My fraction can be written as a sum of 9 unit fractions. Each unit fraction is one twelfth of a whole. What is my fraction?
The fraction is 9/12.
To solve this problem, let's break it down step-by-step.
A unit fraction is a fraction with a numerator of 1. In this case, each unit fraction represents one twelfth of a whole.
So, to find your fraction, we need to add 9 unit fractions together. Let's start by writing out the equation:
1/x + 1/x + 1/x + 1/x + 1/x + 1/x + 1/x + 1/x + 1/x = the given fraction
Since we have 9 unit fractions, the denominator will be 9x.
Now, we need to find a common denominator for all the fractions on the left side of the equation. The common denominator will be 9x, so we need to multiply each fraction by an appropriate factor to get the denominator of 9x.
The equation becomes:
1/(9x) + 1/(9x) + 1/(9x) + 1/(9x) + 1/(9x) + 1/(9x) + 1/(9x) + 1/(9x) + 1/(9x) = the given fraction
Simplifying the left side of the equation:
9/(9x) = the given fraction
The denominators on the left side cancel out:
9/x = the given fraction
Now, we can see that the given fraction is 9 divided by the unknown denominator x. Thus, your fraction can be represented as 9/x, where x is the denominator that we're trying to find.
To find the fraction that can be written as a sum of 9 unit fractions, where each unit fraction is one twelfth of a whole, we need to divide 1 by 9.
Step 1: Divide 1 by 9
1 รท 9 = 1/9
Therefore, your fraction is 1/9.