Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Aug 10, 2023

Find the fraction of books in a library that are both fiction and paperback, given that $\frac{2}{9}$ of the books are fiction and $\frac{5}{7}$ of the fiction books are paperback.

STEP 1

Assumptions1. The fraction of books that are fiction is $\frac{}{9}$ . The fraction of fiction books that are paperback is $\frac{5}{7}$
3. We are looking for the fraction of all books that are both fiction and paperback

STEP 2

To find the fraction of all books that are both fiction and paperback, we need to multiply the fraction of books that are fiction by the fraction of those fiction books that are paperback.
$Fraction\, of\, fiction\, paperbacks = Fraction\, of\, fiction \\times Fraction\, of\, paperbacks\, among\, fiction$

STEP 3

Now, plug in the given values for the fraction of books that are fiction and the fraction of those fiction books that are paperback.
$Fraction\, of\, fiction\, paperbacks = \frac{2}{9} \\times \frac{5}{7}$

STEP 4

Calculate the fraction of all books that are both fiction and paperback.
$Fraction\, of\, fiction\, paperbacks = \frac{2}{9} \\times \frac{}{7} = \frac{10}{63}$ The fraction of the books in the library that are both fiction and paperbacks is $\frac{10}{63}$ .

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