Answer: The answer is: " <u> </u><u>45 </u> % " .
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→ " Twenty-seven is <u> 45 </u> % of 60. "
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Step-by-step explanation:
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The question asks:
" 27 is what % {percentage] of 60 " ? ;
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So: " 27 = (n/100) * 60 " ; Solve for "n" ;
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Method 1:
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→ (n/100) * 60 = 27 ;
Divide each side by 60 :
→ [ (n/100) * 60 ] / 60 = 27 /60 ;
to get:
→ (n/100) = 27/60 ;
Now: Cross-factor multiply:
→ 60n = (27)*(100) ;
to get:
→ 60n = 2700 ;
Divide each side by "60" ;
→ 60n = 2700/ 60 ;
to get: n = 45 ;
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→ The answer is: 45 % .
→ " Twenty-seven is <u>45 %</u> of 60."
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Method 2:
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The question asks:
" 27 is what % {percentage] of 60 " ?
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To solve this problem:
Rephrase this question as:
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" 27 is 60% of what number ? "
→ The answer will be the same!
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→ 27 = (60/100)* n ; Solve for "n" ;
Multiply each side of the equation by "100" ; to eliminate the fraction:
→ 100 * 27 = 100 * [ (60/100)* n ] ;
to get:
→ 2700 = 60n ;
↔ 60n = 2700 ;
Divide Each Side of the equation by "60" ;
→ 60n/60 = 2700 / 60 ;
to get: n = 45 ;
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→ The answer is: 45 % .
→ " Twenty-seven is <u>45 %</u> of 60."
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Method 2: Variant 1 of 2:
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When we have:
→ 27 = (60/100)* n ; Solve for "n" ;
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Note that: "(60/100) = (60÷ 100) = (6 ÷ 10)" ; since: in "(60/100)" ; the "zero" from the "<u>numerator</u>" cancels out; <u>And</u>: the "last zero" in "100" — from the "<u>denominator</u>" cancels out; since we are dividing "each side" of the fraction by "10" ;
→ "(60÷10) / (600÷10)" = " 6/10 " ;
→ " (6/10)" ; that is; "six-tenths"} ;
→ can be represented by: " 0.6 " ;
→ {by convention; but specifically, here is the explanation} — as follows:
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→ "(6/10)" = " (6 ÷ 10) " ;
<u>Note</u>: When dividing a number by "10" ; we take the original number; and move the decimal point to the left; & then we rewrite that number as the "answer".
<u>Note</u>: When multiplying or dividing by a positive, non-zero integer factor of "10" that has at least 1 (one) "zero" after that particular factor of "10". We can get the answer by taking the original number & moving the decimal point the number of spaces as designated by the number of zeros following the particular [aforementioned factor of "10".].
We move the decimal point to the right if we are multiplying; and to the left if we are dividing. In this case, <u>we are dividing</u> "6" by "10 " :
→ " 6 ÷ 10 = ? " ;
→ " 6. ÷ 10 = ? " ;
We take the: " 6. " ; and move the decimal point "<u>one space backward [i.e. "to the left</u>"]; since we are <u>dividing by "</u><u>10</u><u>"</u> ;
→ to get: " .6 " ; & we rewrite this value as "0.6" in a rewritten equation:
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So; we take our equation:
→ 27 = (60/100)*n ; And rewrite—substituting "0.6" for
"(60/100)"— as follows:
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→ 27 = (0.6)n ; ↔ (0.6) n = 27 ;
Multiply each side of the equation by "10" ; to eliminate the decimal:
→ 10 * [ (0.6)n ] = 27 * 10 ;
to get:
→ 6n = 270 ;
Divide each side of the equation by "6" ; to isolate "n" on one side of the equation; & to solve for "n" ;
→ 6n / 6 = 270 / 6 ;
to get: n = 45 ;
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→ The answer is: 45 % .
→ " Twenty-seven is <u>45 %</u> of 60."
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Method 2 (variant 2 of 2):
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We have the equation: 27 = (60/100)* n ; Solve for "n" ;
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<u>Note</u>: From Method 2 (variant) 1 of 2— see above):
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<u>Note</u>: Refer to the point at which we have:
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→ " { (60÷10) / (600÷10)" = " (6/10) " ; that is; "six-tenths"} ;
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Note that the fraction— "(6/10)" ; can be further simplified:
→ "(6/10)" = "(6÷2) / (10÷2)" = "(3/5)" ;
Now, we can rewrite the equation;
→ We replace "(60/100)" ; with: "(3/5)" :
→ 27 = (3/5)* n ; Solve for "n" ;
↔ (3/5)* n = 27 ;
↔ (3n/5) = 27 ;
Multiply Each Side of the equation by "5" ;
→ 5* (3n/5) = 27 * 5 ;
to get:
→ 3n = 135 ;
Divide Each side of the equation by "3" ; to isolate "n" on one side of the equation; & to solve for "n" ;
→ 3n / 3 = 135 / 3 ;
to get: n = 45 ;
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→ The answer is: 45 % .
→ " Twenty-seven is <u>45 %</u> of 60."
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Hope this answer is helpful!
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