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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[tex] \frac{2}{5} [/tex] * 15 = [(15 ÷ 5) * 2] = 3 * 2 = 6 .
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Method 2)
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[tex] \frac{2}{5} [/tex] * 15 ;
= [tex] \frac{2}{5} [/tex] * [tex] \frac{15}{1} [/tex] ;
= [tex] \frac{2*15}{5*1} [/tex] = [tex] \frac{30}{5} [/tex] = 6 .
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Method 3)
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[tex] \frac{2}{5} [/tex] * 15 ;
= [tex] \frac{2}{5} [/tex] * [tex] \frac{15}{1} [/tex] ;
→ 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: = [tex] \frac{2}{1} [/tex] * [tex] \frac{3}{1} [/tex] ;
→ 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: " [tex] \frac{2}{1} [/tex] = 2 "; AND: [tex] \frac{3}{1} [/tex] = 3 .
→ So: [tex] \frac{2}{1} [/tex] * [tex] \frac{3}{1} [/tex] = {2 * 3} = 6 .
→ Alternately, we can continue as follows:
[tex] \frac{2}{1} [/tex] * [tex] \frac{3}{1} [/tex] ;
= [tex] \frac{2*3}{1*1} [/tex] = [tex] \frac{6}{1} [/tex] = 6 .
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Method 4)
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[tex] \frac{2}{5} [/tex] * 15 ;
= [tex] \frac{2}{5} [/tex] * [tex] \frac{15}{1} [/tex] ;
= [tex] \frac{2*15}{5*1} [/tex]
→ 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:
→ [tex] \frac{2*3}{1*1} [/tex] ;
→ At this point: since: "2 * 3 = 6" ; & since "1*1 = 1" ;
We can rewrite as:
→ [tex] \frac{2*3}{1*1} [/tex] = [tex] \frac{6}{1} = 6 .
Alternately, at the point when we have:
→ [tex] \frac{2*3}{1*1} [/tex] ;
→ 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):
→ [tex] \frac{2*3}{1*1} [/tex] = { 2 * 3 } = 6 .
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Method 5)
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[tex] \frac{2}{5} [/tex] * 15 = ?
→ Convert "[tex] \frac{2}{5} [/tex]" to a decimal value:
Note: [tex] \frac{2}{5} [/tex] = ? / 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: [tex] \frac{2}{5} [/tex] ;
= [tex] \frac{2*2}{5*2} [/tex] ;
= [tex] \frac{4}{10} [/tex] ;
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" ;
→ [tex] \frac{2}{5} [/tex] = [tex] \frac{4}{10} [/tex] = 0.4 .
Alternately, use a calculator to convert "[tex] \frac{2}{5} [/tex]" to a decimal value:
→ [tex] \frac{2}{5} [/tex] = 2 ÷ 5 = 0.4 .
Now, we can rewrite:
→ [tex] \frac{2}{5} [/tex] * 15 ;
as: "(0.4)(15)" ; & calculate:
→ (0.4)(15) = 6 .
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The answer is: "6 (six) books" .
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