9 1/6 x 21/2

Answer 1

To perform the multiplication of the mixed fraction \(9 \frac{1}{6}\) with the improper fraction \( \frac{21}{2}\), it is easier to first convert the mixed fraction into an improper fraction.

A mixed fraction \(a \frac{b}{c}\) can be converted to an improper fraction by multiplying the whole number \(a\) by the denominator \(c\) and adding the numerator \(b\), then placing that result over the original denominator \(c\).

For \(9 \frac{1}{6}\):
The whole number is 9, the numerator is 1, and the denominator is 6.

So, transforming the mixed number to an improper fraction, you do \(9 \times 6 + 1 = 54 + 1 = 55\), resulting in \( \frac{55}{6}\).

Now, we multiply \( \frac{55}{6}\) by \( \frac{21}{2}\):

\( \frac{55}{6} \times \frac{21}{2} = \frac{55 \times 21}{6 \times 2}\)

Multiplying the numerators:

\(55 \times 21 = 1155\)

Multiplying the denominators:

\(6 \times 2 = 12\)

So we get:

\( \frac{1155}{12}\)

Now you might want to simplify this improper fraction by dividing 1155 by 12:

\(1155 \div 12 = 96\) with a remainder of \(3\),

So the mixed fraction form is \(96 \frac{3}{12}\), but you can simplify the fractional part further since \(3 \) and \(12\) have a common factor of 3:

\( \frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}\)

Thus, the result is:

\(96 \frac{1}{4}\)

So, \(9 \frac{1}{6}\) times \( \frac{21}{2}\) equals \(96 \frac{1}{4}\).