RATIO AND PROPORTION

Proportion as Ratio
(Teacher Copy)

### Activity  3:  Finding Distance

Students set up and solve proportions.   It is assumed that Activity 3 had been previously completed and is available to the students.  It is also assumed that Activities 6 & 8 have been completed.

To set up and solve proportions.

### Introduction:

When you were finding ratios, you were also using proportions.  A proportion is statement indicating that one ratio is equal to another.  We say that any pair of entries in the tables we have in previous activities is proportional to any other pair of entries.

Part A

 Revolutions 1 2 3 4 5 Distance (cm) 239 478 717 959 1195

The proportions that relate one revolution to 2, 3, and 4 revolutions are 1/239 = 2/478,  1/239 = 3/717,  and  1/239 = 4/956, respectively.

The proportion which relates the gear ratios is  22/44 = 25/50, or alternately, 44/22 = 50/25.

Part B

1. You travel 464 miles in 8 hours.
2. The pump pumps 720 gallons in 45 minutes and 1920  gallons in 2 hours.
3. The two towns are 200 miles apart.
4. Amy got 60 free golf balls.
5. The stamping machine will make 736 parts in 8 hours.
6. 90 kph is  about 54 mph.

Part C (individual activity)

X = 288    X = 121   X = 850.5

X = 16    X = 20    X = 544.5

Closing Discussion Are the following proportions the same?  Why or why not?  The two proportions are not the same.  In the first case X=100 and in the second case X=4.

10/50 = 20/x         10/50 = x/20

How can you make sure that you always have "X" in the correct position when setting up a proportion? Make sure that the numerators correspond to the same type of value;  likewise, for the denominators.