Question

Dexter read 11 science fiction books and 5 history books. Lena read 9 science fiction books and 4 history books. Compare the students' ratios of science fiction books to history books. 1. Determine the ratios' form: science fiction books to history books 2. Write the ratios as fractions: Dexter: 11 5 ; Lena: 9 4 3. Rewrite with a common denominator. 4. Compare. 5. Answer the question. Determine which shows the correct comparison of the ratios for this problem.

Answer 1

d

Explanation:

Answer 2

1.
`Dexter = 11:5`
`Lena = 9:4`

2.
`Dexter = (11)/(5)`
`Lena = (9)/(4)`

3.
`Dexter = (44)/(20)`
`Lena = (45)/(20)`

4.
`(45)/(20) > (44)/(20)`

Explanation:

Given

Dexter

`Science\ Fiction = 11`

`History = 5`

Lena

`Science\ Fiction = 9`

`History = 4`

Solving (1): Write as ratio

Represent Science Fiction with S and History with H

For Dexter;

`Ratio = S : H`

`Dexter = 11:5`

`Lena = 9:4`

Solving (2): Write ratio as fraction

`Fraction = (S)/(H)`

`Dexter = (11)/(5)`

`Lena = (9)/(4)`

Solving (3): Write as a common denominator

`Dexter = (11)/(5)`

Multiply by
`(4)/(4)`

`Dexter = (11)/(5) * (4)/(4)`

`Dexter = (44)/(20)`

`Lena = (9)/(4)`

Multiply by
`(5)/(5)`

`Lena = (9)/(4) * (5)/(5)`

`Lena = (45)/(20)`

Solving (4): Compare both fractions

By comparison;

`(45)/(20)` is greater than
`(44)/(20)`

So, we have:

`(45)/(20) > (44)/(20)`