Question

Two-fifths of the fish in Gary's fish tank are guppies.One-fourth of the guppies are red.What fraction of the fish in Gary's tank are red guppies?Show your work.

Answer 1

How many fish are there in all? We need that to answer the question.

Answer 2

`(1)/(10)`

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
`=\text{x}`

Number of guppies in tank are
`=(2)/(5)\text{of total fish}`

Number of guppies in tank are
`=(2)/(5)\text{x}`

Number of red guppies in tank are
`=(1)/(4)\text{of total guppies}`

`(1)/(4)*(2)/(5)\text{x}`

`(1)/(10)\text{x}`

Now,

fraction of the fish in Gary's tank that are red guppies

`=\frac{\text{red guppies}}{\text{total fish in Gary's tank}}`

`\frac{(1)/(10)\text{x}}{\text{x}}`

`(1)/(10)`

Hence
`(1)/(10)` of total fish are red guppies.