SOLUTION: A farmer use 9/16 of his farm for maize and 4/21 for root crops, what fraction of the farm is used for other crops?

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Question 1187534: A farmer use 9/16 of his farm for maize and 4/21 for root crops, what fraction of the farm is used for other crops?
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
A farmer highlight%28cross%28use%29%29 uses 9/16 of his farm for maize and 4/21 for root crops, what fraction of the farm is used for other crops?
~~~~~~~~~~~~~~~~~ 

    1+-+9%2F16+-+4%2F21  is for other crops.


    1+-+9%2F16+-+4%2F21 =  %2816%2A21%29%2F%2816%2A21%29+-+%289%2A21%29%2F%2816%2A21%29+-+%284%2A16%29%2F%2816%2A21%29 = %2816%2A21+-+9%2A21+-+4%2A16%29%2F%2816%2A21%29 = 83%2F336.    ANSWER

Solved, and all necessary explanations are given.



Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x = the whole farm.
9/16 * x is maize
4/21 * x is root crops.
your equation is:
9/16 * x + 4/21 * x = y
y is the amount of your land that is currently being used.
multiply both sides of that equation by (16 * 21) to get:
9 * 21 * x + 4 * 16 * x = (16 * 21) * y
factor out the x to get:
(9 * 21 + 4 * 16) * x = (16 * 21) * y
simplify to get:
253 * x = 336 * y
divide both sides of the equation by 336 to get:
253 / 336 * x = y
the amount of land that is left to use is equal to x - y.
x - y is equal to x - 253/336 * x = 336/336 * x - 253/336 * x = 83/336 * x.

use your calculator to see if that can be simplified.
it can't, so that's your answer.

you can confirm the solution is good by using your calculator.
start with 9/16 * x + 4/21 * x = y.
factor out the x to get:
(9/16 + 4/21) * x = y
use you calculator to get:
.7529761905 * x = y
solve for x - y to get:
x - y = x - .7529761905 * x = (1 - .7529761905) * x = .24702385095 * x
multiply that by 336 to get 83.
.24702385095 * x is the same as 83/336, confirming your answer is correct.

the amount of land that was used is 253/336 * x.
the amount of land that is still available to be used is 83/336.
253/336 + 83/336 = 336/336 = all the land that is already being used and still available to be used.

copying down all those decimal places is a chore, unless you have a calculator with multiple memories that can be used.
the calculator i use is the ti-84 plus.
that has over 20 memory areas that can be used, so i just copy the answer to memory and use the values that are in memory, rather than copying them down manually each time.
it's even more accurate because you store more than the decimal digits that are displayed.