Problem 124 Hard Difficulty

If the circle represents a whole, find the missing value.
(FIGURE CANNOT COPY)

Answer

$\frac{1}{20}$

Related Courses

Algebra

Elementary and Intermediate Algebra

Chapter 1

An Introduction to Algebra

Section 2

Fractions

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Problem 124

Video Transcript

this tutorial goes to your question 124 from chapter one, Section two. And we're giving this diagram of a circle. And we're told that if these air the proportion deal, if these are the sections that we know, what is the unknown section? How much of the circle? So we know that obviously all of this is gonna equal one hole, and we also know that we have three different denominators. So these fractions are essentially using three different units. We have to convert them all to the same unit. So I know that 1/2 plus 1/4 plus 1/5 plus my missing piece is gonna equal one hole. But I need to figure out what the common denominator is gonna be. The lowest common denominator. Eso I know that five is prime s O. That means I'm gonna multiply it by the number so I do five times two. That's gonna be 10. And since four is not a factor of 10 I'm gonna multiply for, uh, let me see what it can go into. That's the factor. So if I multiply five times for so five times two is 10 but tens on a fat have multiple of four. So instead of do five times for that's 20 and two is a factor of 20. So so five times to write that out is 10 but four is not a factor of 10. So five times four is 20 and two is a factor of 20 s. Oh, my common denominators here are tech. I mean, is 20. So I am going to create ah equivalent fractions using a form of one to make, uh, equivalent fractions with common denominators selling here right out my equations here heart. So my missing factor here two times 10 is 20 eso one times 10 is 10. So I used my My one was in the form of 10/10 and I just did here five times four is 20. So my missing factor here is five on DSO. My form of one is 5/5 and one time spy This five and then my missing factor here is 45 times four is 20 and one times four is for So really, What I have here is 10 20th plus five 20 s plus four 20th plus My missing piece is going to equal one hole. Well, now I can write my some I know that it's going to be 10 plus five plus four. Over Here you go. 10 plus five plus four over 20. Plus my missing piece on temple If I was 15. 15 plus four is 19. So this is gonna be 19. Here we go. 19 over 20. Plus, my missing piece equals one. Well, I need how many more pieces to get me to 2020 if I need one more piece. So my missing piece is going to be 1/20 because 19 to what rain out of, please. There. Because 19 20th C plus 1/20 is going to give me 2020. It's which is one. So this right here this section is 1/20 on the whole.

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