Question

1. $12\frac{3}{4} + 6\frac{3}{8}$
2. $14\frac{7}{10} + 3\frac{3}{5}$
3. $8\frac{5}{8} + 7\frac{7}{16}$

Explanation:

Problem 10: \( 12\frac{3}{4} + 6\frac{3}{8} \)

Step 1: Convert to improper fractions or find common denominator for fractions.

The denominators are 4 and 8. The common denominator is 8. Convert \( \frac{3}{4} \) to eighths: \( \frac{3}{4} = \frac{3\times2}{4\times2} = \frac{6}{8} \)
Now the expression becomes \( 12\frac{6}{8} + 6\frac{3}{8} \)

Step 2: Add the whole numbers and the fractions separately.

Whole numbers: \( 12 + 6 = 18 \)
Fractions: \( \frac{6}{8} + \frac{3}{8} = \frac{9}{8} = 1\frac{1}{8} \)

Step 3: Combine the results.

\( 18 + 1\frac{1}{8} = 19\frac{1}{8} \)

Step 1: Find common denominator for fractions.

Denominators are 10 and 5. Common denominator is 10. Convert \( \frac{3}{5} \) to tenths: \( \frac{3}{5} = \frac{3\times2}{5\times2} = \frac{6}{10} \)
Expression becomes \( 14\frac{7}{10} + 3\frac{6}{10} \)

Step 2: Add whole numbers and fractions.

Whole numbers: \( 14 + 3 = 17 \)
Fractions: \( \frac{7}{10} + \frac{6}{10} = \frac{13}{10} = 1\frac{3}{10} \)

Step 3: Combine results.

\( 17 + 1\frac{3}{10} = 18\frac{3}{10} \)

Step 1: Find common denominator for fractions.

Denominators are 8 and 16. Common denominator is 16. Convert \( \frac{5}{8} \) to sixteenths: \( \frac{5}{8} = \frac{5\times2}{8\times2} = \frac{10}{16} \)
Expression becomes \( 8\frac{10}{16} + 7\frac{7}{16} \)

Step 2: Add whole numbers and fractions.

Whole numbers: \( 8 + 7 = 15 \)
Fractions: \( \frac{10}{16} + \frac{7}{16} = \frac{17}{16} = 1\frac{1}{16} \)

Step 3: Combine results.

\( 15 + 1\frac{1}{16} = 16\frac{1}{16} \)

Answer:

\( 19\frac{1}{8} \)

Problem 11: \( 14\frac{7}{10} + 3\frac{3}{5} \)