Question

Divide 2/3 by 8/15. Simplify your answer

Answer 1

Answer:

5/4

Step-by-step explanation:  

(2/3)/(8/15)

= (2/3)(15/8)

= (2*15)/(3*8)

= 30/24

= 5/4

Answer 2

The correct answer is:  " $\frac{5}{4}$ " ; {written as an improper fraction} ;

                                 or:  " 1.25 " ; {written as a decimal value} ;
                                 or:  " $1\frac{1}{4}$ " ;  {written as a mixed number fraction}.
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Step-by-step explanation:

Given:   $\frac{2}{3}$ ÷ $\frac{8}{15}$ = ? {for which we shall solve}.

Note:  'Dividing by' a value; results in the same value as 'multiplying by' its reciprocal value [that is: 'multiplying by its inverted form'].

This is especially noteworthy in problems that involve 'dividing by fractions'.

So, to solve and simply our given problem:
$\frac{2}{3} * \frac{15}{8}$  =  ? ;
Note:  The 2 cancels out to 1 ; and the 8 cancels out to 4 ;
         The 3 cancels out to 1 ; and the 15 cancels out to 5 ;
→ since:  {8 ÷ 4 =  2 } ;  &  {2 ÷ 2 = 1} ;
        and :

→ since:   {15 ÷ 3 = 5 } ;  & {3 ÷ 3 = 1 } .
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We can rewrite our "further simplified" expression as:
→   $\frac{1}{1}$ * $\frac{5}{4}$  ;

=  "  1 *   $\frac{5}{4}$  " ;

=  "  $\frac{5}{4}$ " .

Further explanations:
1)  Note:  Re:  the "commutative property" of multiplication:
         " a * b = b * a " ;  or, write as:   " ab = ba " ;    
As such:      "  1  *   \frac{5}{4}  " ;  is the same as:
              ↔  "   $\frac{5}{4}$  * 1 " .

2)  Note:  Re:  the identity property of multiplication:
 Any value, multiplied by "1", results in/ retains its same value}.  
As such;  our calculated value:
        "   $\frac{5}{4}$   *  1  "   =    \frac{5}{4}  " .

3)  Note:  Re: the division of one (1) property of division:
Any value, divided by "1" ; results in that same initial value.
As such:  our calculated value:  " $\frac{1}{1}$  = (1 ÷ 1) = 1 " ;

4)  Note:  Re:  the division by itself property of division:
Any value (except "0"), divided by itself, is equal to "1 " ;
As such:  our calculated value:  " $\frac{1}{1}$  = (1 ÷ 1) = 1 " ;
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So, this answer—which is the most simplified, improper fraction—
is: " $\frac{5}{4}$ " .

Or, to write as a mixed fraction:
   Use the mnemonic:

     $\frac{n}{d}$  = M $\frac{a}{d}$ ;

That is: "numerator/denominator =  M( $\frac{a}{d}$ )"  ; {"M a/d" !} l

⇒ in which M is the [calculated singular whole number portion within the mixed number equivalent] ;
⇒ followed by " $\frac{a}{d}$ "  ; in which d is the same denominator as that of the improper fraction ;
⇒ & in which a is the calculated numerator value for the fraction portion for this number ;

So:  " \frac{5}{4}} "  =  (5 ÷ 4)  = 1.25 =   1 $\frac{1}{4}$  " .
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Long division method:
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              1 R 1 ; ⇒    1 + (1/4) ;  that is;  " 1 + (remainder) / (divisor)";
          4⟌5                                           →  1  +  ( 1 / 4)  ;
          −  4                                           =   "  1 $\frac{1}{4}$  ".            
               1       ;               So, " $1\frac{1}{4}$  " ;  as a mixed number fraction.

or:  Use a fraction calculator to convert improper fractions into mixed number fractions.

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or:  Use a calculator:  " {5 ÷ 4} = 1.25 " .

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The correct answer is:  " $\frac{5}{4}$ " ; {written as an improper fraction} ;

                                 or:  " 1.25 " ; {written as a decimal value} ;
                                 or:  "  $1\frac{1}{4}$  " ;  {written as a mixed number fraction}.
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Hope this answer is helpful!

Wishing you the best!

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