To solve this problem, we need to follow these steps:
1. Understand the increase by 20%:
- Increasing a value [tex]\( x \)[/tex] by [tex]\( 20\% \)[/tex] means we add [tex]\( 20\% \)[/tex] of [tex]\( x \)[/tex] to [tex]\( x \)[/tex].
2. Convert 20% to a fraction:
- [tex]\( 20\% \)[/tex] can be written as [tex]\( \frac{20}{100} \)[/tex], which simplifies to [tex]\( \frac{1}{5} \)[/tex].
3. Calculate the increased amount:
- To increase [tex]\( x \)[/tex] by [tex]\( 20\% \)[/tex], we multiply [tex]\( x \)[/tex] by [tex]\( \frac{1}{5} \)[/tex] and add this to [tex]\( x \)[/tex].
- Mathematically, this is:
[tex]\[
x + \left( \frac{1}{5} \times x \right)
\][/tex]
4. Factor [tex]\( x \)[/tex] out:
- We can rewrite the expression by factoring [tex]\( x \)[/tex]:
[tex]\[
x + \frac{1}{5}x = x \left( 1 + \frac{1}{5} \right)
\][/tex]
5. Simplify the expression inside the parentheses:
- Combine the terms inside the parentheses:
[tex]\[
1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{5 + 1}{5} = \frac{6}{5}
\][/tex]
6. Final expression:
- The increased value is then:
[tex]\[
x \times \frac{6}{5}
\][/tex]
So, when [tex]\( x \)[/tex] is increased by [tex]\( 20\% \)[/tex], the new value is [tex]\( \frac{6}{5}x \)[/tex].
Therefore, the result as a fraction in its simplest form is:
[tex]\[
\frac{6}{5}x
\][/tex]
