Question

1. $z - 9\frac{1}{3} + = 1\frac{5}{9}$

Explanation:

The equation in the image seems to have a typo (the extra '+' sign). Assuming the correct equation is \( z - 9\frac{1}{3}=1\frac{5}{9} \), we can solve for \( z \) as follows:

Step 1: Add \( 9\frac{1}{3} \) to both sides

To isolate \( z \), we add \( 9\frac{1}{3} \) to both sides of the equation.
\( z=1\frac{5}{9}+9\frac{1}{3} \)

Step 2: Convert mixed numbers to improper fractions

Convert \( 1\frac{5}{9} \) to \( \frac{14}{9} \) and \( 9\frac{1}{3} \) to \( \frac{28}{3} \).
\( z = \frac{14}{9}+\frac{28}{3} \)

Step 3: Find a common denominator

The common denominator of 9 and 3 is 9. Rewrite \( \frac{28}{3} \) as \( \frac{84}{9} \).
\( z=\frac{14}{9}+\frac{84}{9} \)

Step 4: Add the fractions

Add the numerators: \( 14 + 84 = 98 \).
\( z=\frac{98}{9} \)

Step 5: Convert back to a mixed number (optional)

\( \frac{98}{9}=10\frac{8}{9} \)

Answer:

\( z = 10\frac{8}{9} \) (or \( z=\frac{98}{9} \))