SPOT ON REVISION - COMMON ERACTIONS DAEE 104 1. Fill in \( <,> \) or \( = \) a. \( \frac{3}{4} \) \( \qquad \) \( \frac{4}{8} \) b. \( \frac{8^{10}}{15} \) C. \( \frac{3}{8} \) \( \qquad \) \( \frac{375}{1000} \) 2. Convert to improper fractions. a. \( 3 \frac{1}{3} \) b. \( 4 \frac{1}{6} \) C. \( 1 \frac{6}{20} \) 3. Convert to mixed numbers. a. \( \frac{7}{3} \) b. \( \frac{14}{2} \) c. \( \frac{24}{5} \) 4. Simplify: a. \( \frac{2}{4}+\frac{3}{6}-\frac{1}{3}= \) b. \( 5 \frac{1}{2}-1 \frac{2}{5}= \) c. \( 2 \frac{2}{3} \times 4 \frac{1}{5}= \)

1. a. We compare \[ \frac{3}{4} \quad \text{and} \quad \frac{4}{8}. \] Since \[ \frac{4}{8}=\frac{1}{2}, \] and \[ \frac{3}{4}>\frac{1}{2}, \] we have \[ \frac{3}{4} > \frac{4}{8}. \] b. The given expression \[ \frac{8^{10}}{15} \] does not provide two items to compare. (If this is a misprint, please clarify the intended comparison.) c. We compare \[ \frac{3}{8} \quad \text{and} \quad \frac{375}{1000}. \] Notice that \[ \frac{375}{1000}=\frac{375\div125}{1000\div125}=\frac{3}{8}, \] so \[ \frac{3}{8} = \frac{375}{1000}. \] 2. Converting to improper fractions: a. For \(3 \frac{1}{3}\): \[ 3 \frac{1}{3} = \frac{3\times3+1}{3}=\frac{9+1}{3}=\frac{10}{3}. \] b. For \(4 \frac{1}{6}\): \[ 4 \frac{1}{6} = \frac{4\times6+1}{6}=\frac{24+1}{6}=\frac{25}{6}. \] c. For \(1 \frac{6}{20}\): \[ 1 \frac{6}{20} = \frac{1\times20+6}{20}=\frac{20+6}{20}=\frac{26}{20}. \] This fraction can be simplified by dividing numerator and denominator by \(2\), giving \[ \frac{26}{20}=\frac{13}{10}. \] 3. Converting to mixed numbers: a. For \(\frac{7}{3}\): Divide \(7\) by \(3\): \[ 7\div3=2 \text{ remainder }1, \] so \[ \frac{7}{3}=2\frac{1}{3}. \] b. For \(\frac{14}{2}\): Since \[ 14\div2=7, \] we have \[ \frac{14}{2}=7. \] c. For \(\frac{24}{5}\): Divide \(24\) by \(5\): \[ 24\div5=4 \text{ remainder }4, \] thus \[ \frac{24}{5}=4\frac{4}{5}. \] 4. Simplify: a. Compute \[ \frac{2}{4}+\frac{3}{6}-\frac{1}{3}. \] First, simplify each term: \[ \frac{2}{4}=\frac{1}{2} \quad \text{and} \quad \frac{3}{6}=\frac{1}{2}. \] Then, \[ \frac{1}{2}+\frac{1}{2}=1, \] and subtracting, \[ 1-\frac{1}{3}=\frac{3}{3}-\frac{1}{3}=\frac{2}{3}. \] b. Compute \[ 5 \frac{1}{2}-1 \frac{2}{5}. \] Convert to improper fractions: \[ 5 \frac{1}{2}=\frac{5\times2+1}{2}=\frac{11}{2}, \] \[ 1 \frac{2}{5}=\frac{1\times5+2}{5}=\frac{7}{5}. \] Find a common denominator (10): \[ \frac{11}{2}=\frac{55}{10},\quad \frac{7}{5}=\frac{14}{10}. \] Subtract: \[ \frac{55}{10}-\frac{14}{10}=\frac{41}{10}=4\frac{1}{10}. \] c. Compute \[ 2 \frac{2}{3}\times 4 \frac{1}{5}. \] Convert to improper fractions: \[ 2 \frac{2}{3}=\frac{2\times3+2}{3}=\frac{8}{3}, \] \[ 4 \frac{1}{5}=\frac{4\times5+1}{5}=\frac{21}{5}. \] Multiply: \[ \frac{8}{3}\times \frac{21}{5}=\frac{8\times21}{3\times5}=\frac{168}{15}. \] Simplify by dividing numerator and denominator by \(3\): \[ \frac{168}{15}=\frac{56}{5}=11\frac{1}{5}. \]