To determine the missing fraction that when added to [tex]\(\frac{5}{8}\)[/tex] gives a sum of 1, we can follow these steps:
1. Set Up the Equation:
We start with the equation given in the problem:
[tex]\[
\frac{5}{8} + \frac{x}{y} = 1
\][/tex]
2. Isolate the Missing Fraction:
We need to find the value of [tex]\(\frac{x}{y}\)[/tex]. To do this, we can subtract [tex]\(\frac{5}{8}\)[/tex] from both sides of the equation:
[tex]\[
\frac{x}{y} = 1 - \frac{5}{8}
\][/tex]
3. Simplify the Right-Hand Side:
To simplify [tex]\(1 - \frac{5}{8}\)[/tex], we need to express the 1 as a fraction with the same denominator as [tex]\(\frac{5}{8}\)[/tex]. Since the denominator of [tex]\(\frac{5}{8}\)[/tex] is 8, we rewrite 1 as [tex]\(\frac{8}{8}\)[/tex]:
[tex]\[
1 = \frac{8}{8}
\][/tex]
Now we can make the subtraction:
[tex]\[
\frac{x}{y} = \frac{8}{8} - \frac{5}{8}
\][/tex]
4. Perform the Subtraction:
With the common denominator, we subtract the numerators:
[tex]\[
\frac{x}{y} = \frac{8 - 5}{8} = \frac{3}{8}
\][/tex]
5. Identify the Missing Fraction:
The fraction on the right-hand side is in its simplest form, so we can identify the numerator and the denominator:
[tex]\[
\frac{x}{y} = \frac{3}{8}
\][/tex]
Therefore, the missing fraction that when added to [tex]\(\frac{5}{8}\)[/tex] results in 1 is:
[tex]\[
\frac{3}{8}
\][/tex]
Hence, the solution to the problem is that the missing fraction in its simplest form is [tex]\(\frac{3}{8}\)[/tex].
