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Answer: The correct answer is: [A]: " [tex]-\frac{7}{18}[/tex] " ; or, write as: " [tex]\frac{-7}{18}[/tex] " .
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Step-by-step explanation:
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We are asked:
What is: " - 0.38 " ; written as a fraction? ;
→ And we are given 3 (three) answer choices:
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[A]: " -7/18 " ; [B]: " 2/5 " ; and: [C]: " -15/36 ".
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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."
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So we have: Choices: [A] & [C].
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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":
[tex]\frac{-15}{36} = \frac{(-15/3)}{(36/3)} = \frac{-5}{12}[/tex] ;
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 " :
→ [tex]\frac{-7}{18} = \frac{?}{36}[/tex] ;
→ Looking at the denominators:
" 18 * ? = 36 " ;
Divide each side by "18" ;
" (18 * ?)" / 18 = 36/18 ;
" ? = 2 " ;
→ " [tex]\frac{-7}{18} = \frac{(-7*2)}{(18*2)} = \frac{-14}{36}[/tex] " ;
Choice [C]: " -15/36 " :
→ " [tex]\frac{-15}{36} = \frac{?}{18}[/tex] " ;
→ Looking at the denominators:
" 36 ÷ ? = 18 " ;
→ " [tex]\frac{36}{?} = 18[/tex] " ;
→ " [tex]18*? = 36[/tex] " ;
Divide each side by "18" ;
" (18 * ?)" / 18 = 36/18 " ;
" ? = 2 " ;
→ " [tex]\frac{-15}{36} = \frac{(-15/2)}{(36/2)}=\frac{-7.5}{18}[/tex] "
Additionally: other:
→ " [tex]\frac{-15}{36} = \frac{(-15/3)}{(36/3)}=\frac{-5}{12}[/tex]
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So, we are left with 2 (two) answer choices:
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Choice: [A]: " [tex]\frac{-7}{18} = \frac{-14}{36}[/tex] " ;
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Choice: [C]: " [tex]\frac{-15}{36} = \frac{-7.5}{18} = \frac{-5}{12}[/tex] " ;
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Using a calculator:
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Choice: [A]: " [tex]\frac{-7}{18}[/tex] = ( -7 ÷ 18) = - 0.3888888888.... " ;
And:
Choice: [C]: " [tex]\frac{-15}{36}[/tex] = ( -15 ÷ 36) = -0.41666666666 ;
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So: The best answer—and correct answer—is clearly:
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Answer choice: [A]: " [tex]- \frac{7}{18}[/tex] " ; or write as: " [tex]\frac{-7}{18}[/tex] " .
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Also: Note: Choice: [A]: " - 7/18 " ;
→ " (- 7 ÷ 18 = - 0.38888888888... )" ; using calculator.
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Note that the digits "8" keep repeating.
Note that this very Brainly question:
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" https://brainly.com/question/24891747 " ;
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Is written as follows:
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" _
-0.38 written as a fraction is ._____ ....and continues" ;
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→ 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:
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{We would rule out "choice: [B]: [tex]\frac{2}{5}[/tex]; a positive value; equal to: " + 0.4".}. ;
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Assuming: we are given: " - 0.38 ; with a repeating bar on the (digit; "8") ;
meaning the "8" goes on infinitely:
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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") ;
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10x − 1x = 9x ;
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10x = - 3.8888888888888888888......
− 1x = - 0.38888888888888888888......
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9x = - 3.5 00000000000000000000.
{Note: " 10x − 1x = 9x " ; " - 3.8 − (-0.3) = - 3.8 + 0.3 = -3.5 "} ;
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→ 9x = - 3.5 00000000000000000000 ....
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→ 9x = - 3.5 ;
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Now, divide Each Side of the equation by "9" ;
to isolate "x" on one side of the equation;
and to solve for "x" :
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→ 9x / 9 = - 3.5 / 9 ;
to get:
→ x = - 3.5 / 9 ;
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Now, to get rid of the decimal value; multiple each side of the equation by "10" :
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→ " x = [tex]\frac{-3.5}{9} = \frac{(-3.5)*10}{9*10} = \frac{-35}{90}[/tex] " ;
This fraction is not among choices [A] or [C]; and it can be further reduced/simplified:
→ " [tex]\frac{-35}{90}[/tex] " ; Divide Each side by "5" :
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→ " [tex]\frac{(-35/5)}{(90/5)} = \frac{-7}{18}[/tex] " ;
→ which is: Answer choice: [A]: " [tex]\frac{-7}{18}[/tex] " .
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Hope this lengthy explanation is of help to you!
Best wishes!
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