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Answer
The result is \(-\frac{16}{15}\) or \(-1\frac{1}{15}\) or \(-1.066\).
Solution
Calculate or simplify the expression \( 3\frac{1}{3}-4\frac{2}{5} \).
Calculate the value by following steps:
- step0: Calculate:
\(3\frac{1}{3}-4\frac{2}{5}\)
- step1: Convert the expressions:
\(\frac{10}{3}-\frac{22}{5}\)
- step2: Reduce fractions to a common denominator:
\(\frac{10\times 5}{3\times 5}-\frac{22\times 3}{5\times 3}\)
- step3: Multiply the numbers:
\(\frac{10\times 5}{15}-\frac{22\times 3}{5\times 3}\)
- step4: Multiply the numbers:
\(\frac{10\times 5}{15}-\frac{22\times 3}{15}\)
- step5: Transform the expression:
\(\frac{10\times 5-22\times 3}{15}\)
- step6: Multiply the numbers:
\(\frac{50-22\times 3}{15}\)
- step7: Multiply the numbers:
\(\frac{50-66}{15}\)
- step8: Subtract the numbers:
\(\frac{-16}{15}\)
- step9: Rewrite the fraction:
\(-\frac{16}{15}\)
The result of \(3\frac{1}{3}-4\frac{2}{5}\) is \(-\frac{16}{15}\) or \(-1\frac{1}{15}\) or \(-1.066\).
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Simplify this solution Beyond the Answer
First, let's convert those mixed numbers into improper fractions for easier calculation. For \( 3 \frac{1}{3} \), you multiply the whole number 3 by the denominator 3, add the numerator 1, giving you \( \frac{10}{3} \). For \( 4 \frac{2}{5} \), do the same: \( 4 \times 5 + 2 = 22 \), leading to \( \frac{22}{5} \). Now you have \( \frac{10}{3} - \frac{22}{5} \). Next, find a common denominator, which would be 15 in this case. Rewriting the fractions gives you \( \frac{50}{15} - \frac{66}{15} \). Subtracting these, you get \( \frac{50 - 66}{15} = \frac{-16}{15} \). So, the final answer is \( -\frac{16}{15} \) or \( -1 \frac{1}{15} \).
