Question

1. \\(6 \frac{7}{12} \times 6 = \\) ________

Explanation:

Convert the mixed number to an improper fraction

Using the Improper Fractions knowledge point, we convert \(6\frac{7}{12}\) by multiplying the whole number by the denominator and adding the numerator:

$$ 6\frac{7}{12} = \frac{6 \times 12 + 7}{12} = \frac{72 + 7}{12} = \frac{79}{12} $$

Set up the multiplication expression

Using the Mixed Number Multiplication knowledge point, we multiply the improper fraction by the whole number \(6\), which can be written as \(\frac{6}{1}\):

$$ \frac{79}{12} \times 6 = \frac{79 \times 6}{12} $$

Simplify the fraction before multiplying

Using the Simplifying Fractions knowledge point, we divide the numerator and denominator by their common factor, \(6\):

$$ \frac{79 \times 6}{12} = \frac{79 \times 1}{2} = \frac{79}{2} $$

Convert the improper fraction back to a mixed number

We divide \(79\) by \(2\) to find the whole number and the remaining fractional part:

$$ 79 \div 2 = 39 \text{ with a remainder of } 1 $$

This gives us:

$$ \frac{79}{2} = 39\frac{1}{2} $$

Answer:

\(6 \frac{7}{12} \times 6 =\) <blank>\(39\frac{1}{2}\)</blank>