Question
Add. \[ \frac{5}{6}+\frac{1}{6 y} \] Simplify your answer as much as possible. \[ \square \frac{\square}{\square} \]
Ask by Tucker Mccarthy. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified answer is \( \frac{5y + 1}{6y} \).
Solution
To add the fractions 5/6 and 1/(6y), first find a common denominator. Since the denominators are 6 and 6y, the common denominator is 6y.
Rewrite 5/6 so that it has a denominator of 6y:
5/6 = (5y)/(6y)
Now add:
(5y)/(6y) + 1/(6y) = (5y + 1)/(6y).
The simplified answer is:
(5y + 1)/(6y).
So, filling in the blanks:
□ = 5y + 1, □ = 6, □ = y.
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Simplify this solution Beyond the Answer
To add the fractions \(\frac{5}{6}\) and \(\frac{1}{6y}\), we first notice that the denominators are both based on 6, allowing us to combine the numerators straight away. This gives us: \[ \frac{5}{6} + \frac{1}{6y} = \frac{5y + 1}{6y} \] Now, our result is expressed as \(\frac{5y + 1}{6y}\), and this fraction is already in its simplest form since the numerator and denominator share no common factors. The final answer is: \[\square \frac{5y + 1}{6y} \]
