Divide 1 by 7:

\(\displaystyle \frac{1}{7} = 1 \div 7 = 0.142857... < 0.143\)

Divide 7 by 11:

\(\displaystyle \frac{7}{11} = 7 \div 11 = 0.636363... > 0.63\)

Divide 3 by 13:

\(\displaystyle \frac{3}{13} = 3 \div 13 = 0.230769... > 0.23\)

\(\displaystyle \frac{3}{13} > 0.23 \Rightarrow -\frac{3}{13} < - 0.23\)

Divide 7 by 12:

\(\displaystyle 7 \div 12 = 0.58333... > 0.58\)

\(\displaystyle \frac{7 }{12} > 0.58\), so \(\displaystyle - \frac{7 }{12} < - 0.58\)

There are two ways to solve this problem. You can convert both to either fractions or decimals so that you can properly compare them. If you want to compare them as decimals, convert Column B to a decimal by dividing 9 by 25, which gives you 0.36. Then, you can see that Column A is greater. If you want to look at both as fractions, put 68 over 100 to get \(\displaystyle \frac{68}{100}.\)This can be further simplifies to \(\displaystyle \frac{17}{25}.\)Therefore, you can see that Column A is greater.

\(\displaystyle \frac{1}{5} = 1 \div 5 = 0.2\)

\(\displaystyle \frac{1}{4} = 1 \div 4 = 0.25\)

\(\displaystyle \frac{1}{10} = 1 \div 10 = 0.1\)

\(\displaystyle \frac{1}{5} + \frac{1}{4} - \frac{1}{10} = 0.2 + 0.25 - 0.1 = 0.45 - 0.1 = 0.35\)

\(\displaystyle \left (\frac{3}{4} \right )^{2} = \frac{3^{2}}{4^{2}} = \frac{9}{16} = 9 \div 16 = 0.5625\)

\(\displaystyle \frac{4}{5} + \frac{3}{4} \cdot \frac{1}{2}\)

\(\displaystyle = \frac{4}{5} + \frac{3\cdot 1}{4\cdot 2}\)

\(\displaystyle = \frac{4}{5} + \frac{3 }{8}\)

\(\displaystyle = \frac{4\cdot 8}{5 \cdot 8} + \frac{5 \cdot 3 }{5 \cdot8}\)

\(\displaystyle = \frac{32}{40} + \frac{15}{40} = \frac{32+ 15 }{40} = \frac{47 }{40}\)

\(\displaystyle \frac{47 }{40} = 47 \div 40 = 1.175\)

\(\displaystyle 2-\left ( \frac{3}{2} \right )^{2}\)

Square the fraction by squaring both the numerator and the denominator.

\(\displaystyle 2-\left ( \frac{3^{2}}{2^{2}} \right )\)

\(\displaystyle 2- \frac{9}{4}\)

To subtract, convert so that each term shares a common denominator.

\(\displaystyle \frac{8}{4}- \frac{9}{4}\)

\(\displaystyle \frac{8-9}{4}\)

\(\displaystyle \frac{-1}{4}\)

\(\displaystyle -\frac{1}{4}\)

Finally, convert to a decimal.

\(\displaystyle - \frac{1}{4} = -1 \div 4 = -0.25\)

\(\displaystyle 10 - \left ( 2 \frac{1}{2}\right )^{2}\)

First, evaluate the term in parenthesis:

\(\displaystyle 10 - \left ( \frac{2 \times 2 + 1}{2}\right )^{2}\)

\(\displaystyle 10 - \left ( \frac{5}{2}\right )^{2}\)

Apply the exponent by sparing the numerator and the denominator.

\(\displaystyle 10 - \left ( \frac{5^{2}}{2^{2}}\right )\)

\(\displaystyle 10 - \frac{25}{4}\)

To subtract, convert the terms to a common denominator.

\(\displaystyle \frac{40}{4} - \frac{25}{4}\)

\(\displaystyle \frac{40-25}{4}\)

\(\displaystyle \frac{15}{4}\)

Divide to convert the fraction to a decimal.

\(\displaystyle 15 \div 4 = 3.75\)