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

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

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

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

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

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

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

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

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

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

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

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

\[ 4.8 \div \frac{33}{4} = \frac{33}{4} \]

Solution

The photo contains solutions to problems involving the addition, subtraction, multiplication, and division of fractions and mixed numbers. I’ll detail the solution to question (e) as it is not complete: e) Convert 4.8 to a fraction and divide it by \(\frac{33}{4}\). Step 1: Convert 4.8 to a fraction. 4.8 can be written as \(\frac{48}{10}\), which simplifies to \(\frac{24}{5}\). Step 2: Write the division as a multiplication of the reciprocal. Divide \(\frac{24}{5}\) by \(\frac{33}{4}\) is the same as multiplying \(\frac{24}{5}\) by \(\frac{4}{33}\). \[ \frac{24}{5} \times \frac{4}{33} \] Step 3: Multiply the numerators and the denominators. \[ \frac{24 \times 4}{5 \times 33} = \frac{96}{165} \] Step 4: Simplify the fraction if possible. The greatest common divisor of 96 and 165 is 3. \[ \frac{96 \div 3}{165 \div 3} = \frac{32}{55} \] Final Answer: \(\frac{32}{55}\)