Question

solve for u.
$u - \frac{4}{5} = 2\frac{3}{4}$

Explanation:

Step1: Add $\frac{4}{5}$ to both sides

To isolate \( u \), we add \(\frac{4}{5}\) to both sides of the equation \( u - \frac{4}{5} = 2\frac{3}{4} \). This gives us \( u = 2\frac{3}{4} + \frac{4}{5} \).

Step2: Convert mixed number to improper fraction

First, convert \( 2\frac{3}{4} \) to an improper fraction. \( 2\frac{3}{4} = \frac{2\times4 + 3}{4} = \frac{11}{4} \).

Step3: Find a common denominator

The common denominator of 4 and 5 is 20. Convert \(\frac{11}{4}\) and \(\frac{4}{5}\) to fractions with denominator 20. \(\frac{11}{4} = \frac{11\times5}{4\times5} = \frac{55}{20}\) and \(\frac{4}{5} = \frac{4\times4}{5\times4} = \frac{16}{20}\).

Step4: Add the fractions

Now add the two fractions: \(\frac{55}{20} + \frac{16}{20} = \frac{55 + 16}{20} = \frac{71}{20}\).

Step5: Convert back to mixed number (optional)

Convert \(\frac{71}{20}\) back to a mixed number: \( \frac{71}{20} = 3\frac{11}{20} \).

Answer:

\( u = 3\frac{11}{20} \) (or \( u = \frac{71}{20} \))