Perform the indicated operation.
$\frac{25}{5 y}+\frac{4}{2 y}$
$\frac{25}{5 y}+\frac{4}{2 y}=$ $\square$ (Simplify your answer.)
Answer (1)
Simplify each fraction: 5 y 25 = y 5 and 2 y 4 = y 2 .
Add the simplified fractions: y 5 + y 2 = y 5 + 2 .
Combine the numerators: y 7 .
The final simplified expression is: y 7 .
Explanation
Problem Analysis We are asked to perform the indicated operation and simplify the expression: 5 y 25 + 2 y 4
Simplifying Fractions First, we simplify each fraction: 5 y 25 = y 5 2 y 4 = y 2
Adding Fractions Now we add the simplified fractions. Since they have a common denominator, we can add the numerators directly: y 5 + y 2 = y 5 + 2 = y 7
Final Answer The simplified expression is: y 7
Examples
Imagine you are sharing a pizza with your friends. If you have 25 slices and 5 friends, each friend gets 5 slices. If you have 4 slices and 2 friends, each friend gets 2 slices. If you combine the two scenarios, and all friends share equally, then each friend gets 7 slices. This problem demonstrates how to combine fractions with a common denominator, which is a fundamental concept in everyday sharing and distribution scenarios.
