Let's solve each problem step by step.
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Calculation: \(5 \times \frac{3}{5}\)
\[ 5 \times \frac{3}{5} = \frac{5 \times 3}{5} = \frac{15}{5} = 3 \] Answer: 3 -
Calculation: \(4 \times \frac{5}{7}\)
\[ 4 \times \frac{5}{7} = \frac{4 \times 5}{7} = \frac{20}{7} \quad (\text{which is } 2 \frac{6}{7}) \] Answer: \(\frac{20}{7}\) or \(2 \frac{6}{7}\) -
Calculation: \(\frac{3}{4} \times \frac{2}{3}\)
\[ \frac{3}{4} \times \frac{2}{3} = \frac{3 \times 2}{4 \times 3} = \frac{6}{12} = \frac{1}{2} \] Answer: \(\frac{1}{2}\) -
Calculation: \(\frac{5}{8} \times \frac{1}{3}\)
\[ \frac{5}{8} \times \frac{1}{3} = \frac{5 \times 1}{8 \times 3} = \frac{5}{24} \] Answer: \(\frac{5}{24}\) -
Calculation: \(2 \frac{2}{6} \times 3 \frac{3}{4}\)
Convert mixed numbers to improper fractions: \[ 2 \frac{2}{6} = \frac{12 + 2}{6} = \frac{14}{6} = \frac{7}{3} \] \[ 3 \frac{3}{4} = \frac{12 + 3}{4} = \frac{15}{4} \] Now multiply: \[ \frac{7}{3} \times \frac{15}{4} = \frac{7 \times 15}{3 \times 4} = \frac{105}{12} \quad (\text{which is } 8 \frac{9}{12} = 8 \frac{3}{4}) \] Answer: \(\frac{105}{12}\) or \(8 \frac{3}{4}\) -
Calculation: \(4 \frac{1}{5} \times 5 \frac{2}{3}\)
Convert mixed numbers to improper fractions: \[ 4 \frac{1}{5} = \frac{20 + 1}{5} = \frac{21}{5} \] \[ 5 \frac{2}{3} = \frac{15 + 2}{3} = \frac{17}{3} \] Now multiply: \[ \frac{21}{5} \times \frac{17}{3} = \frac{21 \times 17}{5 \times 3} = \frac{357}{15} \quad (\text{which is } 23 \frac{12}{15} = 23 \frac{4}{5}) \] Answer: \(\frac{357}{15}\) or \(23 \frac{4}{5}\)
Now for the comparison problems (7-9):
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Calculation: \( \frac{3}{3} \times 1 \frac{2}{5} \) compared to \( 1 \frac{2}{5} \)
\[ \frac{3}{3} = 1 \quad \text{therefore, } 1 \times 1 \frac{2}{5} = 1 \frac{2}{5} \] Answer: \(=\) -
Calculation: \( \frac{7}{2} \times 2 \frac{3}{4} \) compared to \( 2 \frac{3}{4} \)
\[ 2 \frac{3}{4} = \frac{11}{4} \] \[ \frac{7}{2} \times \frac{11}{4} = \frac{77}{8} = 9 \frac{5}{8} \quad \text{(greater than \( 2 \frac{3}{4} \))} \] Answer: \(>\) -
Calculation: \( \frac{2}{4} \times 1 \frac{6}{7} \) compared to \( 1 \frac{6}{7} \)
\[ \frac{2}{4} = \frac{1}{2} \quad \text{therefore, } \frac{1}{2} \times 1 \frac{6}{7} = \frac{1}{2} \times \frac{13}{7} = \frac{13}{14} \] Since \( \frac{13}{14} < 1 \frac{6}{7} \) Answer: \(<\)
Summary of answers:
- 3
- \(\frac{20}{7}\)
- \(\frac{1}{2}\)
- \(\frac{5}{24}\)
- \(\frac{105}{12}\) or \(8 \frac{3}{4}\)
- \(\frac{357}{15}\) or \(23 \frac{4}{5}\)
- \(=\)
- \(>\)
- \(<\)