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We need to evaluate the expression $(-3\frac{2}{3}) \div 6\frac{7}{8} - \frac{1}{3}$.

ArithmeticFractionsMixed NumbersArithmetic Operations
2025/6/1

1. Problem Description

We need to evaluate the expression (−323)÷678−13(-3\frac{2}{3}) \div 6\frac{7}{8} - \frac{1}{3}.

2. Solution Steps

First, convert the mixed numbers to improper fractions:
−323=−3×3+23=−9+23=−113 -3\frac{2}{3} = -\frac{3 \times 3 + 2}{3} = -\frac{9+2}{3} = -\frac{11}{3}
678=6×8+78=48+78=558 6\frac{7}{8} = \frac{6 \times 8 + 7}{8} = \frac{48+7}{8} = \frac{55}{8}
The expression becomes:
−113÷558−13 -\frac{11}{3} \div \frac{55}{8} - \frac{1}{3}
Next, perform the division by multiplying by the reciprocal:
−113÷558=−113×855=−11×83×55=−11×83×5×11=−83×5=−815 -\frac{11}{3} \div \frac{55}{8} = -\frac{11}{3} \times \frac{8}{55} = -\frac{11 \times 8}{3 \times 55} = -\frac{11 \times 8}{3 \times 5 \times 11} = -\frac{8}{3 \times 5} = -\frac{8}{15}
Now substitute this back into the original expression:
−815−13 -\frac{8}{15} - \frac{1}{3}
To subtract the fractions, find a common denominator, which is 15:
−815−13=−815−1×53×5=−815−515 -\frac{8}{15} - \frac{1}{3} = -\frac{8}{15} - \frac{1 \times 5}{3 \times 5} = -\frac{8}{15} - \frac{5}{15}
−815−515=−8−515=−1315=−1315 -\frac{8}{15} - \frac{5}{15} = \frac{-8-5}{15} = \frac{-13}{15} = -\frac{13}{15}

3. Final Answer

−1315-\frac{13}{15}

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