Question

select the correct answer.
sam bought $2\frac{1}{4}$ pounds of swiss cheese and $1\frac{1}{2}$ pounds of cheddar at the deli. how many pounds of cheese did sam buy altogether?
\\(\bigcirc\\) a. $3\frac{2}{2}$
\\(\bigcirc\\) b. $3\frac{3}{4}$
\\(\bigcirc\\) c. $3\frac{2}{4}$
\\(\bigcirc\\) d. $3\frac{2}{6}$

Explanation:

Step1: Convert mixed numbers to improper fractions

$2\frac{1}{4} = \frac{2\times4 + 1}{4} = \frac{9}{4}$, $1\frac{1}{2} = \frac{1\times2 + 1}{2} = \frac{3}{2}$

Step2: Find common denominator for addition

$\frac{3}{2} = \frac{3\times2}{2\times2} = \frac{6}{4}$

Step3: Add the two fractions

$\frac{9}{4} + \frac{6}{4} = \frac{15}{4}$

Step4: Convert back to mixed number

$\frac{15}{4} = 3\frac{3}{4}$

Answer:

B. $3\frac{3}{4}$