Question

which is the sum of $8\frac{3}{4}+2\frac{1}{2}$? (1 point) $\bigcirc 11\frac{1}{6}$ $\bigcirc 11\frac{1}{4}$ $\bigcirc 10\frac{1}{2}$ $\bigcirc 10\frac{1}{4}$

Explanation:

Step1: Add the whole numbers

Add the whole number parts of the mixed numbers: \(8 + 2 = 10\)

Step2: Add the fractions

First, rewrite \(\frac{1}{2}\) with a denominator of 4: \(\frac{1}{2}=\frac{2}{4}\)
Then add the fractional parts: \(\frac{3}{4}+\frac{2}{4}=\frac{3 + 2}{4}=\frac{5}{4}\)

Step3: Simplify the improper fraction

\(\frac{5}{4}=1\frac{1}{4}\)

Step4: Add the results from Step1 and Step3

Add the whole number from Step1 and the mixed number from Step3: \(10+1\frac{1}{4}=11\frac{1}{4}\)? Wait, no, wait. Wait, Step1 was \(8 + 2 = 10\), then Step2: \(\frac{3}{4}+\frac{1}{2}=\frac{3}{4}+\frac{2}{4}=\frac{5}{4}=1\frac{1}{4}\). Then Step4: \(10+1\frac{1}{4}=11\frac{1}{4}\)? But wait, let's check again. Wait, \(8\frac{3}{4}+2\frac{1}{2}\). Let's convert to improper fractions. \(8\frac{3}{4}=\frac{35}{4}\), \(2\frac{1}{2}=\frac{5}{2}=\frac{10}{4}\). Then \(\frac{35}{4}+\frac{10}{4}=\frac{45}{4}=11\frac{1}{4}\). Wait, but the options include \(11\frac{1}{4}\) as the second option. Wait, but let me check my steps again. Wait, Step1: whole numbers 8 + 2 = 10. Step2: fractions \(\frac{3}{4}+\frac{1}{2}\). Convert \(\frac{1}{2}\) to fourths: \(\frac{2}{4}\). Then \(\frac{3}{4}+\frac{2}{4}=\frac{5}{4}=1\frac{1}{4}\). Then Step3: add 10 and \(1\frac{1}{4}\): \(10 + 1\frac{1}{4}=11\frac{1}{4}\). So the correct answer is \(11\frac{1}{4}\), which is the second option.

Answer:

B. \(11\frac{1}{4}\)