Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
Given: Two-fifths of the fish in Gary's fish tank are guppies.One-fourth of the guppies are red.
To Find: What fraction of the fish in Gary's tank are red guppies.
Solution:
Let total number of fish in tank be [tex]=\text{x}[/tex]
Number of guppies in tank are [tex]=\frac{2}{5}\text{of total fish}[/tex]
Number of guppies in tank are [tex]=\frac{2}{5}\text{x}[/tex]
Number of red guppies in tank are [tex]=\frac{1}{4}\text{of total guppies}[/tex]
[tex]\frac{1}{4}\times\frac{2}{5}\text{x}[/tex]
[tex]\frac{1}{10}\text{x}[/tex]
Now,
fraction of the fish in Gary's tank that are red guppies
[tex]=\frac{\text{red guppies}}{\text{total fish in Gary's tank}}[/tex]
[tex]\frac{\frac{1}{10}\text{x}}{\text{x}}[/tex]
[tex]\frac{1}{10}[/tex]
Hence [tex]\frac{1}{10}[/tex] of total fish are red guppies.
