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

\[ 8\frac{5}{6} = \frac{53}{6} \]

\[ 3\frac{2}{7} = \frac{23}{7} \]

\[ \frac{53}{6} + \frac{23}{7} = \frac{371}{42} + \frac{138}{42} = \frac{509}{42} \]

\[ \text{Common denominator} = 42 \]

\[ \frac{53}{6} + \frac{23}{7} = \frac{371}{42} + \frac{138}{42} = \frac{509}{42} \]

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

\[ -\frac{3}{8} - \left(-\frac{5}{24}\right) = -\frac{3}{8} + \frac{5}{24} \]

\[ \text{Common denominator} = 24 \]

\[ -\frac{3}{8} = -\frac{9}{24} \]

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

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

\[ 8\frac{7}{8} = \frac{71}{8} \]

\[ 9\frac{2}{5} = \frac{47}{5} \]

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

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

\[ -\frac{2}{11} + \left(-2\frac{4}{5}\right) = -\frac{2}{11} + \left(-\frac{14}{5}\right) \]

\[ -\frac{2}{11} \times \frac{14}{5} = \frac{10}{154} = \frac{5}{77} \]

e) \(4.8 + \frac{33}{4}\)

Solution

Here are the solutions for each part of the problem shown in the image: a) \(\frac{8}{5} + \frac{3}{2}\) Convert mixed numbers to improper fractions. \[ 8 \frac{5}{6} = \frac{53}{6} \quad \text{and} \quad 3 \frac{2}{7} = \frac{23}{7} \] Find a common denominator, which is 42. \[ \frac{371}{42} + \frac{138}{42} = \frac{509}{42} \] b) \(-\frac{3}{8} - \left( -\frac{5}{24} \right)\) Remove the parentheses. \[ -\frac{3}{8} + \frac{5}{24} \] Find a common denominator, which is 24. \[ -\frac{9}{24} + \frac{5}{24} = -\frac{4}{24} = -\frac{1}{6} \] c) \(8 \frac{7}{8} \times 9 \frac{2}{5}\) Convert mixed numbers to improper fractions. \[ 8 \frac{7}{8} = \frac{71}{8} \quad \text{and} \quad 9 \frac{2}{5} = \frac{47}{5} \] Multiply the fractions. \[ \frac{71}{8} \times \frac{47}{5} = \frac{3337}{40} \] Convert the result back to a mixed number: \[ 3337 \div 40 = 83 \quad \text{remainder} \, 17 \quad \Rightarrow \quad 83 \frac{17}{40} \] d) \(-\frac{2}{11} + \left( -\frac{2}{4\frac{5}{5}} \right)\) The fractions are: \[ -\frac{2}{11} \quad \text{and} \quad -\frac{15}{44} \] Find the equivalent multiplication fraction. \[ -\frac{2}{11} \times \frac{15}{11} = -\frac{10}{154} = -\frac{5}{77} \] e) \(4.8 \div \frac{33}{4}\) Convert \(4.8\) to a fraction. \[ 4.8 = \frac{24}{5} \] Divide by \(\frac{33}{4}\). \[ \frac{24}{5} \times \frac{4}{33} = \frac{96}{165} \] Simplify the fraction. \[ = \frac{32}{55} \] These are the steps and answers to each problem.