Question

Mariah borrowed 15 books from the library last month. She's already read 2/5 of them. How many of the 15 books has she read?

Answer 1

The answer is:  "6 (six) books" .
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Explanation:
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The number of books is:  "(⅖)*15" .
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Method 1)
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   $\frac{2}{5}$ * 15 =  [(15 ÷ 5) * 2] = 3 * 2 = 6 .
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Method 2) 
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$\frac{2}{5}$ * 15 ;

= $\frac{2}{5}$ * $\frac{15}{1}$ ;

= $\frac{2*15}{5*1}$ = $\frac{30}{5}$ = 6 .
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Method 3)
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$\frac{2}{5}$ * 15 ;

= $\frac{2}{5}$ * $\frac{15}{1}$ ;

   → 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: = $\frac{2}{1}$ * $\frac{3}{1}$ ;

                    → 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:  " $\frac{2}{1}$ = 2 ";  AND:  $\frac{3}{1}$ = 3 .

→  So: $\frac{2}{1}$ * $\frac{3}{1}$  = {2 * 3} = 6 .

→ Alternately, we can continue as follows:

$\frac{2}{1}$ * $\frac{3}{1}$ ;

=  $\frac{2*3}{1*1}$ = $\frac{6}{1}$ = 6 .
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Method 4)
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$\frac{2}{5}$ * 15 ;

           = $\frac{2}{5}$ * $\frac{15}{1}$ ;

           = $\frac{2*15}{5*1}$ 

               →  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:

               →  $\frac{2*3}{1*1}$ ;

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

→  $\frac{2*3}{1*1}$   =  $\frac{6}{1} = 6 .\\Alternately, at the point when we have:\\→ [tex] \frac{2*3}{1*1}$  ;  

→  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):

   →  $\frac{2*3}{1*1}$   = { 2 * 3 }  = 6 .
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Method 5)
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$\frac{2}{5}$ * 15 = ?

→ Convert "$\frac{2}{5}$" to a decimal value:

Note:   $\frac{2}{5}$  = ? / 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:  $\frac{2}{5}$ ;
           
                =  $\frac{2*2}{5*2}$ ;
                        
                = $\frac{4}{10}$ ; 

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"  ;
 
        → $\frac{2}{5}$  = $\frac{4}{10}$ =  0.4  .

Alternately, use a calculator to convert "$\frac{2}{5}$" to a decimal value:

      →  $\frac{2}{5}$  =  2 ÷ 5 = 0.4 .

Now, we can rewrite:

     →   $\frac{2}{5}$ * 15  ;

as:  "(0.4)(15)" ; & calculate:
 
      → (0.4)(15) = 6 .
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 The answer is:  "6 (six) books" .
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Answer 2

She has read 6 of the books from the library.