5-(3-1 7/20): 9/25+ 1/8=0,485

Let's break down the equation step by step. You have the expression: \[ 5 - (3 - 1 \frac{7}{20}) : \frac{9}{25} + \frac{1}{8} \] ### Step 1: Solve the expression inside the parentheses. First, convert \( 1 \frac{7}{20} \) to an improper fraction: \[ 1 \frac{7}{20} = \frac{20 + 7}{20} = \frac{27}{20} \] Now, calculate \( 3 - \frac{27}{20} \): To do this, express \( 3 \) as a fraction: \[ 3 = \frac{60}{20} \] (because \( 3 = 3 \times \frac{20}{20} \)) Now: \[ 3 - \frac{27}{20} = \frac{60}{20} - \frac{27}{20} = \frac{60 - 27}{20} = \frac{33}{20} \] ### Step 2: Substitute back into the expression Now your expression looks like this: \[ 5 - \frac{33}{20} : \frac{9}{25} + \frac{1}{8} \] ### Step 3: Solve the division Calculating \( \frac{33}{20} : \frac{9}{25} \) means multiplying by the reciprocal: \[ \frac{33}{20} \times \frac{25}{9} = \frac{33 \times 25}{20 \times 9} = \frac{825}{180} \] ### Step 4: Simplify the fraction To simplify \( \frac{825}{180} \): - Find the GCD of 825 and 180, which is 45. - Now divide both the numerator and denominator by 45: \[ \frac{825 \div 45}{180 \div 45} = \frac{55}{12} \] So we have: \[ 5 - \frac{55}{12} + \frac{1}{8} \] ### Step 5: Convert 5 to a fraction Convert \( 5 \) to a fraction with a common denominator of 12 (which is \( 5 = \frac{60}{12} \)): Now the expression: \[ \frac{60}{12} - \frac{55}{12} + \frac{1}{8} \] ### Step 6: Calculate the subtraction and addition Now, \[ \frac{60 - 55}{12} + \frac{1}{8} = \frac{5}{12} + \frac{1}{8} \] ### Step 7: Find a common denominator for \( \frac{5}{12} + \frac{1}{8} \) The least common multiple of 12 and 8 is 24. Convert \( \frac{5}{12} \) and \( \frac{1}{8} \) to have a denominator of 24: \[ \frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24} \] \[ \frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24} \] ### Step 8: Now sum them up: \[ \frac{10}{24} + \frac{3}{24} = \frac{10 + 3}{24} = \frac{13}{24} \] ### Conclusion Finally, the value of the expression is: \[ \frac{13}{24} \approx 0.5417 \] Thus, the statement that the expression equals \( 0.485 \) is incorrect. The correct approximate value is about \( 0.5417 \).