Questions: Add: (3m)/(2n) + (5n)/(4m)

Transcript text: Add: $\frac{3 m}{2 n}+\frac{5 n}{4 m}$

Solution

Solution Steps

To add the fractions $\frac{3m}{2n} + \frac{5n}{4m}$, we need to find a common denominator. The common denominator for $2n$ and $4m$ is $4mn$. Once we have the common denominator, we can rewrite each fraction with this common denominator and then add the numerators.

Step 1: Understand the Problem

We need to add the two fractions $\frac{3m}{2n}$ and $\frac{5n}{4m}$.

Step 2: Find a Common Denominator

To add fractions, we need a common denominator. The denominators here are $2n$ and $4m$. The least common multiple (LCM) of $2n$ and $4m$ is $4mn$.

Step 3: Rewrite Each Fraction with the Common Denominator

Rewrite each fraction so that they have the common denominator $4mn$.

\[ \frac{3m}{2n} = \frac{3m \cdot 2m}{2n \cdot 2m} = \frac{6m^2}{4mn} \]

\[ \frac{5n}{4m} = \frac{5n \cdot n}{4m \cdot n} = \frac{5n^2}{4mn} \]

Step 4: Add the Fractions

Now that both fractions have the same denominator, we can add them directly:

\[ \frac{6m^2}{4mn} + \frac{5n^2}{4mn} = \frac{6m^2 + 5n^2}{4mn} \]

Step 5: Simplify the Result