Question

What is 1/2 x 2/3 x 3/4

Answer 1

       
I believe the answer is 0.25

Answer 2

The answer is:  "  $\frac{1}{4}$ " ;  or, write as:  "0.25" .
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Explanation:
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Method 1)
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$\frac{1}{2}$*$\frac{2}{3}$*$\frac{3}{4}$ ;

= $\frac{1 * 2 * 3}{2* 3 *4}$ ;

= $\frac{6}{24}$ ; 

= $\frac{6/6}{24/6}$ ;

= $\frac{1}{4}$ ;  or, write as:  "0.25" .
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Method 2)
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$\frac{1}{2}$*$\frac{2}{3}$*$\frac{3}{4}$ ;

= $\frac{1 * 2 * 3}{2* 3 *4}$ ;

→ The "2's" & "3's" in both the numerator & denominator "cancel out" to "1" ;  {since:  "(2÷2=1)" ; and "(3÷3=1" ) ; 

→ And we have:

   →  $\frac{1 * 1 * 1}{1 * 1 * 4}$ ;

            =  $\frac{1}{4}$ ;  or; write as:  "0.25" .
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Method 3)  (similar to "Method 2" above):
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$\frac{1}{2}$*$\frac{2}{3}$*$\frac{3}{4}$ ;

= $\frac{1 * 2 * 3}{2* 3 *4}$ ;

→ The "2" in numerator cancels out to "1" ; and the "4" in the denominator cancels to "2" ;  {since:  "(4÷2=2)" ; and since: "(2÷2=1)" ;

→  The "3's" in both the numerator AND denominator "cancel out" to "1" ;                      {since:  "(3÷3=1" ) ; 

→ And we have:

   →  $\frac{1 * 1 * 1}{2 * 1 * 2}$ ;

            =  $\frac{1}{4}$ ;  or; write as:  "0.25" .
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Method 4)
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$\frac{1}{2}$*$\frac{2}{3}$*$\frac{3}{4}$ ;

→ Cancel out the "2" in the denominator of "$\frac{1}{2}$" ; to a "1" ; AND cancel out the "2" in the numerator of "$\frac{2}{3}$ " ; to a "1" ;
       {since: "{2÷2=1}" ;
 
 → Cancel out the "3" in the denominator of "$\frac{2}{3}$ " ; to a "1" ;
AND cancel out the "3" in the numerator of: "$\frac{3}{4}$" ; to a "1" ;
      {since:  "(3÷3=1}" ;

→ And we have:

   →  $\frac{1}{1}$ * $\frac{1}{1}$ * $\frac{1}{4}$ ; 

              = $\frac{1 * 1 * 1}{1 * 1 *4}$ ; 
           
              =  $\frac{1}{4}$ ;  or; write as:  "0.25" .
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Variation:
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At the point when we have:
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   → $\frac{1}{1}$ * $\frac{1}{1}$ * $\frac{1}{4}$ ; 
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We can eliminate the: 

"  $\frac{1}{1}$  *  $\frac{1}{1}$  " ;

{since: "  $\frac{1}{1}$ = 1 " ; 

{and since:  "  $\frac{1}{1}$  *  $\frac{1}{1}$  "  =  1 * 1 = 1 ; 

and since: "1", multiplied by any value, equals that exact same value; 
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THAT IS:
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    → $\frac{1}{1}$  *  $\frac{1}{1}$   *  $\frac{1}{4}$  ;

         =  1  *  1  *  $\frac{1}{4}$ ;

         =  (1 * 1)  *  $\frac{1}{4}$ ;

         =    1 *   $\frac{1}{4}$  ;
  
         =    $\frac{1}{4}$ ;  or, write as:  "0.25" .
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Method 5)   (similar to "Method 4" above):
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$\frac{1}{2}$*$\frac{2}{3}$*$\frac{3}{4}$  ;

  → Cancel out the "2" in the numerator of "$\frac{2}{3}$" ; to a " 1 " ; 
AND cancel out the "4" in the denominator of "$\frac{3}{4}$"; to a "2" ;
       {since: "{4÷2=2}" ; and since: "{2÷2=1}" ; 

  → Cancel out the "3" in the denominator of "$\frac{2}{3}$ " ; to a "1" ;
AND cancel out the "3" in the numerator of: "$\frac{3}{4}$" ; to a "1" ;
      {since:  "(3÷3=1}" ;

→ And we have:
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   →  $\frac{1}{2}$ * $\frac{1}{1}$ * $\frac{1}{2}$ ; 

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

                      =  $\frac{1}{4}$ ; or, write as:  "0.25" .
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Variation:
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At the point when we have:
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   →  $\frac{1}{2}$ * $\frac{1}{1}$ * $\frac{1}{2}$ ; 
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We can eliminate the: 

"  $\frac{1}{1}$  " ; 

{since: "  $\frac{1}{1}$  =  1 " } ; 

{and since: "1", multiplied by any value, equals that exact same value} ; 
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THAT IS:
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   →  $\frac{1}{2}$ * $\frac{1}{1}$ * $\frac{1}{2}$ ; 

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

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

          =    $\frac{1*1}{2*2}$  ;

              =  $\frac{1}{4}$ ; or, write as:  "0.25" .
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