Question

1. $3\frac{1}{4} + z = 6\frac{3}{4}$

Explanation:

Step1: Subtract \( 3\frac{1}{4} \) from both sides

To solve for \( z \), we subtract \( 3\frac{1}{4} \) from both sides of the equation \( 3\frac{1}{4}+z = 6\frac{3}{4} \). This gives us \( z=6\frac{3}{4}-3\frac{1}{4} \).

Step2: Subtract the whole numbers and fractions separately

First, subtract the whole numbers: \( 6 - 3=3 \). Then, subtract the fractions: \( \frac{3}{4}-\frac{1}{4}=\frac{2}{4}=\frac{1}{2} \).

Step3: Combine the results

Combine the whole number and the fraction: \( 3+\frac{1}{2}=3\frac{1}{2} \).

Answer:

\( z = 3\frac{1}{2} \)