To solve the multiplication problem [tex]\(2 \frac{3}{4} \times \frac{4}{5}\)[/tex], follow these steps:
1. Convert the mixed number to an improper fraction:
The mixed number [tex]\(2 \frac{3}{4}\)[/tex] needs to be converted to an improper fraction.
[tex]\[
2 \frac{3}{4} = 2 + \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}
\][/tex]
2. Multiply the improper fraction by the other fraction:
Now, we need to multiply [tex]\(\frac{11}{4}\)[/tex] with [tex]\(\frac{4}{5}\)[/tex]:
[tex]\[
\frac{11}{4} \times \frac{4}{5} = \frac{11 \times 4}{4 \times 5} = \frac{44}{20}
\][/tex]
3. Simplify the result:
Simplify [tex]\(\frac{44}{20}\)[/tex] by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 4 in this case:
[tex]\[
\frac{44 \div 4}{20 \div 4} = \frac{11}{5}
\][/tex]
Converting [tex]\(\frac{11}{5}\)[/tex] to a decimal will give us:
[tex]\[
\frac{11}{5} = 2.2
\][/tex]
4. Interpret the result:
The mixed number [tex]\(2 \frac{3}{4}\)[/tex] converts to [tex]\(2.75\)[/tex], and when multiplied by [tex]\(\frac{4}{5}\)[/tex], the result is [tex]\(2.2\)[/tex].
So, [tex]\(2 \frac{3}{4} \times \frac{4}{5} = 2.2\)[/tex].
