6.4.4 Practice with Dividing Fractions
The calculator can be accessed on the left-hand side bar under the Toolkit.
Activity: Dividing Fractions
(a) In your math notebook, work out the following calculations by hand. It may be tempting to use the calculator, but it will be better practice if you resist. You can verify your answers using the calculator afterwards.
Remember that you can make a whole number a fraction by placing it over 1. How do you convert division by a fraction into a multiplication problem?
- (ii) Change the first fraction into an improper fraction before dividing:
(b) If it takes of an hour to clean one car, how many cars can be cleaned in hours?
Did you try drawing a time line broken into quarter hours? How many of these quarter hours does it take to clean one car? You are trying to determine how many hours are in hours. If you were trying to determine how many times 4 goes into 20, what operation would you perform?
(b) Here, we need to find how many times “three-quarters” goes into “seven and a half.” One way to approach the problem is to use a time line, where each hour is broken into quarters. We would then let 3 of these quarters represent one car.
We see that 10 cars could be cleaned in hours.
Another method would be to realize that you are being asked to determine how many times goes into . The calculation is . Thus, 10 cars can be cleaned in the given time.
Imagine that you are trying to put a fence along the side of a garden. The side of the garden measures feet. The fencing available is made of panels, which measure feet each. How many panels will be needed?
What operation could you use to determine how many times feet goes into feet? Drawing a sketch of the garden could be helpful, too!
(c) We need to find how many foot segments there are in feet. The calculation is:
So, because the panels must be purchased in whole units, eight panels will be too short, and nine panels are needed.
You did it! You’ve worked with fractions and will now be able to tackle new problems.