To solve the problem of multiplying the whole number [tex]\(6\)[/tex] by the fraction [tex]\(\frac{3}{20}\)[/tex] and expressing the result in simplest form, follow these steps:
1. Multiply the Whole Number by the Numerator:
Begin by treating the whole number [tex]\(6\)[/tex] as a fraction where the denominator is [tex]\(1\)[/tex]. This gives us:
[tex]\[
6 = \frac{6}{1}
\][/tex]
Now, multiply [tex]\(\frac{6}{1}\)[/tex] by [tex]\(\frac{3}{20}\)[/tex]:
[tex]\[
6 \times \frac{3}{20} = \frac{6 \times 3}{1 \times 20} = \frac{18}{20}
\][/tex]
2. Simplify the Fraction:
The next step is to simplify the fraction [tex]\(\frac{18}{20}\)[/tex]. To do this, we need to find the greatest common divisor (GCD) of the numerator and the denominator.
- The GCD of [tex]\(18\)[/tex] and [tex]\(20\)[/tex] is [tex]\(2\)[/tex].
Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]
Therefore, the fraction in its simplest form is [tex]\(\frac{9}{10}\)[/tex].
So, the answer to [tex]\(6 \times \frac{3}{20}\)[/tex] is:
[tex]\[
\frac{9}{10}
\][/tex]
