6.4.4 Practice with Dividing Fractions

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Activity symbol 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.

  • (i) four division two divided by three
  • (ii) seven divided by 15
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Discussion

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?

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Answer

  • (i) equation sequence four division two divided by three equals four multiplication three divided by two equals four squared divided by one multiplication three divided by two sub one equals two multiplication three divided by one equals six divided by one equals six
  • (ii) Change the first fraction into an improper fraction before dividing: equation sequence seven divided by 15 equals eight divided by three sub one multiplication 15 super five divided by seven equals eight multiplication five divided by one multiplication seven equals 40 divided by seven equals

(b) If it takes three divided by four of an hour to clean one car, how many cars can be cleaned in hours?

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Discussion

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 three divided by four hours are in hours. If you were trying to determine how many times 4 goes into 20, what operation would you perform?

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Answer

(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 three divided by four goes into . The calculation is equation sequence three divided by four equals 15 divided by two division three divided by four equals 15 super five divided by two sub one multiplication four squared divided by three sub one equals five multiplication two divided by one multiplication one equals 10 divided by one equals 10. 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?

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Discussion

What operation could you use to determine how many times feet goes into feet? Drawing a sketch of the garden could be helpful, too!

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Answer

(c) We need to find how many foot segments there are in feet. The calculation is:

equation sequence 57 divided by two division seven divided by two equals 57 divided by two sub one multiplication two super one divided by seven equals 57 divided by seven equals

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.

6.4.3 Dividing Mixed Numbers and Fractions

6.5 Self-Check