4) 48 3/5 : 6 3/4 * 5/12 - 2 5/6 + 1 75/94 * (1 1/2 * 1/3 - 13:26)

Решение:

Давай решим этот пример по шагам, соблюдая порядок действий:

1. Первым действием вычислим выражение в последних скобках: The OCR result contained some inaccuracies. The correct fractions are: 48 3/5, 6 3/4, 5/12, 2 5/6, 1 75/94, 1 1/2, 1/3. The calculation is: 48 3/5 : 6 3/4 * 5/12 - 2 5/6 + 1 75/94 * (1 1/2 * 1/3 - 13:26).
2. Step 1: Solve the expression in the last parentheses.
• First, calculate the division:
• \[ 13 \div 26 = \frac{13}{26} = \frac{1}{2} \]
• Next, perform the multiplication:
• \[ 1 \frac{1}{2} \times \frac{1}{3} \]
• Convert the mixed number to an improper fraction:
• \[ \frac{3}{2} \times \frac{1}{3} = \frac{3 \times 1}{2 \times 3} = \frac{3}{6} = \frac{1}{2} \]
• Now, subtract the results:
• \[ \frac{1}{2} - \frac{1}{2} = 0 \]
3. Step 2: Rewrite the entire expression with the simplified parentheses.
• Since the result of the parentheses is 0, the entire term multiplied by it will be 0.
• \[ 48 \frac{3}{5} : 6 \frac{3}{4} \times \frac{5}{12} - 2 \frac{5}{6} + 1 \frac{75}{94} \times 0 \]
• \[ 48 \frac{3}{5} : 6 \frac{3}{4} \times \frac{5}{12} - 2 \frac{5}{6} + 0 \]
4. Step 3: Convert mixed numbers to improper fractions for division and multiplication.
• \[ 48 \frac{3}{5} = \frac{48 \times 5 + 3}{5} = \frac{240 + 3}{5} = \frac{243}{5} \]
• \[ 6 \frac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4} \]
• \[ 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \]
5. Step 4: Perform division and multiplication from left to right.
• Division:
• \[ \frac{243}{5} \div \frac{27}{4} = \frac{243}{5} \times \frac{4}{27} \]
• Simplify before multiplying: 243 divided by 27 is 9.
• \[ \frac{9}{5} \times \frac{4}{1} = \frac{36}{5} \]
• Multiplication:
• \[ \frac{36}{5} \times \frac{5}{12} \]
• Simplify before multiplying: 5 in the numerator and denominator cancel out. 36 divided by 12 is 3.
• \[ \frac{3}{1} \times \frac{1}{1} = 3 \]
6. Step 5: Perform subtraction.
• \[ 3 - \frac{17}{6} \]
• Convert 3 to a fraction with denominator 6:
• \[ \frac{18}{6} - \frac{17}{6} = \frac{18 - 17}{6} = \frac{1}{6} \]

Ответ:

1/6