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pav-90 [236]
3 years ago
9

_ -0.38 written as a fraction is ._____O -7/18O 2/5O -15/36​

Mathematics
2 answers:
vivado [14]3 years ago
8 0

Answer:  The correct answer is:  [A]:  "  -\frac{7}{18}  " ; or, write as:  " \frac{-7}{18} " .

__________

Step-by-step explanation:

__________

<u>We are asked</u>:  

What is:  " - 0.38 " ;  written as a fraction? ;

         → And we are given 3 (three) answer choices:

__________

[A]:  " -7/18 " ;   [B]:  " 2/5 " ;  and: [C]:  " -15/36 ".

__________

Of these 3 (three) choices:

 We can rule out "Choice [B]".

Reason:  This answer choice is the only "positive value" among the 3 (three) answer choices) ; and our given decimal value is a "negative value."

__________

So we have:  Choices:  [A] & [C].

__________

Between: [A]: " -7/18" ; and [C]:  "-15/36 " ;

We can look at each choice; and notice the following:

   1) Answer choice [C]: can be further simplified as a fraction;  since both the numerator AND the denominator can be divided (evenly) by "3":

     \frac{-15}{36} = \frac{(-15/3)}{(36/3)} = \frac{-5}{12}  ;

  2)  Choice [C]:  has a denominator of "36" .

      Choice  [A]: has a denominator of "18" ; which is "one-half" the value of "36" .

         So:  Choice: [A}:  " -7/18 " :

                    →  \frac{-7}{18} = \frac{?}{36} ;

                    →  Looking at the denominators:

                            " 18 * ? = 36 " ;

                          Divide each side by "18" ;

                             " (18 * ?)" / 18 = 36/18 ;

                                      " ? = 2 " ;

                    →   " \frac{-7}{18} = \frac{(-7*2)}{(18*2)} = \frac{-14}{36} " ;

                Choice [C]:  " -15/36 " :

                    →   " \frac{-15}{36} = \frac{?}{18}  " ;

                    →  Looking at the denominators:

                            " 36 ÷ ? = 18 " ;    

                    →  " \frac{36}{?} = 18 " ;

                       → " 18*? = 36 " ;

                         Divide each side by "18" ;

                            " (18 * ?)" / 18 = 36/18 " ;

                                   " ? = 2 " ;

                    → " \frac{-15}{36} = \frac{(-15/2)}{(36/2)}=\frac{-7.5}{18} "

                Additionally: other:

                   → " \frac{-15}{36} = \frac{(-15/3)}{(36/3)}=\frac{-5}{12}

__________

So, we are left with 2 (two) answer choices:

__________

Choice: [A]:  " \frac{-7}{18} = \frac{-14}{36} " ;

__________

Choice: [C]: " \frac{-15}{36} = \frac{-7.5}{18} = \frac{-5}{12} " ;

__________

Using a calculator:

__________

Choice:  [A]:  " \frac{-7}{18} = ( -7 ÷ 18) =  - 0.3888888888.... " ;

And:

Choice:  [C]: " \frac{-15}{36} = ( -15 ÷ 36) = -0.41666666666 ;

__________

So:  The best answer—and correct answer—is clearly:

__________

 Answer choice:  [A]: " - \frac{7}{18} " ;  or write as: " \frac{-7}{18} " .

__________

<u>Also</u>: <u>Note</u>:  Choice: [A]:  " - 7/18 " ;

  → " (- 7 ÷ 18 =  - 0.38888888888... )" ;  using calculator.

__________

Note that the digits "8" keep repeating.

Note that this very Brainly question:

__________

 " brainly.com/question/24891747 " ;

__________

Is written as follows:

__________

" _

 -0.38 written as a fraction is ._____  ....and continues" ;

__________

→ so it could have been written meaning to denote that there was a "repeating bar" on the digit "8" in the decimal.

→ If so, here is one way the answer could be solved without a calculator:

__________

{We would rule out "choice: [B]:  \frac{2}{5}; a positive value; equal to: " + 0.4".}. ;

__________

Assuming: we are given:  " - 0.38 ;  with a repeating bar on the (digit; "8") ;

meaning the "8" goes on infinitely:

__________

Let:  x = - 0.38 (with the repeating bar on the (digit, "8" ) ;

And thus: "10x" would equal "10 times that value:

 →  10x = - 3.8 (with a repeating bar on the (digit, "8") ;

__________

10x − 1x = 9x ;

__________

  10x  =  - 3.8888888888888888888......

−   1x  =  - 0.38888888888888888888......

______________________________

   9x =  - 3.5 00000000000000000000.

{<u>Note</u>: " 10x − 1x = 9x " ;   " - 3.8 − (-0.3) =  - 3.8 + 0.3 =  -3.5 "} ;

__________

→     9x =  - 3.5 00000000000000000000 ....

__________

 →  9x = - 3.5 ;

__________

Now, divide Each Side of the equation by "9" ;

 to isolate "x" on one side of the equation;

 and to solve for "x" :

__________

 →  9x / 9 =  - 3.5 / 9 ;

to get:

    →   x = - 3.5 / 9 ;

__________

Now, to get rid of the decimal value; multiple each side of the equation by   "10" :

__________

    →  " x = \frac{-3.5}{9} = \frac{(-3.5)*10}{9*10} = \frac{-35}{90} " ;

This fraction is not among choices [A] or [C];  and it can be further reduced/simplified:

    →  " \frac{-35}{90} "  ;  Divide Each side by "5" :

__________

    →  " \frac{(-35/5)}{(90/5)} = \frac{-7}{18} " ;

    →  which is:  Answer choice:  [A]:  " \frac{-7}{18} " .

__________

Hope this lengthy explanation is of help to you!

 Best wishes!

__________

Paladinen [302]3 years ago
7 0
19
50 because -0.38= 38/100
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