Let's solve the given equation step by step.
We start with the equation:
[tex]\[ \frac{1}{5} = \frac{3}{15} + \frac{2}{3} \][/tex]
1. Simplify the fractions if necessary:
- [tex]\(\frac{1}{5}\)[/tex] is already in its simplest form.
- [tex]\(\frac{3}{15}\)[/tex] can also be simplified. [tex]\(\frac{3}{15}\)[/tex] simplifies to [tex]\(\frac{1}{5}\)[/tex].
2. Calculate the decimal equivalents:
- The decimal equivalent of [tex]\(\frac{1}{5}\)[/tex] is [tex]\(0.2\)[/tex].
- The decimal equivalent of [tex]\(\frac{3}{15}\)[/tex] (or [tex]\(\frac{1}{5}\)[/tex] simplified) is [tex]\(0.2\)[/tex].
- The decimal equivalent of [tex]\(\frac{2}{3}\)[/tex] is approximately [tex]\(0.6666666666666666\)[/tex].
3. Perform the calculations for each side of the equation:
- The left side of the equation is [tex]\(\frac{1}{5}\)[/tex], which we already found to be [tex]\(0.2\)[/tex].
- The right side of the equation is the sum of [tex]\(\frac{3}{15}\)[/tex] and [tex]\(\frac{2}{3}\)[/tex]. We have:
[tex]\[
\frac{3}{15} + \frac{2}{3} = 0.2 + 0.6666666666666666 = 0.8666666666666667
\][/tex]
4. Conclusion:
- The left side of the equation is [tex]\(0.2\)[/tex].
- The right side of the equation is approximately [tex]\(0.8666666666666667\)[/tex].
- Since [tex]\(0.2 \neq 0.8666666666666667\)[/tex], the given equation [tex]\(\frac{1}{5} = \frac{3}{15} + \frac{2}{3}\)[/tex] does not hold true.
Thus, after breaking down the steps and evaluating each fraction, it is clear that the left side and the right side of the equation are not equal.
