Compare the fractions:
Q`5/8 "and 7/12"`,
(ii) `5/9 "and 11/15"`
(iii)`11/12"and"15/16`

Answer

To compare the fractions \( \frac{5}{8} \) and \( \frac{7}{12} \), \( \frac{5}{9} \) and \( \frac{11}{15} \), and \( \frac{11}{12} \) and \( \frac{15}{16} \), we will follow these steps:

### Step 1: Compare \( \frac{5}{8} \) and \( \frac{7}{12} \)

1. **Find the LCM of the denominators (8 and 12)**:
- The multiples of 8 are: 8, 16, 24, 32, ...
- The multiples of 12 are: 12, 24, 36, ...
- The least common multiple (LCM) is 24.

2. **Convert both fractions to have the same denominator**:
- For \( \frac{5}{8} \):
\[ \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24} \]
- For \( \frac{7}{12} \):
\[ \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24} \]

3. **Compare the numerators**:
- Since \( 15 > 14 \), we conclude that:
\[ \frac{5}{8} > \frac{7}{12} \]

### Step 2: Compare \( \frac{5}{9} \) and \( \frac{11}{15} \)

1. **Find the LCM of the denominators (9 and 15)**:
- The multiples of 9 are: 9, 18, 27, 36, 45, ...
- The multiples of 15 are: 15, 30, 45, ...
- The least common multiple (LCM) is 45.

2. **Convert both fractions to have the same denominator**:
- For \( \frac{5}{9} \):
\[ \frac{5}{9} = \frac{5 \times 5}{9 \times 5} = \frac{25}{45} \]
- For \( \frac{11}{15} \):
\[ \frac{11}{15} = \frac{11 \times 3}{15 \times 3} = \frac{33}{45} \]

3. **Compare the numerators**:
- Since \( 25 < 33 \), we conclude that:
\[ \frac{5}{9} < \frac{11}{15} \]

### Step 3: Compare \( \frac{11}{12} \) and \( \frac{15}{16} \)

1. **Find the LCM of the denominators (12 and 16)**:
- The multiples of 12 are: 12, 24, 36, 48, ...
- The multiples of 16 are: 16, 32, 48, ...
- The least common multiple (LCM) is 48.

2. **Convert both fractions to have the same denominator**:
- For \( \frac{11}{12} \):
\[ \frac{11}{12} = \frac{11 \times 4}{12 \times 4} = \frac{44}{48} \]
- For \( \frac{15}{16} \):
\[ \frac{15}{16} = \frac{15 \times 3}{16 \times 3} = \frac{45}{48} \]

3. **Compare the numerators**:
- Since \( 44 < 45 \), we conclude that:
\[ \frac{11}{12} < \frac{15}{16} \]

### Summary of Comparisons:
1. \( \frac{5}{8} > \frac{7}{12} \)
2. \( \frac{5}{9} < \frac{11}{15} \)
3. \( \frac{11}{12} < \frac{15}{16} \)