Question

Jacob has some cookies. 3/4 of his cookies are chocolate chip. Out of the chocolate chip cookies 1/8 of them have nuts as well. What fraction of Jacobs cookies are chocolate chip cookies with nuts?

Answer 1

Well, we can find the answer by multiplying the two fractions. 3/4*1/8 equals 3/32.

Answer 2

The answer is:  " $\frac{1}{6}$ " . 
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Explanation:
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Given the fractions: 

"3/4" ;  and "1/8" ; 

Note the "denominators:  "4" and "8" .

We can easily convert "3/4" to its fraction value with a denominator of "8" ; 

→ "3/4" =  " (what value?) / 8"  ?

→  Look at the "denominators" :
 
 →  4 * (what value?) = "8" ? ;  → "8 ÷ 4 = "2" ; 

→ So, 4 * 2  = 8 ;  for the "denominator" ;  so we multiply by "2" in the 
"numerator" , as well:

→ "(3/4)" = (3*2)/(4*2) = "6/8" ;
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→  "3/4"  =  "6/8" ; 
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→  Note:  The entire batch of cookies is:  "8/8" ; or "1 whole" ; 
       {since:  "8/8" = "{8÷8 = 1 whole}" ; 
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Given:  "3/4" of the {entire batch of} his cookies are chocolate chip." ; 

i.e.    "6/8 out of 8/8" are chocolate chips ;  
 
6/8 are chocolate chips;

1/8 out of 6/8 are {"chocolate chip with nuts"} ;
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  ==> What fraction of cookies are {"chocolate chip with nuts"} ?
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To get the answer;  we simplify:  "1/8 out of 6/8";  

or, simplify, "1/8 out of 3/4" ; 

that is:

" $\frac{1}{8}$  ÷  $\frac{3}{4}$ " = ? {our answer} ?? ; 

→  " $\frac{1}{8}$  ÷  $\frac{3}{4}$ " ;

→   Note:  When we divide 2 (TWO)  fractions;  we find the equivalent by writing the expression with a multiplication sign; AND by "inverting" (or taking the "reciprocal" of) the "second" fraction ; 

   =      " $\frac{1}{8}$  *  $\frac{4}{3}$ " ; 
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Note:  The "4" cancels out to a "1" ; and the "8" cancels out to a "2" ; 

since:  "{8 ÷ 4 = 2}" ;  and since:  "{4 ÷ 4 = 1 }" ,
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And we can rewrite the expression as:
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→     " $\frac{1}{2}$  *  $\frac{1}{3}$ " ; 

And simplify further:

      =  " $\frac{(1*1)}{(2*3)}$  ; 

      =  " $\frac{1}{6}$ " .
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The answer is:  " $\frac{1}{6}$ " .

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  Variant:  At the point {above} which we have:
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 →      " $\frac{1}{8}$  *  $\frac{4}{3}$ " ; 
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Simplify further; as following: 

       =  " $\frac{(1*4)}{(8*3)}$ ; 

       =  " $\frac{4}{24}$ " ;

       =  " (4 ÷ 4) / (24 ÷ 4) "  ;
 
       =  " $\frac{1}{6}$ " .

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The answer is:  " $\frac{1}{6}$ " . 
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