Mathematics, 11.09.2019 23:30, arrow87654

If you eat one quarter of a pizza and your dog eats one eighth of it, what percent is left over?

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answered: Elency

The answer is: 62.5 % (left over).

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Step-by-step explanation:

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$\frac{1}{4} + \frac{1}{8} = ?$ ;

Change "(1/4)" to: "(?/8)" ;

What is "(?)" ? ;

→ (1/4) = (?/8) ;

notice the denominators;

(1/4) = (?/8) ; In the first fraction, how does the "denominator", "4" ; turn to "8" ? Specifically, since we dealing with "fractions", what number do we multiply "4" by, to get: "8" ??? ;

→ " 4 * ? = 8 " ?? ;

→ " 8 ÷ 4 = ? " ;

= 2 ;

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so " 1/4 = ?/8 " ;

Since we multiply the denominator, "4" ; by "2" , to get:

"8" (the denominator in the other fraction);

we multiply the numerator, "1" ; by "2" ; to get:

"2" (the denominator in the other fraction):

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→ " $\frac{1}{4} = \frac{(1*2)}{(4*2)} = \frac{2}{8}$ ;

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Now, the amount of the pizza that "you" ate is: "(2/8)" ;

The amount of the pizza eaten by "your dog" is: "(1/8)" ;

Let's add up the amount of pizza eaten:

$\frac{2}{8} + \frac{1}{8} = \frac{(2+1)}{8} = \frac{3}{8}$ .

The total amount of the pizza would be: " $\frac{8}{8}$ " .

Note: " $\frac{8}{8}$ = 8 ÷ 8 = 1 whole [pizza].

To find the amount left over, subtract the amount eaten; "(3/8)" ; from the whole pizza; "(8/8)" ; as follows:

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→ $\frac{8}{8} - \frac{3}{8} = \frac{(8-3)}{8} = \frac{5}{8}$ .

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Now, the question asks, what percent is left over? ;

So, we convert "(5/8)" into a percentage;

Change "(5/8)" to: "(?/100)" ;

→ Notice the denominators;

(5/8) = (?/100) ; In the first fraction, how does the "denominator", "8" ; turn to "100" ? Specifically, since we dealing with "fractions", what number do we multiply "8" by, to get: "100" ??? ;

→ " 8 * ? = 100 " ?? ;

→ " 100 ÷ 8 = ? " ;

= 12.5 ;

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so " 5/8 = ?/100 " ;

Since we multiply the denominator, "8" ; by "12.5" , to get:

"100" (the denominator in the other fraction);

we multiply the numerator, "5" ; by "12.5" ; to get:

"2" (the denominator in the other fraction):

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→ " $\frac{5}{8} = \frac{(5*12.5)}{(100*12.5)} = \frac{62.5}{100}$ ;