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3 years ago

Justify why a/b x b/c x c/d x d/ e is equal to a/e when b,c,d, and e are not zero?

1 answer:

5 0

When you multiply fractions, you multiply across, right? so, for example 5/7 times 4/9 will give you 20/63. So, if you do this to this problem, you will have abcd/bcde. but now you are able to cancel out the b and c and d. think of it like reducing. 5/10 is 1/2. Why? because if you reduce/factor out a 5, you get a 1 in the numerator and a 2 in the denominator. same thing here; you can factor out a b, c, and d(because they show up in both num. and denom. so what you are left with is a/e. Cheers!

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3 years ago

Twenty-seven is % of 60 help mee asap

jok3333 [9.3K]

Answer: The answer is: " 45 % " .

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→ " Twenty-seven is 45 % 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 45 % 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 ;

________________________________________________

→ The answer is: 45 % .

→ " Twenty-seven is 45 % of 60."

________________________________________________

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 "numerator" cancels out; And: the "last zero" in "100" — from the "denominator" 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) " ;

Note: 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".

Note: 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, we are dividing "6" by "10 " :

→ " 6 ÷ 10 = ? " ;

→ " 6. ÷ 10 = ? " ;

We take the: " 6. " ; and move the decimal point "one space backward [i.e. "to the left"]; since we are dividing by "10" ;

→ 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 45 % of 60."

________________________________________________

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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Note: From Method 2 (variant) 1 of 2— see above):

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Note: 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 45 % of 60."

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Hope this answer is helpful!

Wishing you the best in your academic endeavors

— and within the "Brainly" community!

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7 0

3 years ago

Read 2 more answers

9. The ticket at right has a perimeter of 42 cm.

Liula [17]

Perimeter simply represents the sum of all side lengths of a shape. The length of the missing side of the ticket is 5 cm; the length of gold line on each ticket is 20 cm, and 2 bottles of gold ink are required to draw gold lines on 200 tickets.