Compare \( \dfrac{3}{4} \) and \( \dfrac{2}{3} \).

Use a common denominator of 12:

• \( \dfrac{3}{4} = \dfrac{9}{12} \)
• \( \dfrac{2}{3} = \dfrac{8}{12} \)

Since \( 9/12 > 8/12 \), we have \( a > b \).

The correct choice is 1.

Use a common denominator of 8:

• \( a = \dfrac{5}{8} \)
• \( b = \dfrac{3}{4} = \dfrac{6}{8} \)

Since \( 5/8 < 6/8 \), we have \( a < b \).

The correct choice is 2.

Use a common denominator of 10:

• \( a = \dfrac{7}{10} \)
• \( b = \dfrac{4}{5} = \dfrac{8}{10} \)

Since \( 7/10 < 8/10 \), we have \( a < b \).

The correct choice is 2.

Use a common denominator of 15:

• \( a = \dfrac{2}{3} = \dfrac{10}{15} \)
• \( b = \dfrac{3}{5} = \dfrac{9}{15} \)

Since \( 10/15 > 9/15 \), we have \( a > b \).

The correct choice is 1.

Convert the mixed number:

\( a = 1\dfrac{1}{4} = \dfrac{5}{4} \).

So \( a = \dfrac{5}{4} = b \).

Therefore \( a = b \).

The correct choice is 3.

Convert to improper fractions:

• \( a = 1\dfrac{1}{2} = \dfrac{3}{2} \)
• \( b = 1\dfrac{3}{5} = \dfrac{8}{5} \)

Compare \( \dfrac{3}{2} \) and \( \dfrac{8}{5} \):

Use a common denominator of 10: \( \dfrac{3}{2} = \dfrac{15}{10}, \ \dfrac{8}{5} = \dfrac{16}{10} \).

Since \( 15/10 < 16/10 \), we have \( a < b \).

The correct choice is 2.

Convert to improper fractions:

• \( a = 2\dfrac{1}{3} = \dfrac{7}{3} \)
• \( b = 2\dfrac{2}{5} = \dfrac{12}{5} \)

Use a common denominator of 15:

\( a = \dfrac{7}{3} = \dfrac{35}{15}, \quad b = \dfrac{12}{5} = \dfrac{36}{15} \).

Since \( 35/15 < 36/15 \), we have \( a < b \).

The correct choice is 2.

Convert the mixed number:

\( a = 1\dfrac{3}{4} = \dfrac{7}{4} \).

So \( a = \dfrac{7}{4} = b \), hence \( a = b \).

The correct choice is 3.

Use a common denominator of 9:

• \( a = \dfrac{4}{9} \)
• \( b = \dfrac{1}{3} = \dfrac{3}{9} \)

Since \( 4/9 > 3/9 \), we have \( a > b \).

The correct choice is 1.

Use a common denominator of 24:

• \( a = \dfrac{5}{6} = \dfrac{20}{24} \)
• \( b = \dfrac{7}{8} = \dfrac{21}{24} \)

Since \( 20/24 < 21/24 \), we have \( a < b \).

The correct choice is 2.