Write the appropriate sign > or < in the following: (1) 2/9 __ 2/7 (2) 3/11 __ 3/13 (3) 8/15 __ 8/17 (4) 7/8 __ 7/15 (5) 6/17 __ 6/11 (6) 9/10 __ 9/11

Steps to Solve

1. Convert to Common Denominator

To compare the fractions, find a common denominator.

For the first pair ( \frac{2}{9} ) and ( \frac{2}{7} ), the common denominator is 63.

Convert both fractions: [ \frac{2}{9} = \frac{2 \times 7}{9 \times 7} = \frac{14}{63} ] [ \frac{2}{7} = \frac{2 \times 9}{7 \times 9} = \frac{18}{63} ]

2. Compare the Numerators

Now compare the numerators of ( \frac{14}{63} ) and ( \frac{18}{63} ).

Since ( 14 < 18 ), we write: [ \frac{2}{9} < \frac{2}{7} ]

3. Repeat for Remaining Pairs

Repeat the process for each set of fractions.

For ( \frac{3}{11} ) and ( \frac{3}{13} ):

• Common denominator is 143: [ \frac{3}{11} = \frac{3 \times 13}{11 \times 13} = \frac{39}{143} ] [ \frac{3}{13} = \frac{3 \times 11}{13 \times 11} = \frac{33}{143} ] Since ( 39 > 33 ), we write: [ \frac{3}{11} > \frac{3}{13} ]

For ( \frac{8}{15} ) and ( \frac{8}{17} ):

• Common denominator is 255: [ \frac{8}{15} = \frac{8 \times 17}{15 \times 17} = \frac{136}{255} ] [ \frac{8}{17} = \frac{8 \times 15}{17 \times 15} = \frac{120}{255} ] Since ( 136 > 120 ), we write: [ \frac{8}{15} > \frac{8}{17} ]

For ( \frac{7}{8} ) and ( \frac{7}{15} ):

• Common denominator is 120: [ \frac{7}{8} = \frac{7 \times 15}{8 \times 15} = \frac{105}{120} ] [ \frac{7}{15} = \frac{7 \times 8}{15 \times 8} = \frac{56}{120} ] Since ( 105 > 56 ), we write: [ \frac{7}{8} > \frac{7}{15} ]

For ( \frac{6}{17} ) and ( \frac{6}{11} ):

• Common denominator is 187: [ \frac{6}{17} = \frac{6 \times 11}{17 \times 11} = \frac{66}{187} ] [ \frac{6}{11} = \frac{6 \times 17}{11 \times 17} = \frac{102}{187} ] Since ( 66 < 102 ), we write: [ \frac{6}{17} < \frac{6}{11} ]

For ( \frac{9}{10} ) and ( \frac{9}{11} ):

• Common denominator is 110: [ \frac{9}{10} = \frac{9 \times 11}{10 \times 11} = \frac{99}{110} ] [ \frac{9}{11} = \frac{9 \times 10}{11 \times 10} = \frac{90}{110} ] Since ( 99 > 90 ), we write: [ \frac{9}{10} > \frac{9}{11} ]