6,8*5/13*2,7*3 3/25:5 2/5 : 1/175

Let's carefully evaluate the given expression step by step: Expression: \[ 6.8 \times 5 / 13 \times 2.7 \times 3 \, \frac{3}{25} : 5 \, \frac{2}{5} : \frac{1}{175} \] --- **Step 1: Convert mixed numbers to improper fractions for clarity** - \( 3 \frac{3}{25} = \frac{3 \times 25 + 3}{25} = \frac{75 + 3}{25} = \frac{78}{25} \) - \( 2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5} \) --- **Step 2: Rewrite the expression** \[ 6.8 \times 5 \div 13 \times 2.7 \times 3 \times \frac{78}{25} \div \frac{12}{5} \div \frac{1}{175} \] Note: The colons (:) denote division. Rearranged with explicit division signs: \[ (6.8 \times 5) \div 13 \times 2.7 \times 3 \times \frac{78}{25} \div \frac{12}{5} \div \frac{1}{175} \] --- **Step 3: Simplify step by step** **a) Calculate \(6.8 \times 5\):** \[ 6.8 \times 5 = 34 \] **b) Now, divide by 13:** \[ 34 \div 13 = \frac{34}{13} \] --- **c) Multiply by 2.7:** \[ \frac{34}{13} \times 2.7 = \frac{34 \times 2.7}{13} \] Calculate numerator: \[ 34 \times 2.7 = (34 \times 2) + (34 \times 0.7) = 68 + 23.8 = 91.8 \] So: \[ \frac{91.8}{13} \] **d) Multiply by 3:** \[ \frac{91.8}{13} \times 3 = \frac{91.8 \times 3}{13} = \frac{275.4}{13} \] --- **e) Multiply by \(\frac{78}{25}\):** \[ \frac{275.4}{13} \times \frac{78}{25} = \frac{275.4 \times 78}{13 \times 25} \] Calculate numerator: \[ 275.4 \times 78 \] Let's compute this: - \( 275.4 \times 78 = (275.4 \times 80) - (275.4 \times 2) \) \[ 275.4 \times 80 = 22,032 \] \[ 275.4 \times 2 = 550.8 \] Subtract: \[ 22,032 - 550.8 = 21,481.2 \] Denominator: \[ 13 \times 25 = 325 \] So, current numerator/denominator: \[ \frac{21,481.2}{325} \] --- **f) Divide by \(\frac{12}{5}\):** Dividing by a fraction is multiplying by its reciprocal: \[ \frac{21,481.2}{325} \times \frac{5}{12} = \frac{21,481.2 \times 5}{325 \times 12} \] Calculate numerator: \[ 21,481.2 \times 5 = 107,406 \] Calculate denominator: \[ 325 \times 12 = 3,900 \] Now, we have: \[ \frac{107,406}{3,900} \] --- **g) Divide by \(\frac{1}{175}\):** Again, dividing by a fraction is multiplying by its reciprocal: \[ \frac{107,406}{3,900} \times 175 = \frac{107,406 \times 175}{3,900} \] Calculate numerator: \[ 107,406 \times 175 \] Break down: - \(107,406 \times 100 = 10,740,600\) - \(107,406 \times 75 = 107,406 \times (50 + 25) = 5,370,300 + 2,685,150 = 8,055,450\) Sum: \[ 10,740,600 + 8,055,450 = 18,796,050 \] Now, numerator = 18,796,050 Division: \[ \frac{18,796,050}{3,900} \] Simplify: Divide numerator and denominator by 150: - numerator: \( 18,796,050 \div 150 = 125,307 \) - denominator: \( 3,900 \div 150 = 26 \) Thus: \[ \frac{125,307}{26} \] Finally, divide numerator by denominator: \[ 125,307 \div 26 \approx 4,824.9 \] --- ### **Final Answer:** \[ \boxed{approximate \, value \approx 4,824.9} \] **So, the value of the entire expression is approximately 4,824.9.**