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