6th Grade Math Textbook, Fundamentals

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1. Complete the table for this 18-speed bicycle with 27-in. wheels.

2.Discuss and Write As the table shows, sometimes two different combinations of

sprockets give the same gear ratio. Design a gear system for an 18-speed bicycle

that has no duplicate gear ratios. Tell how you choose the numbers you use.

page 189 for exercise sets.

Enrichment:

Bicycle-Gear Math

Objective To investigate the mathematics involved in bicycle gears

An 18-speed bicycle has nine sprockets on its rear wheel and two
sprockets attached to the pedals. A sprocketis a wheel with
teeth on which a chain can move. A bicycle gearis a combination
of a front sprocket and a rear sprocket, connected by a chain.
So an 18-speed bicycle has 2 • 9, or 18, gears because it has
2 front sprockets and 9 rear sprockets.

The ratio of the number of teeth on the front sprocket to the number of teeth

on the rear sprocket is called the gear ratio. The gear ratio tells you the number

of times the rear sprocket turns each time the front sprocket turns once.

Suppose a bicycle with 28-inch diameter wheels has been put in a gear for which

the front sprocket has 38 teeth and the rear sprocket has 19 teeth. Find its gear ratio.

gear ratio  2

If you know the gear ratio and the diameter of the wheels, you can figure out how far a

bicycle travels with each pedal stroke.

The circumference of a bicycle wheel with a 28-in. diameter is 28in.

How far does the bicycle travel with each pedal stroke?

Let ddistance traveled by the bicycle with each pedal stroke

dgear ratio • circumference 2 • 28

2 • 28 • 3.14 175.84  176

The bicycle travels about 176 in. with each pedal stroke.

As the gear ratio increases, the amount of work needed to move the bicycle increases.

It is harder to pedal the bicycle at the higher gear ratios, but a bicyclist uses a higher

gear to be able to travel farther on fewer pedal strokes.

front teeth

rear teeth

38

19

Front Teeth Rear Teeth Gear Ratio Distance for 1 Pedal Stroke(to nearest inch)

48 12

48 16

48 18

54 12

54 16

54 18

Think

Because the gear

ratio is 2, the wheel

turns twicewith each

pedal stroke.