To simplify the mixed number \(3 \frac{7}{12}\), you can leave it as is in its current form because it is already in its simplest mixed number form. However, if you want to convert it to an improper fraction, you can do the following:
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Multiply the whole number (3) by the denominator (12): \[ 3 \times 12 = 36 \]
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Add the numerator (7) to this result: \[ 36 + 7 = 43 \]
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The improper fraction will have this sum as the numerator and the original denominator (12) as the denominator: \[ \frac{43}{12} \]
So, \(3 \frac{7}{12}\) can also be expressed as the improper fraction \(\frac{43}{12}\).
In conclusion, both \(3 \frac{7}{12}\) and \(\frac{43}{12}\) are correct forms, but \(3 \frac{7}{12}\) is already in simplest mixed number form.