Sure, let's work through this problem step by step.
1. Convert the mixed number [tex]\(3 \frac{3}{4}\)[/tex] to an improper fraction:
- Properly, a mixed number [tex]\(a \frac{b}{c}\)[/tex] can be converted to an improper fraction by the formula:
[tex]\[
a + \frac{b}{c} = \frac{(a \times c) + b}{c}
\][/tex]
Applying this to our mixed number [tex]\(3 \frac{3}{4}\)[/tex]:
[tex]\[
3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}
\][/tex]
2. Multiply the improper fraction by [tex]\(\frac{2}{5}\)[/tex]:
- The multiplication of two fractions [tex]\(\frac{a}{b} \times \frac{c}{d}\)[/tex] results in:
[tex]\[
\frac{a \times c}{b \times d}
\][/tex]
Using our fractions [tex]\(\frac{15}{4} \times \frac{2}{5}\)[/tex]:
[tex]\[
\frac{15 \times 2}{4 \times 5} = \frac{30}{20}
\][/tex]
3. Simplify the resulting fraction [tex]\(\frac{30}{20}\)[/tex]:
- We need to find the Greatest Common Divisor (GCD) of 30 and 20 to simplify the fraction:
[tex]\[
\frac{30}{20} = \frac{30 \div 10}{20 \div 10} = \frac{3}{2}
\][/tex]
4. Convert the improper fraction [tex]\(\frac{3}{2}\)[/tex] to a mixed number:
- To convert an improper fraction to a mixed number, we divide the numerator by the denominator and express the result:
[tex]\[
\frac{3}{2} = 1 \frac{1}{2}
\][/tex]
Therefore, the product of [tex]\(3 \frac{3}{4} \times \frac{2}{5}\)[/tex] is:
[tex]\[
1 \frac{1}{2}
\][/tex]
So, the whole number part of the mixed number is [tex]\(1\)[/tex].
