( egyptian fractions are fractions where the numerator can only be one) find two egyptian fractions where when added together it equalls 11/32
let them be 1/a and 1/b
we are given
1/a + 1/b = 11/32
adding the left side with a common denominator ...
(a+b)/(ab) = 11/32 or 22/64 or 33/96 or ....
so .... a+b = 11 and ab = 32
no integer solutions
a+b = 22 and ab = 64
no integer solutions
a+b = 33, ab = 96
no integer solution
...
a+b = 99 , ab = 288
a= 3, b = 96
1/3 + 1/96 = 99/288 = 11/32
thankyou
To find two Egyptian fractions whose sum is equal to 11/32, we need to express 11/32 as a sum of fractions, where the numerator of each fraction is equal to 1. Here's a step-by-step explanation of how to do it:
Step 1: Take the reciprocal of 11/32.
The reciprocal of a fraction (a/b) is obtained by flipping the numerator and denominator, resulting in the fraction (b/a). So, the reciprocal of 11/32 is 32/11.
Step 2: Determine the largest unit fraction less than or equal to 32/11.
A unit fraction is defined as a fraction with a numerator of 1. To find the largest unit fraction less than or equal to 32/11, divide 1 by the whole number part of 32/11, which is 2. We get 1/(32/11) = 11/32.
Therefore, we can express 11/32 as the sum of two Egyptian fractions: 1/2 + 11/32.
Please note that there might be multiple solutions to this problem, and the fractions provided are only one possible solution.