The answer is: "
6 (six) books" .
___________________________________________Explanation:___________________________________________The number of books is: "(
⅖)*15" .
___________________________________________Method 1)___________________________________________ 
* 15 = [(15 ÷ 5) * 2] = 3 * 2 =
6 .
___________________________________________Method 2) ___________________________________________
* 15 ;
=

*

;
=

=

=
6 .
_________________________________________________Method 3)_________________________________________________
* 15 ;
=

*

;
→ At this point, we can "cancel out" the "5" to a "1"; &
we can "cancel out" the "15" to a "3" ;
→ {Since: "15 ÷ 5 = 3" ; and since: "5 ÷ 5 = 1"}.
→ And rewrite as: =

*

;
→ At this point, we can rewrite as:
" 2 * 3 " ; and: "2 * 3 =
6 " .
→ {since: "any value, divided by "1", equals that same value};
As such: "

= 2 "; AND:

= 3 .
→ So:

*

= {2 * 3} =
6 .
→ Alternately, we can continue as follows:

*

;
=

=

=
6 .
______________________________________________________ Method 4)_____________________________________________________
* 15 ;
=

*

;
=
→ At this point, we can "cancel out" the "15" in the numerator to a "3"; & we can "cancel out" the "5" in the denominator to a "1" ;
{Since: "15 ÷ 5 = 3" ; and since: "5 ÷ 5 = 1" ;
→ and rewrite as follows:
→

;
→ At this point: since: "2 * 3 = 6" ; & since "1*1 = 1" ;
We can rewrite as:
→

=
![\frac{6}{1} = 6 .\\Alternately, at the point when we have:\\→ [tex] \frac{2*3}{1*1}](https://tex.z-dn.net/?f=%20%5Cfrac%7B6%7D%7B1%7D%20%3D%20%3Cstrong%3E6%3C%2Fstrong%3E%20.%5C%5CAlternately%2C%20at%20the%20point%20when%20we%20have%3A%5C%5C%E2%86%92%20%20%5Btex%5D%20%5Cfrac%7B2%2A3%7D%7B1%2A1%7D%20)
;
→ We can ELIMINATE the "denominator" completely;
Since the denominator, "(1*1)" is equal to "1" ; and since any value (e.g. the "numerator"); divided by "1" (e.g. the value of the denominator); equals the same value (e.g. that same value of the numerator);
As such, we can rewrite; and simplify; our expression (as follows):
→

= { 2 * 3 } =
6 .
_________________________________________________ Method 5)_________________________________________________
* 15 = ?
→ Convert "

" to a decimal value:
Note:

= ? / 10 ???
What value belongs in the "question mark" ??
→ Let us examine the denominators.
We have "5" and "10".
→ 5 * (what value?) = 10? (answer: "2" , by recognition);
→Nonetheless, to get that value: "10 ÷ 5 = ? " ; The answer is: "2" ;
→ To confirm: "5 * 2 =? 10? Yes!
→ As such:

;
=

;
=

;
Convert this value to a decimal value;
→ 4/10 = 4 ÷ 10 ;
→ To divide by "10" ; Take the decimal value (The decimal value in "4" is considered the value "directly after the "4"); and move that value backward ONE decimal space; {since we are DIVIDING by "10" ; and "10" has ONE "zero"}; to get: ".4" ; → Write as: "0.4" ;
→

=

= 0.4 .
Alternately, use a calculator to convert "

" to a decimal value:
→

= 2 ÷ 5 = 0.4 .
Now, we can rewrite:
→

* 15 ;
as: "(0.4)(15)" ; & calculate:
→ (0.4)(15) =
6 .
_______________________________________________
The answer is: "
6 (six) books" .
_______________________________________________