Answer: 1/5
Step-by-step explanation:
The total of all fractions of the spinner must be 1, or 100%. We can set the total of all the fractions to be 1, and solve for the missing one.
[tex]\frac{3}{20}+\frac{1}{4}+\frac{2}{5}+x=1[/tex]
The least common multiple of all the denominators is 20, so we can write each fraction with denominator of 20.
[tex]\frac{3}{20}+\frac{5}{20}+\frac{8}{20}+x =\frac{20}{20}[/tex]
Adding all the fractions on the left-hand side, we get
[tex]\frac{16}{20}+x=\frac{20}{20}[/tex]
We can subtract [tex]\frac{16}{20}[/tex] from both sides to isolate x.
[tex]\frac{16}{20} + x - \frac{16}{20} = \frac{20}{20} - \frac{16}{20}[/tex]
[tex]x = \frac{4}{20}[/tex]
We can finally simplify the fraction by dividing both the top and bottom by 4. Doing this, we get
[tex]x=\frac{1}{5}[/tex]
