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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 :

MrRoyal

Answer:

1. [tex]Dexter = 11:5[/tex]  [tex]Lena = 9:4[/tex]

2. [tex]Dexter = \frac{11}{5}[/tex]  [tex]Lena = \frac{9}{4}[/tex]

3. [tex]Dexter = \frac{44}{20}[/tex]   [tex]Lena = \frac{45}{20}[/tex]

4. [tex]\frac{45}{20} > \frac{44}{20}[/tex]

Step-by-step explanation:

Given

Dexter

[tex]Science\ Fiction = 11[/tex]

[tex]History = 5[/tex]

Lena

[tex]Science\ Fiction = 9[/tex]

[tex]History = 4[/tex]

Solving (1): Write as ratio

Represent Science Fiction with S and History with H

For Dexter;

[tex]Ratio = S : H[/tex]

[tex]Dexter = 11:5[/tex]

[tex]Lena = 9:4[/tex]

Solving (2): Write ratio as fraction

[tex]Fraction = \frac{S}{H}[/tex]

[tex]Dexter = \frac{11}{5}[/tex]

[tex]Lena = \frac{9}{4}[/tex]

Solving (3): Write as a common denominator

[tex]Dexter = \frac{11}{5}[/tex]

Multiply by [tex]\frac{4}{4}[/tex]

[tex]Dexter = \frac{11}{5} * \frac{4}{4}[/tex]

[tex]Dexter = \frac{44}{20}[/tex]

[tex]Lena = \frac{9}{4}[/tex]

Multiply by [tex]\frac{5}{5}[/tex]

[tex]Lena = \frac{9}{4} * \frac{5}{5}[/tex]

[tex]Lena = \frac{45}{20}[/tex]

Solving (4): Compare both fractions

By comparison;

[tex]\frac{45}{20}[/tex] is greater than [tex]\frac{44}{20}[/tex]

So, we have:

[tex]\frac{45}{20} > \frac{44}{20}[/tex]

Answer:

d

Step-by-step explanation:

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