# Fractions as rates

### Objective

Reducing fractions, converting fractions to decimals

Calculators

### Optional pre-knowledge

Column graphs (bar charts)

Recently the College organized a Fun Walk from Kolonia to Palikir. The walkers started from Palm Terrace in Kolonia at 6:30 A.M. on a sunny Saturday morning. Team T3 reached Sekere School at 7:18 A.M, the Dolon Community store at 7:40 A.M., the FSM Capital at 7:48 A.M., finally arriving at the Palikir national campus at 8:14 A.M.

### How long?

 1 How many minutes did it take for Team T3 to go from Palm Terrace to Sekere school? ___ 2 How many minutes did it take for Team T3 to go from Sekere School to Dolon Community store? ___ 3 How many minutes did it take for Team T3 to go from Dolon Community store to FSM Capital? ___ 4 How many minutes did it take for Team T3 to go from FSM Capital to the Palkir National Campus? ___ 5 How many total minutes did it take for Team T3 to go from Palm Terrace to the Palkir National Campus? ___

### How far?

The distant from Palm Terrace to Sekere school is 4.3 kilometers (km).

The distant from Sekere School to Dolon Community store is 1.8 km.

The distant from Dolon Community store to FSM Capital is 0.9 km

The distant from FSM Capital to the Palkir National Campus is 2.4 kilometers.

 6 How far is the total distance from Palm Terrace to Sekere School? ___

### How fast?

#### Decimal hours

Speed in the metric system (used by all countries in the world except for Liberia, Burma, and the United States) is expressed in kilometers per hour. The kilometers for each leg of the walk is known, but the time is in minutes not hours. The times will have to be converted to minutes.

One hour = sixty minutes or 1 hour = 60 minutes.

Dividing both sides by 60 minutes results in: 1 hour/60 minutes = 60 minutes/60 minutes

or, after canceling on the right, 1 hour/60 minutes = 1

When one is multiplied by a number, we get the number back again. For example, 2 × 1= 2 and 15 × 1 =15.

We can take the first leg, 48 minutes, and multiply by 1 hour/60 minutes and change only the units of time without changing the length of time because 1 hour/60 minutes is equal to one.

48 minutes × 1 hour/60 minutes= 48/60 hour (the minutes canceled)

Divide the top and bottom by two to reduce to: 24/30.

Then divide by two top and bottom to reduce to 12/15, reduce the top and bottom one more time by dividing the top and bottom by 3 to get 4/5. Divide 4 by 5 to get 0.8 hours.

Fill in the rest of the chart below:

 Leg Time in minutes Minutes divided by 60 Reduced fractional hours Decimal hours From Palm Terrace to Sekere 48 48/60 4/5 0.8 7 From Sekere to Dolon store ___ ___ ___ ___ 8 From Dolon store to FSM capital ___ ___ ___ ___ 9 From FSM Capital to Palikir campus ___ ___ ___ ___ 10 Total time from Palm Terrace to Palikir campus ___ ___ ___ ___

#### Speed in kilometers per hour

To determine how fast team T3 went on each leg, divide the distance of each leg in kilometes by the decimal hours for each leg. The first row of the next table is done as an example.

 Leg Distance in km Decimal hours Speed in km/hr From Palm Terrace to Sekere 4.3 0.8 5.375 11 From Sekere to Dolon store 1.8 ___ ___ 12 From Dolon store to FSM capital 0.9 ___ ___ 13 From FSM Capital to Palikir campus 2.4 ___ ___ 14 From Palm Terrace to Palikir campus ___(from #6) ___ ___
 15 On what leg was Team T3 the slowest? ___ 16 Why might that leg have been the slowest? ___ 17 On what leg was Team T3 the fastest? ___ 18 Why might that leg have been the fastest? ___

[Instructors option: a column graph ("bar chart") could be made by the students of this data if they know how to do a bar chart]

The (total distance in kilometers)/(total decimal time in hours) is the average speed. The average speed for Team T3 is calculated in the last column of number 14 above.

Team Outer Island covered the total distance in 1 hour and 30 minutes, Team FAO in 1 hour and 55 minutes, and the last stragglers made it to the campus in 2 hours and 10 minutes. Calculate the average speed for each group.

 Team Time Distance Decimal hours Speed in km/hr 19 Outer Island 1:30 ___(from #6) ___ ___ 20 Team T3 1:44 ___(from #6) ___(from #10) ___(from #14) 21 Team FAO 1:55 ___(from #6) ___ ___ 22 Stragglers 2:10 ___(from #6) ___ ___

Developed by Dana Lee Ling with the support and funding of a U.S. Department of Education Title III grant and the support of the College of Micronesia - FSM. Notebook material ©1996 College of Micronesia - FSM. For further information on this project, contact dleeling@comfsm.fm Designed and run on Micron Millenia P5 - 133 MHz with 32 MB RAM, Windows 95 OS.