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

Answer:

1. $Dexter = 11:5$  $Lena = 9:4$

2. $Dexter = \frac{11}{5}$  $Lena = \frac{9}{4}$

3. $Dexter = \frac{44}{20}$   $Lena = \frac{45}{20}$

4. $\frac{45}{20} > \frac{44}{20}$

Step-by-step 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

$Fraction = \frac{S}{H}$

$Dexter = \frac{11}{5}$

$Lena = \frac{9}{4}$

Solving (3): Write as a common denominator

$Dexter = \frac{11}{5}$

Multiply by $\frac{4}{4}$

$Dexter = \frac{11}{5} * \frac{4}{4}$

$Dexter = \frac{44}{20}$

$Lena = \frac{9}{4}$

Multiply by $\frac{5}{5}$

$Lena = \frac{9}{4} * \frac{5}{5}$

$Lena = \frac{45}{20}$

Solving (4): Compare both fractions

By comparison;

$\frac{45}{20}$ is greater than $\frac{44}{20}$

So, we have:

$\frac{45}{20} > \frac{44}{20}$