21. Choose all that are true. \( \begin{array}{l}\square \frac{1}{12} \times \frac{3}{4}=\frac{49}{16} \\ 8 \frac{5}{6} \times 2=17 \frac{2}{3} \\ 5 \frac{1}{2} \times 5 \frac{1}{2}=30 \frac{1}{4} \\ 9 \frac{1}{5} \times \frac{3}{5}=9 \frac{4}{5} \\ 6 \frac{3}{4} \times 3 \frac{1}{4}=19\end{array} \)

Calculate the value by following steps: - step0: Calculate: \(5+\frac{1}{2}\times 5+\frac{1}{2}\) - step1: Multiply: \(5+\frac{5}{2}+\frac{1}{2}\) - step2: Reduce fractions to a common denominator: \(\frac{5\times 2}{2}+\frac{5}{2}+\frac{1}{2}\) - step3: Transform the expression: \(\frac{5\times 2+5+1}{2}\) - step4: Multiply the numbers: \(\frac{10+5+1}{2}\) - step5: Add the numbers: \(\frac{16}{2}\) - step6: Reduce the numbers: \(\frac{8}{1}\) - step7: Calculate: \(8\) Calculate or simplify the expression \( 6 + 3/4 * 3 + 1/4 \). Calculate the value by following steps: - step0: Calculate: \(6+\frac{3}{4}\times 3+\frac{1}{4}\) - step1: Multiply the numbers: \(6+\frac{9}{4}+\frac{1}{4}\) - step2: Reduce fractions to a common denominator: \(\frac{6\times 4}{4}+\frac{9}{4}+\frac{1}{4}\) - step3: Transform the expression: \(\frac{6\times 4+9+1}{4}\) - step4: Multiply the numbers: \(\frac{24+9+1}{4}\) - step5: Add the numbers: \(\frac{34}{4}\) - step6: Reduce the fraction: \(\frac{17}{2}\) Calculate or simplify the expression \( 8 + 5/6 * 2 \). Calculate the value by following steps: - step0: Calculate: \(8+\frac{5}{6}\times 2\) - step1: Multiply the numbers: \(8+\frac{5}{3}\) - step2: Reduce fractions to a common denominator: \(\frac{8\times 3}{3}+\frac{5}{3}\) - step3: Transform the expression: \(\frac{8\times 3+5}{3}\) - step4: Multiply the numbers: \(\frac{24+5}{3}\) - step5: Add the numbers: \(\frac{29}{3}\) Calculate or simplify the expression \( 1/12 * 3/4 \). Calculate the value by following steps: - step0: Calculate: \(\frac{\frac{1}{12}\times 3}{4}\) - step1: Multiply the numbers: \(\frac{\frac{1}{4}}{4}\) - step2: Multiply by the reciprocal: \(\frac{1}{4}\times \frac{1}{4}\) - step3: Multiply the fractions: \(\frac{1}{4\times 4}\) - step4: Multiply: \(\frac{1}{16}\) Calculate or simplify the expression \( 9 + 1/5 * 3/5 \). Calculate the value by following steps: - step0: Calculate: \(9+\frac{\frac{1}{5}\times 3}{5}\) - step1: Multiply: \(9+\frac{\frac{3}{5}}{5}\) - step2: Divide the terms: \(9+\frac{3}{25}\) - step3: Reduce fractions to a common denominator: \(\frac{9\times 25}{25}+\frac{3}{25}\) - step4: Transform the expression: \(\frac{9\times 25+3}{25}\) - step5: Multiply the numbers: \(\frac{225+3}{25}\) - step6: Add the numbers: \(\frac{228}{25}\) Let's evaluate each statement step by step: 1. **Statement:** \( \frac{1}{12} \times \frac{3}{4} = \frac{49}{16} \) - Calculation: \[ \frac{1}{12} \times \frac{3}{4} = \frac{1 \times 3}{12 \times 4} = \frac{3}{48} = \frac{1}{16} \] - Result: \( \frac{1}{16} \neq \frac{49}{16} \) (False) 2. **Statement:** \( 8 \frac{5}{6} \times 2 = 17 \frac{2}{3} \) - Calculation: \[ 8 \frac{5}{6} = \frac{53}{6} \] \[ \frac{53}{6} \times 2 = \frac{106}{6} = \frac{53}{3} = 17 \frac{2}{3} \] - Result: True 3. **Statement:** \( 5 \frac{1}{2} \times 5 \frac{1}{2} = 30 \frac{1}{4} \) - Calculation: \[ 5 \frac{1}{2} = \frac{11}{2} \] \[ \frac{11}{2} \times \frac{11}{2} = \frac{121}{4} = 30 \frac{1}{4} \] - Result: True 4. **Statement:** \( 9 \frac{1}{5} \times \frac{3}{5} = 9 \frac{4}{5} \) - Calculation: \[ 9 \frac{1}{5} = \frac{46}{5} \] \[ \frac{46}{5} \times \frac{3}{5} = \frac{138}{25} = 9 \frac{3}{25} \] - Result: \( 9 \frac{3}{25} \neq 9 \frac{4}{5} \) (False) 5. **Statement:** \( 6 \frac{3}{4} \times 3 \frac{1}{4} = 19 \) - Calculation: \[ 6 \frac{3}{4} = \frac{27}{4}, \quad 3 \frac{1}{4} = \frac{13}{4} \] \[ \frac{27}{4} \times \frac{13}{4} = \frac{351}{16} = 21.9375 \] - Result: \( 21.9375 \neq 19 \) (False) ### Summary of Results: - **True Statements:** - \( 8 \frac{5}{6} \times 2 = 17 \frac{2}{3} \) - \( 5 \frac{1}{2} \times 5 \frac{1}{2} = 30 \frac{1}{4} \) - **False Statements:** - \( \frac{1}{12} \times \frac{3}{4} = \frac{49}{16} \) - \( 9 \frac{1}{5} \times \frac{3}{5} = 9 \frac{4}{5} \) - \( 6 \frac{3}{4} \times 3 \frac{1}{4} = 19 \)