Ratios can be written in a variety of forms. The ratio of 2 to
3 can be written using a colon (2:3) or a fraction (2/3). In order
to answer the following questions, look back at the table in Part B of
Activity 6 for the number of teeth
on the front sprocket of a bicycle compared to the number of teeth on the
Write the gear ratios in Activity
6 (Part B) in simplest form using a colon and using a fraction.
To determine the speed of the bicycle in each combination of gears,
you divided the number of teeth in the rear sprocket into the number of
teeth in the front sprocket. Explain, in writing, why we did not
give these answers in colon or fraction form.
In manufacturing, it is important to keep track of the number of defective
parts or products being produced. Rather than simply counting the
number of defective parts, company officials usually consider the number
of defects per hundred, thousand, or million parts.
Suppose that the Lightning Electric Company was making complex light
switches and had a defect rate of 25 parts per hundred. Why
would the figure 25 parts per hundred be considered a ratio?
Fill in the table below to show the number of parts produced in the
top row and the number of defective parts in the bottom row. The
top row should have the entries 100, 200, 300, 400, and 500.
What number must you multiply the top row by to get the bottom row?
Draw an x-y graph on your graph paper for the data in the table; each
line on the graph paper should represent 25 units. Label the x-axis
"Number of Parts" and the y-axis "Number of Defects". Plot the points
listed in your table and then connect them with a line.
Next, find a point on the line that is between two points. Carefully,
draw a horizontal line (to the left) from your new point to the y-axis
and measure it in millimeters. Record the distance below. Also,
draw a vertical line (down) from your new point to the x-axis. Measure
What number must you multiply the horizontal distance by to get
the vertical distance?
Explain how the numbers you just found relate to the top and bottom
rows of the table.
Do you think that choosing a different point on the line and repeating
the measurements would result in a different ratio of the horizontal distance
to the vertical distance? Why or why not?
Use your calculator to find Ö2.
Write your answer rounded to the nearest tenth.
Before people had sophisticated measure instruments, distances had
to be approximated. Distances across a river or a canyon could be
particularly troublesome. Even so, precise measurements were often
desired. How would you judge the amount of rope needed to construct
a bridge made of rope and wood that needed to be built over a rushing river
if you didn't have any sophisticated tools? You will soon find out.
Refer to the Reference Sheet. Let's
say that the picture represents the place where a bridge is to be built.
You have noticed two prominent landmarks—a tree and a rock—and have marked
two spots directly across the river from them. Next you measured
the distance between the two marked spots and found that they were 300
To make the picture as realistic as possible, you first drew the river
with the tree and the Marked Spot A. You located the rock in your
picture at 28 degrees, the same angle that the rock is located from Marked
Spot A. Finally, you completed with picture as shown.
The two marked spots and the rock form a triangle. Draw the triangle
on the picture. The triangle on the page is similar to a triangle
formed by the actual tree and the two marked spots. Your two triangles
are similar, which means that the ratio of corresponding sides will be
the same number. You decide to measure the distances on the picture
and use that ratio to find the same ratio that works with a side of 300
Use your ruler to measure to the nearest 1/8 inch (rounding up for
mid-distances): the distance from A to B (scaled-distance #1),
and from B to the closest edge of the rock (scaled-distance #2).
Next, divide scaled-distance #1 by scaled-distance #2 to get the ratio
of length 1 to length 2. Decide how you can use this information
to find the approximate real-life distance across the river.
1. distance from A to B is
inches (scaled-distance #1)
2. distance from B to the rock is
inches (scaled-distance #2)
3. ratio of scaled-distance #2 to scaled-distance #1
4. actual distance across the river is
1. If your speedometer needle is pointing to 55, what ratio is indicated?
What kind of ratio is it (same units or different units)? How would
you state this ratio formally? How would you write it?
2. Most car speedometers have both English (miles per hour) and metric
(kilometers per hour) units. How could you make a table to show the
ratio of miles per hour to kilometers per hour?
Last updated on 1/30/1999