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The numerator of a fraction is three less than the denominator. Tripling the numerator and quadrupling the denominator results in a fraction equal to $3 / 5$ Determine the original fraction.

$$12 / 15$$

Algebra

Chapter 0

Reviewing the Basics

Section 1

Solving Linear Equations

Equations and Inequalities

Missouri State University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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alright. For this question, we have another fraction and we're gonna be a scene linear equations in order to solve this. And it's linear because the unknown is raised to the power of one. And we know that addition and subtraction under each other and multiplication and division under each other. So and this fraction, we know that the numerator off the fraction is three lessen the denominator and first would just simply write our fraction, which is X over y are given that our numerator is three less than the numerator. So I mean, our numerator is three less than the denominator. So it's three numbers smaller than the denominator. So it's X equals Why am I this tree? And they were also given the fact that if we triple our numerator in quadruple our denominator, we're going to end up with 3/5. So this is three x by four wine. Yes, he put 2 3/5 bigger and now we can replace this X value with y minus three because we know what excess. And that's exactly what we're going to do, which is going to replace X with y my history. Now we have three times Y minus three. Divided by four y equals 3/5. We're going to simplify this and a little bit. Um, so we're gonna put this in like this? Here we go. So we can simplify this a little bit further down. So this is three white, minus nine parentheses. Divided by four. Wine equals three or five. We could just multiply both sides of the equation by four. Wine are gonna do this simply just told isolate our wise. So now we're gonna have three way everywhere minus nine number, the left side. And for the 1/4 y times for white is going to cancel out. So we're gonna have on the right side 3/5 times. Four Y. Yeah. Are simply that's just going to be 12. Wine over five. Oh, that's 12 wine divided by five. And we'll simplify this even further down by multiplying both sides of the equation by five. Look likely. Five. We're gonna distribute the five to this, um, to these parentheses, so it's gonna be 15 way 15. Thanks. Wine minus 45 because nine times nine times five is 45 equals club white. And that's because one or five times five cancels out. It's just one. And now we can shift the 12 fight to the left side and the negative 45 to the right side. So we're going to subtract minus 12 y on both sides of the equation. That's gonna give us three white, right? It's 45. We'll see room. We're going to shift the 45 to the other side. We're gonna ask 45 to both sides of big question. So now we're gonna have three white equals 45 right both sides by three. So isolate why? And that's going to give us why. Equals 15. Oh, our denominator equals 15, and we're gonna plug this value back into the first equation. X equals Y ministry to get the numerator. So we're going to get X equals 15 ministry, which is 12. So our original fraction is simply 12 x over why 15, 12 or 15

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