To find the product of [tex]\( 3 \frac{1}{5} \)[/tex] and [tex]\( \frac{3}{4} \)[/tex], follow these steps step-by-step:
1. Convert the mixed number to an improper fraction:
The mixed number [tex]\( 3 \frac{1}{5} \)[/tex] can be written as an improper fraction:
[tex]\[
3 \frac{1}{5} = 3 + \frac{1}{5} = \frac{3 \cdot 5 + 1}{5} = \frac{16}{5}
\][/tex]
2. Multiply the fractions:
Now, multiply the improper fraction [tex]\( \frac{16}{5} \)[/tex] by [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[
\frac{16}{5} \cdot \frac{3}{4} = \frac{16 \cdot 3}{5 \cdot 4} = \frac{48}{20}
\][/tex]
3. Simplify the fraction:
Find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 48 and 20 is 4.
Divide the numerator and the denominator by the GCD to simplify:
[tex]\[
\frac{48 \div 4}{20 \div 4} = \frac{12}{5}
\][/tex]
4. Convert the improper fraction to a mixed number (if necessary):
The improper fraction [tex]\( \frac{12}{5} \)[/tex] can be expressed as a mixed number:
[tex]\[
\frac{12}{5} = 2 \frac{2}{5}
\][/tex]
Therefore, the product [tex]\( 3 \frac{1}{5} \cdot \frac{3}{4} \)[/tex] simplified is:
[tex]\[
2 \frac{2}{5}
\][/tex]
