Question

1. $5\frac{1}{3} + 3\frac{5}{6}$
2. $2\frac{1}{2} + 6\frac{3}{4}$
3. $4\frac{5}{6} + 5\frac{7}{12}$
4. $2\frac{1}{4} + 4\frac{5}{8}$
5. $4\frac{5}{8} + 6\frac{1}{2}$
6. $2\frac{1}{3} + 4\frac{5}{12}$

Explanation:

Problem 5: \( 5\frac{1}{3} + 3\frac{5}{6} \)

Step 1: Convert to improper fractions

\( 5\frac{1}{3} = \frac{5\times3 + 1}{3} = \frac{16}{3} \)
\( 3\frac{5}{6} = \frac{3\times6 + 5}{6} = \frac{23}{6} \)

Step 2: Find a common denominator (6)

\( \frac{16}{3} = \frac{16\times2}{3\times2} = \frac{32}{6} \)

Step 3: Add the fractions

\( \frac{32}{6} + \frac{23}{6} = \frac{32 + 23}{6} = \frac{55}{6} \)

Step 4: Convert back to a mixed number

\( \frac{55}{6} = 9\frac{1}{6} \)

Step 1: Convert to improper fractions

\( 2\frac{1}{2} = \frac{2\times2 + 1}{2} = \frac{5}{2} \)
\( 6\frac{3}{4} = \frac{6\times4 + 3}{4} = \frac{27}{4} \)

Step 2: Find a common denominator (4)

\( \frac{5}{2} = \frac{5\times2}{2\times2} = \frac{10}{4} \)

Step 3: Add the fractions

\( \frac{10}{4} + \frac{27}{4} = \frac{10 + 27}{4} = \frac{37}{4} \)

Step 4: Convert back to a mixed number

\( \frac{37}{4} = 9\frac{1}{4} \)

Step 1: Convert to improper fractions

\( 4\frac{5}{6} = \frac{4\times6 + 5}{6} = \frac{29}{6} \)
\( 5\frac{7}{12} = \frac{5\times12 + 7}{12} = \frac{67}{12} \)

Step 2: Find a common denominator (12)

\( \frac{29}{6} = \frac{29\times2}{6\times2} = \frac{58}{12} \)

Step 3: Add the fractions

\( \frac{58}{12} + \frac{67}{12} = \frac{58 + 67}{12} = \frac{125}{12} \)

Step 4: Convert back to a mixed number

\( \frac{125}{12} = 10\frac{5}{12} \)

Answer:

\( 9\frac{1}{6} \)

Problem 6: \( 2\frac{1}{2} + 6\frac{3}{4} \)