Teacher Mechanics
Gears Introduction to Gear Ratios
Note to the teacher
In this page, students will be introduced to the concept of gear ratio. Gear ratio is defined as the number of times the
driving axle must revolve in order to make the driven axle revolve exactly once. In this page, students will learn to
determine the gear ratio by dividing the number of teeth on the driven gear by the number of teeth on the driving gear.
They will then simplify this fraction, if possible, and convert it to a decimal to determine the gear ratio. Students will have
to use both fractions and decimals to make these calculations. While the worksheet is designed to help students learn how
to determine gear ratio, and may be successfully completed by students with little background in this area, the existing
ability to multiply and simplify fractions, and the ability to convert fractions to decimals, will be necessary to successfully
complete the worksheet. Teachers may wish to review any or all of these skills depending on their students’ background.
Note that there are no instructions regarding rounding. The answers assume rounding to 2 digits beyond the decimal
place, except for known fractions. Teachers may wish to supply additional instructions. If they do not, students’ answers
may vary slightly according to what rounding conventions they use.
Instructions
Based on the information provided about the gears shown on this page, answer the following questions. What is the gear
ratio for the combination? How many times must the driving gear go around for the driven gear to make one revolution?
Note: The driving gear is always on the right. Possible gear sizes are 40, 24, 14 and 8 tooth gears.
1.
(# Teeth on driven gear)
Gear Ratio
Simplified fraction
40
=
8
5
1
=
5
(# Teeth on driving gear)
5.43
©2005 Robomatter Inc. RE 2.5_RW 1.1
Mechanics Teacher
Gears Introduction to Gear Ratios
Students are expected to use the following procedure:
•
•
•
•
Identify gear sizes of each gear by counting teeth.
Enter the correct values in the boxes labeled “(# Teeth on driven gear)” and “(# Teeth on driving gear)”
Simplify this fraction and enter it in the box labeled “Simplified fraction”
Convert this fraction to a decimal.
Approximate classroom time: 10-20 minutes depending on students’ background
Students successfully completing the worksheet will be able to:
1.
2.
3.
4.
Define gear ratio
Identify gear size by counting teeth
Simplify fractions
Convert fractions to decimals
Standards addressed:
Math Standards
Numbers and Operations
Algebra
Geometry
Measurement
Problem Solving
Connections
Technology Standards
The Nature of Technology Standard 1
Design Standards 8, 9
Abilities for a Technological World Standard 12
Using Technology to Design the Future Standards 16, 18, 19
Science Standards
Content Standard B
Content Standard E
Note: Workbook answers begin on the next page.
©2005 Robomatter Inc. RE 2.5_RW 1.1
5.44
Teacher Mechanics
Gears Introduction to Gear Ratios
Instructions
Based on the information provided about the gears shown on this page, answer the following questions. What is the gear
ratio for the combination? How many times must the driving gear go around for the driven gear to make one revolution?
Note: The driving gear is always on the right. Possible gear sizes are 40, 24, 14 and 8 tooth gears.
For all answers, the gear ratio is always the number of teeth on the driven gear divided by the
number of teeth on the driving gear:
1.
(# Teeth on driven gear)
Gear Ratio
Simplified fraction
40
=
8
5
1
=
5
(# Teeth on driving gear)
2.
(# Teeth on driven gear)
24
24
Gear Ratio
Simplified fraction
=
1
1
=
1
(# Teeth on driving gear)
3.
(# Teeth on driven gear)
8
24
Simplified fraction
=
1
3
Gear Ratio
=
.33
(# Teeth on driving gear)
4.
(# Teeth on driven gear)
24
14
Gear Ratio
Simplified fraction
=
12
7
=
1.71
(# Teeth on driving gear)
5.
(# Teeth on driven gear)
14
8
Simplified fraction
=
5.45
7
4
Gear Ratio
=
1.75
©2005 Robomatter Inc. RE 2.5_RW 1.1