Question

evaluate the expression $x + y$ when $x = 1\frac{2}{3}$ and $y = \frac{2}{5}$. write in simplest form.

Explanation:

Step1: Convert mixed number to improper fraction

$1\frac{2}{3} = \frac{1\times3 + 2}{3} = \frac{5}{3}$

Step2: Substitute values into expression

$x + y = \frac{5}{3} + \frac{2}{5}$

Step3: Find common denominator (15) and add

$\frac{5\times5}{3\times5} + \frac{2\times3}{5\times3} = \frac{25}{15} + \frac{6}{15} = \frac{31}{15}$

Step4: Convert to mixed number (simplest form)

$\frac{31}{15} = 2\frac{1}{15}$

Answer:

$2\frac{1}{15}$ or $\frac{31}{15}$