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### Problem 2: $ 2\frac{5}{8} - 1\frac{2}{4} $
# Explanation:
## Step 1: Convert mixed numbers to improper fractions
$ 2\frac{5}{8}=\frac{2\times8 + 5}{8}=\frac{21}{8} $, $ 1\frac{2}{4}=\frac{1\times4+2}{4}=\frac{6}{4}=\frac{3}{2} $ (simplify $ \frac{6}{4} $ to $ \frac{3}{2} $)
## Step 2: Find a common denominator (8) and rewrite fractions
$ \frac{3}{2}=\frac{3\times4}{2\times4}=\frac{12}{8} $, so $ \frac{21}{8}-\frac{12}{8} $
## Step 3: Subtract the numerators
$ \frac{21 - 12}{8}=\frac{9}{8} $
## Step 4: Convert back to mixed number (or simplify)
$ \frac{9}{8}=1\frac{1}{8} $
# Answer:
$ 2\frac{5}{8}-1\frac{2}{4}=\frac{21}{8}-\frac{6}{4}=\frac{21}{8}-\frac{12}{8}=\frac{9}{8}=1\frac{1}{8} $

### Problem 3: $ 5\frac{1}{9} - 3\frac{8}{18} $
# Explanation:
## Step 1: Convert mixed numbers to improper fractions
$ 5\frac{1}{9}=\frac{5\times9 + 1}{9}=\frac{46}{9} $, $ 3\frac{8}{18}=\frac{3\times18+8}{18}=\frac{62}{18}=\frac{31}{9} $ (simplify $ \frac{62}{18} $ by dividing numerator and denominator by 2)
## Step 2: Subtract the fractions (same denominator)
$ \frac{46}{9}-\frac{31}{9}=\frac{46 - 31}{9}=\frac{15}{9} $
## Step 3: Simplify the fraction
$ \frac{15}{9}=\frac{5}{3}=1\frac{2}{3} $
# Answer:
$ 5\frac{1}{9}-3\frac{8}{18}=\frac{46}{9}-\frac{62}{18}=\frac{46}{9}-\frac{31}{9}=\frac{15}{9}=1\frac{2}{3} $

### Problem 4: $ 4\frac{2}{3} - 1\frac{2}{6} $
# Explanation:
## Step 1: Convert mixed numbers to improper fractions
$ 4\frac{2}{3}=\frac{4\times3 + 2}{3}=\frac{14}{3} $, $ 1\frac{2}{6}=\frac{1\times6+2}{6}=\frac{8}{6}=\frac{4}{3} $ (simplify $ \frac{8}{6} $ by dividing numerator and denominator by 2)
## Step 2: Subtract the fractions (same denominator)
$ \frac{14}{3}-\frac{4}{3}=\frac{14 - 4}{3}=\frac{10}{3} $
## Step 3: Convert back to mixed number
$ \frac{10}{3}=3\frac{1}{3} $
# Answer:
$ 4\frac{2}{3}-1\frac{2}{6}=\frac{14}{3}-\frac{8}{6}=\frac{14}{3}-\frac{4}{3}=\frac{10}{3}=3\frac{1}{3} $

### Problem 5: $ 5\frac{5}{14} - 1\frac{3}{7} $
# Explanation:
## Step 1: Convert mixed numbers to improper fractions
$ 5\frac{5}{14}=\frac{5\times14 + 5}{14}=\frac{75}{14} $, $ 1\frac{3}{7}=\frac{1\times7+3}{7}=\frac{10}{7} $
## Step 2: Find a common denominator (14) and rewrite fractions
$ \frac{10}{7}=\frac{10\times2}{7\times2}=\frac{20}{14} $, so $ \frac{75}{14}-\frac{20}{14} $
## Step 3: Subtract the numerators
$ \frac{75 - 20}{14}=\frac{55}{14} $
## Step 4: Convert back to mixed number
$ \frac{55}{14}=3\frac{13}{14} $
# Answer:
$ 5\frac{5}{14}-1\frac{3}{7}=\frac{75}{14}-\frac{10}{7}=\frac{75}{14}-\frac{20}{14}=\frac{55}{14}=3\frac{13}{14} $

### Problem 6: $ 5\frac{1}{2} - 3\frac{5}{6} $
# Explanation:
## Step 1: Convert mixed numbers to improper fractions
$ 5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2} $, $ 3\frac{5}{6}=\frac{3\times6+5}{6}=\frac{23}{6} $
## Step 2: Find a common denominator (6) and rewrite fractions
$ \frac{11}{2}=\frac{11\times3}{2\times3}=\frac{33}{6} $, so $ \frac{33}{6}-\frac{23}{6} $
## Step 3: Subtract the numerators
$ \frac{33 - 23}{6}=\frac{10}{6} $
## Step 4: Simplify the fraction
$ \frac{10}{6}=\frac{5}{3}=1\frac{2}{3} $
# Answer:
$ 5\frac{1}{2}-3\frac{5}{6}=\frac{11}{2}-\frac{23}{6}=\frac{33}{6}-\frac{23}{6}=\frac{10}{6}=1\frac{2}{3} $

### Problem 7: $ 4\frac{1}{2} - 2\frac{12}{18} $
# Explanation:
## Step 1: Convert mixed numbers to improper fractions
$ 4\frac{1}{2}=\frac{4\times2 + 1}{2}=\frac{9}{2} $, $ 2\frac{12}{18}=\frac{2\times18+12}{18}=\frac{48}{18}=\frac{8}{3} $ (simplify $ \frac{48}{18} $ by dividing numerator and denominator by 6)
## Step 2: Find a common denominator (6) and rewrite fractions
$ \frac{9}{2}=\frac{9\times3}{2\times3}=\frac{27}{6} $, $ \frac{8}{3}=\frac{8\times2}{3\times2}=\frac{16}{6} $, so $ \frac{27}{6}-\frac{16}{6} $
## Step 3: Subtract the numerators
$ \frac{27 - 16}{6}=\frac{11}{6} $
## Step 4: Convert back to mixed number
$ \frac{11}{6}=1\frac{5}{6} $
# Answer:
$ 4\frac{1}{2}-2\frac{12}{18}=\frac{9}{2}-\frac{48}{18}=\frac{27}{6}-\frac{16}{6}=\frac{11}{6}=1\frac{5}{6} $

### Problem 8: $ 5\frac{1}{6} - 2\frac{1}{2} $
# Explanation:
## Step 1: Convert mixed numbers to improper fractions
$ 5\frac{1}{6}=\frac{5\times6 + 1}{6}=\frac{31}{6} $, $ 2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2} $
## Step 2: Find a common denominator (6) and rewrite fractions
$ \frac{5}{2}=\frac{5\times3}{2\times3}=\frac{15}{6} $, so $ \frac{31}{6}-\frac{15}{6} $
## Step 3: Subtract the numerators
$ \frac{31 - 15}{6}=\frac{16}{6} $
## Step 4: Simplify the fraction
$ \frac{16}{6}=\frac{8}{3}=2\frac{2}{3} $
# Answer:
$ 5\frac{1}{6}-2\frac{1}{2}=\frac{31}{6}-\frac{5}{2}=\frac{31}{6}-\frac{15}{6}=\frac{16}{6}=2\frac{2}{3} $

### Problem 9: $ 4\frac{3}{18} - 2\frac{4}{6} $
# Explanation:
## Step 1: Simplify fractions (optional) and convert to improper fractions
Simplify $ \frac{3}{18}=\frac{1}{6} $, so $ 4\frac{1}{6}=\frac{4\times6 + 1}{6}=\frac{25}{6} $; $ 2\frac{4}{6}=2\frac{2}{3}=\frac{2\times3 + 2}{3}=\frac{8}{3} $
## Step 2: Find a common denominator (6) and rewrite fractions
$ \frac{8}{3}=\frac{8\times2}{3\times2}=\frac{16}{6} $, so $ \frac{25}{6}-\frac{16}{6} $
## Step 3: Subtract the numerators
$ \frac{25 - 16}{6}=\frac{9}{6} $
## Step 4: Simplify the fraction
$ \frac{9}{6}=\frac{3}{2}=1\frac{1}{2} $
# Answer:
$ 4\frac{3}{18}-2\frac{4}{6}=\frac{25}{6}-\frac{8}{3}=\frac{25}{6}-\frac{16}{6}=\frac{9}{6}=1\frac{1}{2} $

### Problem 10: $ 5\frac{5}{16} - 3\frac{6}{8} $
# Explanation:
## Step 1: Convert mixed numbers to improper fractions
$ 5\frac{5}{16}=\frac{5\times16 + 5}{16}=\frac{85}{16} $, $ 3\frac{6}{8}=3\frac{3}{4}=\frac{3\times4 + 3}{4}=\frac{15}{4} $ (simplify $ \frac{6}{8} $ to $ \frac{3}{4} $)
## Step 2: Find a common denominator (16) and rewrite fractions
$ \frac{15}{4}=\frac{15\times4}{4\times4}=\frac{60}{16} $, so $ \frac{85}{16}-\frac{60}{16} $
## Step 3: Subtract the numerators
$ \frac{85 - 60}{16}=\frac{25}{16} $
## Step 4: Convert back to mixed number
$ \frac{25}{16}=1\frac{9}{16} $
# Answer:
$ 5\frac{5}{16}-3\frac{6}{8}=\frac{85}{16}-\frac{15}{4}=\frac{85}{16}-\frac{60}{16}=\frac{25}{16}=1\frac{9}{16} $

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Question

Explanation:

Problem 2: \( 2\frac{5}{8} - 1\frac{2}{4} \)

Step 1: Convert mixed numbers to improper fractions

Step 2: Find a common denominator (8) and rewrite fractions

Step 3: Subtract the numerators

Step 4: Convert back to mixed number (or simplify)

Step 1: Convert mixed numbers to improper fractions

Step 2: Subtract the fractions (same denominator)

Step 3: Simplify the fraction

Step 1: Convert mixed numbers to improper fractions

Step 2: Subtract the fractions (same denominator)

Step 3: Convert back to mixed number

Answer:

Problem 3: \( 5\frac{1}{9} - 3\frac{8}{18} \)