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" .
___________________________________________
Step-by-step explanation:
___________________________________________
The number of books is: "(⅖)*15" .
___________________________________________
Method 1)
___________________________________________

`(2)/(5)` * 15 = [(15 ÷ 5) * 2] = 3 * 2 = 6 .
___________________________________________
Method 2)
___________________________________________


`(2)/(5)` * 15 ;

=
`(2)/(5)` *
`(15)/(1)` ;

=
`(2*15)/(5*1)` =
`(30)/(5)` = 6 .
_________________________________________________

Method 3)
_________________________________________________

`(2)/(5)` * 15 ;

=
`(2)/(5)` *
`(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: =
`(2)/(1)` *
`(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: "
`(2)/(1)` = 2 "; AND:
`(3)/(1)` = 3 .

→ So:
`(2)/(1)` *
`(3)/(1)` = {2 * 3} = 6 .

→ Alternately, we can continue as follows:


`(2)/(1)` *
`(3)/(1)` ;

=
`(2*3)/(1*1)` =
`(6)/(1)` = 6 .
______________________________________________________

Method 4)
_____________________________________________________


`(2)/(5)` * 15 ;

=
`(2)/(5)` *
`(15)/(1)` ;

=
`(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:

→
`(2*3)/(1*1)` ;

→ At this point: since: "2 * 3 = 6" ; & since "1*1 = 1" ;

We can rewrite as:

→
`(2*3)/(1*1)` =
`image` ;

→ 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)/(1*1)` = { 2 * 3 } = 6 .
_________________________________________________

Method 5)
_________________________________________________


`(2)/(5)` * 15 = ?

→ Convert "
`(2)/(5)`" to a decimal value:

Note:
`(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:
`(2)/(5)` ;

=
`(2*2)/(5*2)` ;

=
`(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" ;

→
`(2)/(5)` =
`(4)/(10)` = 0.4 .

Alternately, use a calculator to convert "
`(2)/(5)`" to a decimal value:

→
`(2)/(5)` = 2 ÷ 5 = 0.4 .

Now, we can rewrite:

→
`(2)/(5)` * 15 ;

as: "(0.4)(15)" ; & calculate:

→ (0.4)(15) = 6 .
_______________________________________________

The answer is: "6 (six) books" .
_______________________________________________

Answer 2

She has read 6 of the books from the library.