To solve the expression "5 minus 3 wholes and 2 sevenths," we first need to convert the mixed number (3 wholes and 2 sevenths) into an improper fraction.
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Convert 3 wholes into sevenths: \[ 3 = \frac{3 \times 7}{7} = \frac{21}{7} \]
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Now, add the 2 sevenths to this: \[ 3 \text{ wholes and } 2 \text{ sevenths} = \frac{21}{7} + \frac{2}{7} = \frac{23}{7} \]
Next, we perform the subtraction: \[ 5 - \frac{23}{7} \]
To subtract, we can convert 5 into a fraction with a denominator of 7: \[ 5 = \frac{5 \times 7}{7} = \frac{35}{7} \]
Now we perform the subtraction: \[ \frac{35}{7} - \frac{23}{7} = \frac{35 - 23}{7} = \frac{12}{7} \]
The result, \(\frac{12}{7}\), can be expressed as a mixed number: \[ \frac{12}{7} = 1 \frac{5}{7} \]
Thus, the final answer is: \[ 5 - 3 \text{ wholes and } 2 \text{ sevenths} = 1 \frac{5}{7} \]