Video: Computing Unit Rates Associated with Ratios of Fractions

Matthew sweeps two-ninths of the hall floor in 15 minutes, or one-quarter of an hour. What fraction of the floor does he sweep in one hour? How long does it take for him to sweep the whole floor?

02:32

Video Transcript

Matthew sweeps two-ninths of the hall floor in 15 minutes, or one-quarter of an hour. What fraction of the floor does he sweep in one hour? And how long does it take for him to sweep the whole floor?

We’ve been given this really helpful diagram. Our bottom line is the time and our top line is how much of the floor has been swept in that same amount of time. In one-fourth of an hour, two-ninths of the hall was swept. And that means every fourth of an hour, two-ninths of the floor can be swept. Two-ninths plus two-ninths will be four-ninths. In half an hour, four-ninths of the floor can be swept. And then by that measure, in three-fourths of an hour, six-ninths of the floor can be swept. And then, in one hour, eight-ninths of the floor can be swept.

Our first question asked, what fraction of the floor does he sweep in one hour? And we found that to be eight-ninths. The second question might not feel as straightforward. How long does it take for him to sweep the whole floor? If we continue out our line a little bit, there is some point where nine-ninths of the floor is swept. And that value is going to be a bit longer than an hour. Now, nine-ninths is one-ninth more than eight-ninths. So one thing that would be helpful for us to find out is how long does it take for Matthew to sweep one-ninth of the floor.

Because these values are proportional, we know that one-ninth is half of two-ninths, and that means it will take half of one-fourth to sweep one-ninth of the floor. Half of one-fourth is one-eighth. What we’re saying here is one-ninth of the floor is swept every one-eighth hour. If we wanted to get nine-ninths of the floor swept, we would multiply the numerator one-ninth by nine. And because these values are proportional, we’ll need to multiply the one-eighth of an hour by nine as well, which gives us nine-eighths of an hour for the whole floor swept. Nine-eighths of an hour is one and one-eighth. And so we can say it would take Matthew one and one-eighth of an hour to sweep the whole floor, which is 67 and a half minutes.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.