%29%22%22%2A%22%227%2F5%22%22%2A%22%223%2F%282%2A2%2A2%29

Cancel a pair of 3's

1%2F5%22%22%2A%22%22cross%283%29%2A5%2F%28cross%283%29%2A7%29%22%22%2A%22%227%2F5%22%22%2A%22%223%2F%282%2A2%2A2%29

1%2F5%22%22%2A%22%225%2F7%22%22%2A%22%227%2F5%22%22%2A%22%223%2F%282%2A2%2A2%29

Cancel a pair of 5's

1%2Fcross%285%29%22%22%2A%22%22cross%285%29%2F7%22%22%2A%22%227%2F5%22%22%2A%22%223%2F%282%2A2%2A2%29

1%2F1%22%22%2A%22%221%2F7%22%22%2A%22%227%2F5%22%22%2A%22%223%2F%282%2A2%2A2%29

Cancel a pair of 7's

1%2F1%22%22%2A%22%221%2Fcross%287%29%22%22%2A%22%22cross%287%29%2F%285%29%22%22%2A%22%223%2F%282%2A2%2A2%29

1%2F1%22%22%2A%22%221%2F1%22%22%2A%22%221%2F5%22%22%2A%22%223%2F%282%2A2%2A2%29

So that becomes:

3%2F%285%2A2%2A2%2A2%29

3%2F40

The next whole number to that is 1

We subtract that from 1 to find out what we must 
add to 3%2F40 to get the next whole number, 1.

1%22%22-%22%223%2F40

Write 1 as 40%2F40

40%2F40%22%22-%22%223%2F40

Answer: 37%2F40

Edwin