Question

operations with mixed numbers
multiply: $4\frac{8}{9} \cdot 1\frac{1}{3}$
question 4 of 8
options:
$6\frac{22}{27}$
$5\frac{8}{27}$
$6\frac{14}{27}$
$4\frac{8}{37}$

Explanation:

Step1: Convert mixed numbers to improper fractions

To multiply mixed numbers, first convert them to improper fractions. For \(4\frac{8}{9}\), the improper fraction is \(\frac{4\times9 + 8}{9}=\frac{36 + 8}{9}=\frac{44}{9}\). For \(1\frac{1}{3}\), the improper fraction is \(\frac{1\times3+ 1}{3}=\frac{3 + 1}{3}=\frac{4}{3}\).

Step2: Multiply the improper fractions

Multiply the two improper fractions: \(\frac{44}{9}\times\frac{4}{3}=\frac{44\times4}{9\times3}=\frac{176}{27}\).

Step3: Convert the result back to a mixed number

Now, convert \(\frac{176}{27}\) back to a mixed number. Divide 176 by 27: \(27\times6 = 162\), and \(176-162 = 14\). So, \(\frac{176}{27}=6\frac{14}{27}\).

Answer:

\(6\frac{14}{27}\) (corresponding to the option with \(6\frac{14}{27}\))