Solve (1/3 + 9/11) × 33: Mixed Fraction Operations

$(\frac{1}{3}+\frac{9}{11})\times33=$

We'll use the distributive property and multiply 33 by each term in the parentheses:

$(\frac{1}{3}\times33)+(\frac{9}{1}\times33)=$

Let's solve the left parentheses. Remember that:

$33=\frac{33}{1}$

$\frac{1}{3}\times\frac{33}{1}=\frac{1\times33}{3\times1}=\frac{33}{3}$

Now let's address the right parentheses, where we'll break down 33 into a smaller multiplication exercise that will help us later with reduction:

$(\frac{9}{11}\times33)=(\frac{9}{11}\times11\times3)$

Now we'll reduce the 11 in the numerator and the 11 in the multiplication exercise and get:

$\frac{33}{3}+9\times3=$

Let's solve the fraction:

$\frac{33}{3}=11$

Now we'll get the exercise:

$11+(9\times3)=$

According to the order of operations, we'll solve what's in the parentheses and get:

$11+27=38$