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the denominator of a certain fraction was 147 greater than its numerator. what was the denominator of this fraction, if after the fraction was reduced it became 5/12 ?

Respuesta :

After reducing the fraction it becomes equal to 5/12. Let the common element which was cancelled out be x. So we can say the original fraction was [tex] \frac{5x}{12x} [/tex].

The denominator of the fraction is 147 greater than the numerator. We can write it as:

12x = 147 + 5x
12x - 5x = 147
7x = 147
x = 21

Thus, the numerator of the fraction was 5 x 21 = 105Denominator of the fraction was 12 x 21 = 252

So the original fraction was [tex] \frac{105}{252} [/tex]

The value of denominator of the fraction, which become 5/12 after the fraction was reduced, is 252.

What is the fraction number?

A fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,

[tex]\dfrac{a}{b}[/tex]

Here, (a) is the numerator and (b) is the denominator.

Suppose the x is the numerator and y is the denominator.

Here, it has given that the denominator of a certain fraction was 147 greater than its numerator. Therefore,

[tex]x+147=y\\x=y-147[/tex]

After the fraction was reduced, the fraction number became 5/12. As, the fraction number value has some even that it reduced in the simple form therefore,

[tex]\dfrac{x}{y}=\dfrac{5}{12}\\{x}=\dfrac{5}{12}\times y[/tex]

Put the value of x, from equation 1, in the above expression as,

[tex]y-147=\dfrac{5}{12}\times y\\12(y-147)=5y\\12y-1764=5y\\12y-5y=1764\\7y=1764\\y=252[/tex]

Hence, the value of denominator of the fraction, which become 5/12 after the fraction was reduced, is 252.

Learn more about the fraction number here:

https://brainly.com/question/78672

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