Order of operations with fractions: Problem type 1 Online Quiz

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Q 1 - Evaluate $\left ( \frac{27}{8}-\frac{14}{8} \right )\times\frac{8}{9}-\frac{2}{3}$

Answer : A

Explanation

Step 1:

$\mathbf {\left ( \frac{27}{8}-\frac{14}{8} \right )}\times\frac{8}{9}-\frac{2}{3}=$

$ \left ( \frac{27-14}{8} \right )\times\frac{8}{9}-\frac{2}{3}=\frac{13}{8} \times \frac{8}{9} - \frac{2}{3}$

Step 2:

$\mathbf{\frac{13}{8}\times\frac{8}{9}}-\frac{2}{3}=\frac{13}{9}-\frac{2}{3}$

Step 3:

$\mathbf{\frac{13}{9}-\frac{2}{3}}=\frac{(13-6)}{9}=\frac{7}{9}$

Step 4:

So, $\left ( \frac{27}{8}-\frac{14}{8} \right ) \times \frac{8}{9} - \frac{2}{3}=\frac{7}{9}$

Q 2 - Evaluate $\left ( \frac{13}{5}-\frac{7}{5} \right ) \times \left ( \frac{5}{9} \right )^2$

Answer : C

Explanation

Step 1:

$\mathbf{\left ( \frac{13}{5} - \frac{7}{5} \right )} \times \left ( \frac{5}{9} \right )^2 = \frac{(13-7)}{5} \times \left ( \frac{5}{9} \right )^2$

$= \frac{6}{5} \times (\frac{5}{9})^2$

Step 2:

$\frac{6}{5} \times \mathbf{\left ( \frac{5}{9} \right )^2}=\frac{6}{5} \times \frac{25}{81}$

Step 3:

$\mathbf{\frac{6}{5} \times \frac{25}{81}}=\frac{10}{27}$

Step 4:

So, $\left ( \frac{13}{5}-\frac{7}{5} \right ) \times \left ( \frac{5}{9} \right )^2 = \frac{10}{27}$

Q 3 - Evaluate $\left ( \frac{4}{7} \div \frac{11}{7} \right ) \times \left ( \frac{6}{5} + \frac{3}{5} \right )$

Answer : B

Explanation

Step 1:

$\mathbf{\left ( \frac{4}{7} \div \frac{11}{7} \right )} \times \mathbf{\left ( \frac{6}{5} + \frac{3}{5} \right )} =$

$\left ( \frac{4}{7} \times \frac{7}{11} \right ) \times \frac{(6+3)}{5} = \frac{4}{11} \times \frac{9}{5}$

Step 2:

$\mathbf{\frac{4}{11} \times \frac{9}{5}} = \frac{36}{55}$

Step 3:

So, $\left ( \frac{4}{7} \div \frac{11}{7} \right ) \times \left ( \frac{6}{5} + \frac{3}{5} \right ) = \frac{36}{55}$

Q 4 - Evaluate $\left ( \frac{15}{9} - \frac{8}{9} \right ) \div \frac{8}{3} + \frac{5}{9}$

Answer : D

Explanation

Step 1:

$\mathbf {\left ( \frac{15}{9} - \frac{8 }{9} \right )} \div \frac{8}{3}+\frac{5}{9} = $

$\frac{(15-8)}{9} \div \frac{8}{3} + \frac{5}{9} = \frac{7}{9} \div \frac{8}{3} +\frac{5}{9}$

Step 2:

$\mathbf {\frac{7}{9} \div \frac{8}{3} + \frac{5}{9}} = \frac{7}{9} \times \frac{3}{8} + \frac{5}{9} = \frac{7}{24} + \frac{5}{9}$

Step 3:

$\mathbf {\frac{7}{24} + \frac{5}{9}} = \frac{(21 + 40)}{72} = \frac{61}{72}$

Step 4:

So, $\left ( \frac{15}{9} - \frac{8}{9} \right ) \div \frac{8}{3} + \frac{5}{9} = \frac{61}{72}$

Q 5 - Evaluate $\frac{9}{8} \div \frac{4}{3} \times \left ( \frac{8}{5}-\frac{4}{9} \right )$

Answer : C

Explanation

Step 1:

$\frac{9}{8} \div \frac{4}{3} \times \mathbf {\left ( \frac{8}{5} - \frac{4}{9} \right )} = $

$\frac{9}{8} \div \frac{4}{3} \times \frac{(72-20)}{45} = \frac{9}{8} \div \frac{4}{3} \times \frac{52}{45}$

Step 2:

$\mathbf {\frac{9}{8} \div \frac{4}{3}} \times \frac{52}{45} =$

$\frac{9}{8} \times \frac{3}{4} \times \frac{52}{45} = \frac{27}{32} \times \frac{52}{45} = \frac{39}{40}$

Step 3:

$\mathbf {\frac{27}{32} \times \frac{52}{45}} = \frac{39}{40}$

Step 4:

So, $\frac{9}{8} \div \frac{4}{3} \times \left ( \frac{8}{5} - \frac{4}{9} \right ) = \frac{39}{40}$

Q 6 - Evaluate $\frac{5}{8} + \frac{3}{4} \div \frac{2^2}{5} - \frac{11}{16}$

Answer : A

Explanation

Step 1:

$\frac{5}{8} + \frac{3}{4} \div \mathbf {\frac{2^2}{5}} - \frac{11}{16} =$

$\frac{5}{8} + \frac{3}{4} \div \frac{4}{5} - \frac{11}{16}$

Step 2:

$\frac{5}{8} + \mathbf {\frac{3}{4} \div \frac{4}{5}} -\frac{11}{16} =$

$\frac{5}{8} + \frac{3}{4} \times \frac{5}{4} - \frac{11}{16} =$

$\frac{5}{8} + \frac{15}{16} - \frac{11}{16}$

Step 3:

$\frac{5}{8} + \frac{15}{16} - \frac{11}{16} = \frac{(10 + 15 - 11)}{16} = \frac{14}{16} = \frac{7}{8}$

Step 4:

So, $\frac{5}{8} + \frac{3}{4} \div \frac{2^2}{5} - \frac{11}{16} = \frac{7}{8}$

Q 7 - Evaluate $\frac{3}{4} - \frac{1}{6} \times \left ( \frac{3}{5} \right )^2 \div \frac{7}{15}$

Answer : B

Explanation

Step 1:

$\frac{3}{14} - \frac{1}{6} \times \mathbf {\left ( \frac{3}{5} \right )^2} \div \frac{7}{15} =$

$\frac{3}{14} - \frac{1}{6} \times \frac{9}{25} \div \frac{7}{15}$

Step 2:

$\frac{3}{14} - \mathbf {\frac{1}{6} \times \frac{9}{25}} \div \frac{7}{15} = \frac{3}{14} - \frac{3}{50} \div \frac{7}{15}$

Step 3:

$\frac{3}{14} - \mathbf {\frac{3}{50} \times \frac{15}{7}} = \frac{3}{14} - \frac{9}{70}$

Step 4:

$\mathbf {\frac{3}{14} - \frac{9}{70}} = \frac{(15-9)}{70} = \frac{6}{70} = \frac{3}{35}$

So, $\frac{3}{14} - \frac{1}{6} \times \left ( \frac{3}{5} \right )^2 \div \frac{7}{15} = \frac{3}{35}$

Q 8 - Evaluate $\left ( \frac{1}{9} \right )^2 \div \frac{5}{18} + \frac{7}{30}$

Answer : D

Explanation

Step 1:

$\mathbf {\left ( \frac{1}{9} \right )^2} \div \frac{5}{18} + \frac{7}{30} = \frac{1}{81} \div \frac{5}{18} + \frac{7}{30}$

Step 2:

$\mathbf {\frac{1}{18} \div \frac{5}{18}} + \frac{7}{30} = \frac{1}{81} \times \frac{18}{5} + \frac{7}{30}$

$\frac{2}{45} + \frac{7}{30}$

Step 3:

$\mathbf {\frac{2}{45} + \frac{7}{30}} = \frac{(4+21)}{90} = \frac{25}{90} = \frac{5}{18}$

Step 4:

So, $\left ( \frac{1}{9} \right )^2 \div \frac{5}{18} + \frac{7}{30} = \frac{5}{18}$

Q 9 - Evaluate $\left ( \frac{5}{8}-\frac{1^2}{5} \right ) \times \frac{5}{3}$

Answer : C

Explanation

Step 1:

$\left ( \frac{5}{8} - \frac{\mathbf {1^2}}{5} \right ) \times \frac{5}{3} = \left ( \frac{5}{8} - \frac{1}{5} \right ) \times \frac{5}{3}$

Step 2:

$\mathbf {\frac{5}{8} - \frac{1}{5}} \times \frac{5}{3} = \frac{(25-8)}{40} \times \frac{5}{3}$

$= \frac{17}{40} \times \frac{5}{3}$

Step 3:

$\mathbf {\frac{17}{40} \times \frac{5}{3}} = \frac{17}{24}$

Step 4:

So, $\left ( \frac{5}{8} - \frac{1^2}{5} \right ) \times \frac{5}{3} = \frac{17}{24}$

Q 10 - Evaluate $\frac{12}{6^2} \times \left ( \frac{5}{6}+\frac{4}{3} \right ) \times \frac{6}{5}$

Answer : A

Explanation

Step 1:

$\frac{12}{6^2} \times \mathbf {\left ( \frac{5}{6} + \frac{4}{3} \right )} \times \frac{6}{5}$

$= \frac{12}{6^2} \times \frac{(5+8)}{6} \times \frac{6}{5} = \frac{12}{6^2} \times \frac{13}{6} \times \frac{6}{5}$

Step 2:

$\frac{12}{\mathbf{6^2}} \times \frac{13}{6} \times \frac{6}{5} = \frac{12}{36} \times \frac{13}{6} \times \frac{6}{5}$

Step 3:

$\mathbf {\frac{12}{36} \times \frac{13}{6}} \times \frac{6}{5} = \frac{13}{18} \times \frac{6}{5}$

Step 4:

$\mathbf {\frac{13}{18} \times \frac{6}{5}} = \frac{13}{15}$

So, $\frac{12}{6^2} \times \left ( \frac{5}{6} + \frac{4}{3} \right ) \times \frac{6}{5} = \frac{13}{15}$

order_of_operations_with_fractions_problem_type1.htm