Question: RATIONAL NUMBERS REVIEW ASSIGNMENT 5. Add, subtract, multiply, or divide the following fractions…

RATIONAL NUMBERS REVIEW ASSIGNMENT

5. Add, subtract, multiply, or divide the following fractions and mixed numbers. Then reduce each one to lowest terms.

a) $8\frac{5}{6} + 3\frac{2}{7}$

$8\frac{5}{6} = \frac{53}{6}$

$3\frac{2}{7} = \frac{23}{7}$

Common denominator = 42

$\frac{53}{6} = \frac{371}{42}$

$\frac{23}{7} = \frac{138}{42}$

$\frac{371}{42} + \frac{138}{42} = \frac{509}{42}$

b) $-\frac{3}{8} - \left(-\frac{5}{24}\right)$

$-\frac{3}{8} - \left(-\frac{5}{24}\right)$

$-\frac{3}{8} + \frac{5}{24}$

Common denominator = 24

$-\frac{3}{8} = -\frac{9}{24}$

$-\frac{9}{24} + \frac{5}{24} = -\frac{4}{24} = -\frac{1}{6}$

c) $8\frac{7}{8} \times 9\frac{2}{5}$

$8\frac{7}{8} = \frac{71}{8}$

$9\frac{2}{5} = \frac{47}{5}$

$\frac{71}{8} \times \frac{47}{5} = \frac{3337}{40}$

$= 83\frac{17}{40}$

d) $-\frac{2}{11} + \left(-2\frac{4}{5}\right)$

$-\frac{2}{11} + \left(-2\frac{4}{5}\right)$

$-\frac{2}{11} + \left(-\frac{14}{5}\right)$

$-\frac{2}{11} \times \frac{15}{15} = \frac{10}{165} = \frac{5}{77}$

e) $4.8 \div \frac{33}{4}$

Solution

To solve problem e) \(4.8 + \frac{33}{4}\): Convert \(4.8\) to a fraction: \[ 4.8 = \frac{48}{10} = \frac{24}{5} \] Find a common denominator for \(\frac{24}{5}\) and \(\frac{33}{4}\), which is 20: \[ \frac{24}{5} = \frac{96}{20} \] \[ \frac{33}{4} = \frac{165}{20} \] Add the two fractions: \[ \frac{96}{20} + \frac{165}{20} = \frac{261}{20} \] Convert \(\frac{261}{20}\) to a mixed number: \[ \frac{261}{20} = 13 \frac{1}{20} \] Final Answer: \(13 \frac{1}{20}\)