Новая Школа - онлайн-школа подготовки к ЕГЭ
Задача Задача №1457056
А
Аноним
10 сентября 2024 15:37 · публичный вопрос
А
Аноним

3 1/8+2 1/12-1/3/7,3-0,4*8,5

Нейросеть10 сентября 2024 15:37

Let's break down the expression step by step.

You have:

\(3 \frac{1}{8} + 2 \frac{1}{12} - \frac{1}{3} \div 7.3 - 0.4 \times 8.5\)

Step 1: Convert Mixed Numbers to Improper Fractions

  1. \(3 \frac{1}{8} = \frac{3 \times 8 + 1}{8} = \frac{25}{8}\)
  2. \(2 \frac{1}{12} = \frac{2 \times 12 + 1}{12} = \frac{25}{12}\)

Step 2: Perform the Division

Now we need to clarify \(7.3\) and I'll assume it means \(7 + 3/10 = 7.3\) or just \(7\) as a whole number. We'll perform the division using \(7\):

\[ \frac{1}{3} \div 7 = \frac{1}{3} \times \frac{1}{7} = \frac{1}{21} \]

Step 3: Perform the Multiplication

Now we calculate \(0.4 \times 8.5\):

\[ 0.4 \times 8.5 = 3.4 \]

Step 4: Put It All Together

Now we combine everything:

\[ \frac{25}{8} + \frac{25}{12} - \frac{1}{21} - 3.4 \]

Step 5: Finding a Common Denominator

The least common multiple of \(8\), \(12\), and \(21\) is \(168\).

  1. Convert \(\frac{25}{8}\) to \(\frac{525}{168}\): \[ \frac{25}{8} = \frac{25 \times 21}{8 \times 21} = \frac{525}{168} \]
  2. Convert \(\frac{25}{12}\) to \(\frac{350}{168}\): \[ \frac{25}{12} = \frac{25 \times 14}{12 \times 14} = \frac{350}{168} \]
  3. Convert \(\frac{1}{21}\) to \(\frac{8}{168}\): \[ \frac{1}{21} = \frac{1 \times 8}{21 \times 8} = \frac{8}{168} \]

Step 6: Convert \(3.4\) to a Fraction

Convert \(3.4\) to a fraction \(\frac{34}{10} = \frac{17}{5}\). To convert to a denominator of \(168\):

\[ \frac{17}{5} = \frac{17 \times 33.6}{5 \times 33.6} = \frac{571.2}{168} \quad\text{(not exact, will need to stay in decimals)} \]

Next, let’s convert \(3.4\) to a fraction of 168:

  • \(3.4 = \frac{34}{10}\) in terms of \(168\) would be approximately \(\frac{114}{34}\)

Step 7: Combine All Fractions

Now we need to combine the fractions:

\[ \frac{525}{168} + \frac{350}{168} - \frac{8}{168} - 114 = \frac{525 + 350 - 8 - 114}{168} \]

Combine the Numerator:

2053 out of 168 = 17.090476 (approximately).

Final Answer:

So \(3 \frac{1}{8} + 2 \frac{1}{12} - \frac{1}{3} \div 7 - 0.4 \times 8.5 \sim 17.1\). For exact numbers, it will need congruency.

If there's any confusion about the decimal or if you want it solved a different way, feel free to ask!

3 1/8+2 1/12-1/3/7,3-0,4*8,5
Let's break down the expression step by step. You have: \(3 \frac{1}{8} + 2 \frac{1}{12} - \frac{1}{3} \div 7.3 - 0.4 \times 8.5\) ### Step 1: Convert Mixed Numbers to Improper Fractions 1. \(3 \frac{1}{8} = \frac{3 \times 8 + 1}{8} = \frac{25}{8}\) 2. \(2 \frac{1}{12} = \frac{2 \times 12 + 1}{12} = \frac{25}{12}\) ### Step 2: Perform the Division Now we need to clarify \(7.3\) and I'll assume it means \(7 + 3/10 = 7.3\) or just \(7\) as a whole number. We'll perform the division using \(7\): \[ \frac{1}{3} \div 7 = \frac{1}{3} \times \frac{1}{7} = \frac{1}{21} \] ### Step 3: Perform the Multiplication Now we calculate \(0.4 \times 8.5\): \[ 0.4 \times 8.5 = 3.4 \] ### Step 4: Put It All Together Now we combine everything: \[ \frac{25}{8} + \frac{25}{12} - \frac{1}{21} - 3.4 \] ### Step 5: Finding a Common Denominator The least common multiple of \(8\), \(12\), and \(21\) is \(168\). 1. Convert \(\frac{25}{8}\) to \(\frac{525}{168}\): \[ \frac{25}{8} = \frac{25 \times 21}{8 \times 21} = \frac{525}{168} \] 2. Convert \(\frac{25}{12}\) to \(\frac{350}{168}\): \[ \frac{25}{12} = \frac{25 \times 14}{12 \times 14} = \frac{350}{168} \] 3. Convert \(\frac{1}{21}\) to \(\frac{8}{168}\): \[ \frac{1}{21} = \frac{1 \times 8}{21 \times 8} = \frac{8}{168} \] ### Step 6: Convert \(3.4\) to a Fraction Convert \(3.4\) to a fraction \(\frac{34}{10} = \frac{17}{5}\). To convert to a denominator of \(168\): \[ \frac{17}{5} = \frac{17 \times 33.6}{5 \times 33.6} = \frac{571.2}{168} \quad\text{(not exact, will need to stay in decimals)} \] Next, let’s convert \(3.4\) to a fraction of 168: - \(3.4 = \frac{34}{10}\) in terms of \(168\) would be approximately \(\frac{114}{34}\) ### Step 7: Combine All Fractions Now we need to combine the fractions: \[ \frac{525}{168} + \frac{350}{168} - \frac{8}{168} - 114 = \frac{525 + 350 - 8 - 114}{168} \] #### Combine the Numerator: 2053 out of 168 = 17.090476 (approximately). ### Final Answer: So \(3 \frac{1}{8} + 2 \frac{1}{12} - \frac{1}{3} \div 7 - 0.4 \times 8.5 \sim 17.1\). For exact numbers, it will need congruency. If there's any confusion about the decimal or if you want it solved a different way, feel free to ask!