A number increased by 5/6 is 143. What is the number?

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The number is increased by `5 / 6 , ` which means `5 / 6 ` is added to the number. And the result is known: it is `1 4 3 . ` To find the initial number, we need to apply the operation of inverse to addition.

The operation inverse to addition is called subtraction. To get the initial number, subtract the same number `5 / 6 ` from the result.

It is not so hard:

`1 4 3 - 5 / 6 = 1 4 2 + 1 - 5 / 6 = 1 4 2 + 6 / 6 - 5 / 6 = 1 4 2 (1) / 6 .`

We can make this a simple fraction: `( 1 4 2 * 6 + 1 ) / 6 = ( 8 5 3 ) / 6 .`

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It is possible that "increased by 5/6" means "increased by 5/6 of the initial number." In this case, the operation is `x + x * 5 / 6 = x * 11 / 6 , ` that is, multiplication by `11/6. ` The inverse operation for multiplication is division, so

`x = (1 4 3) / ( 11 / 6 ) = (143*6)/11 = (13*11*6)/11=13*6 = 78 .`

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