Question

1. $2\frac{2}{3} + y = 4\frac{1}{4}$

Explanation:

Step1: Convert mixed numbers to improper fractions

$2\frac{2}{3} = \frac{2\times3 + 2}{3} = \frac{8}{3}$, $4\frac{1}{4} = \frac{4\times4 + 1}{4} = \frac{17}{4}$
The equation becomes: $\frac{8}{3} + y = \frac{17}{4}$

Step2: Isolate y by subtracting $\frac{8}{3}$

$y = \frac{17}{4} - \frac{8}{3}$

Step3: Find common denominator (12) and subtract

$\frac{17}{4} = \frac{17\times3}{4\times3} = \frac{51}{12}$, $\frac{8}{3} = \frac{8\times4}{3\times4} = \frac{32}{12}$
$y = \frac{51}{12} - \frac{32}{12} = \frac{19}{12}$

Step4: Convert to mixed number (optional)

$\frac{19}{12} = 1\frac{7}{12}$

Answer:

$y = \frac{19}{12}$ or $1\frac{7}{12}$