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: "
`(1)/(4)` " ; or, write as: "0.25" .
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Step-by-step explanation:
__________
Method 1)
__________

`(1)/(2)`*
`(2)/(3)`*
`(3)/(4)` ;

=
`(1 * 2 * 3)/(2* 3 *4)` ;

=
`(6)/(24)` ;

=
`(6/6)/(24/6)` ;

=
`(1)/(4)` ; or, write as: "0.25" .
_________________
Method 2)
_________________

`(1)/(2)`*
`(2)/(3)`*
`(3)/(4)` ;

=
`(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:

→
`(1 * 1 * 1)/(1 * 1 * 4)` ;

=
`(1)/(4)` ; or; write as: "0.25" .
________________
Method 3) (similar to "Method 2" above):
_________________

`(1)/(2)`*
`(2)/(3)`*
`(3)/(4)` ;

=
`(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:

→
`(1 * 1 * 1)/(2 * 1 * 2)` ;

=
`(1)/(4)` ; or; write as: "0.25" .
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Method 4)
_______________

`(1)/(2)`*
`(2)/(3)`*
`(3)/(4)` ;

→ Cancel out the "2" in the denominator of "
`(1)/(2)`" ; to a "1" ; AND cancel out the "2" in the numerator of "
`(2)/(3)` " ; to a "1" ;
{since: "{2÷2=1}" ;

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

→ And we have:

→
`(1)/(1)` *
`(1)/(1)` *
`(1)/(4)` ;

=
`(1 * 1 * 1)/(1 * 1 *4)` ;

=
`(1)/(4)` ; or; write as: "0.25" .
________________
Variation:
________________
At the point when we have:
________________

→
`(1)/(1)` *
`(1)/(1)` *
`(1)/(4)` ;
________________
We can eliminate the:

"
`(1)/(1)` * 
`(1)/(1)` " ;

{since: "
`(1)/(1)` = 1 " ;

{and since: "
`(1)/(1)` * 
`(1)/(1)` " = 1 * 1 = 1 ;

and since: "1", multiplied by any value, equals that exact same value;
_____________
THAT IS:
_____________
→ 
`(1)/(1)` * 
`(1)/(1)` *
`(1)/(4)` ;

= 1 * 1 *
`(1)/(4)` ;

= (1 * 1) *
`(1)/(4)` ;

= 1 *
`(1)/(4)` ;

=
`(1)/(4)` ; or, write as: "0.25" .
_____________
Method 5) (similar to "Method 4" above):
____________________

`(1)/(2)`*
`(2)/(3)`*
`(3)/(4)` ;

→ Cancel out the "2" in the numerator of "
`(2)/(3)`" ; to a " 1 " ;
AND cancel out the "4" in the denominator of "
`(3)/(4)`"; to a "2" ;
{since: "{4÷2=2}" ; and since: "{2÷2=1}" ;

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

→ And we have:
_____________
→
`(1)/(2)` *
`(1)/(1)` *
`(1)/(2)` ;

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

=
`(1)/(4)` ; or, write as: "0.25" .
__________
Variation:
__________
At the point when we have:
__________
→
`(1)/(2)` *
`(1)/(1)` *
`(1)/(2)` ;
__________
We can eliminate the:

"
`(1)/(1)` " ;

{since: "
`(1)/(1)` = 1 " } ;

{and since: "1", multiplied by any value, equals that exact same value} ;
___________
THAT IS:
___________
→
`(1)/(2)` *
`(1)/(1)` *
`(1)/(2)` ;

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

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

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

=
`(1)/(4)` ; or, write as: "0.25" .
__________________________________________________________