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?

2 answers:

8 0

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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