To solve the expression \(-3 \frac{2}{7} - 4 \frac{1}{3}\), we will follow these steps:
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Convert the mixed numbers to improper fractions.
For \(-3 \frac{2}{7}\): \[ -3 \frac{2}{7} = -\left(3 \times 7 + 2\right)/7 = -\frac{21 + 2}{7} = -\frac{23}{7} \]
For \(4 \frac{1}{3}\): \[ 4 \frac{1}{3} = 4 \times 3 + 1/3 = \frac{12 + 1}{3} = \frac{13}{3} \]
Now we rewrite the expression: \[ -\frac{23}{7} - \frac{13}{3} \]
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Find a common denominator.
The denominators are \(7\) and \(3\). The least common multiple of \(7\) and \(3\) is \(21\).
We will convert both fractions to have a denominator of \(21\): \[ -\frac{23}{7} = -\frac{23 \times 3}{7 \times 3} = -\frac{69}{21} \] \[ -\frac{13}{3} = -\frac{13 \times 7}{3 \times 7} = -\frac{91}{21} \]
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Now subtract the two fractions: \[ -\frac{69}{21} - \frac{91}{21} = -\frac{69 + 91}{21} = -\frac{160}{21} \]
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Convert the improper fraction to a mixed number: To convert \(-\frac{160}{21}\) into a mixed number: \[ 160 \div 21 = 7 \quad \text{(whole part)} \] \[ 160 - (21 \times 7) = 160 - 147 = 13 \quad \text{(remainder)} \] Therefore, \(-\frac{160}{21}\) equals \(-7 \frac{13}{21}\).
Thus, the final answer is: \[ -7 \frac{13}{21} \]
In the format [whole number] [numerator]/[denominator], the answer can be written as: \[ -7 \quad 13 \quad 21 \]