Decimals And Ratio Worksheet (Page 7 of 13) in pdf

STEM

Real Over the years, images have been shown in many different

Real / STEM Some cyclists prefer ﬁ xed wheel bikes, with no gears.

rectangular shapes, usually expressed as aspect ratios, width : height.

Typically a front cog has 50 teeth and a rear cog has 20 teeth.

a What is the ratio of front cog teeth to rear cog teeth?

b How many times does the rear wheel turn for every turn of the

height

pedals?

A typical road bike travels 195.3 cm for every rotation of the rear wheel.

width

c How many times must a cyclist turn the pedals to travel 1 km?

a Convert each aspect ratio to a unit ratio.

i 5 : 3 (European widescreen)

ii 3 : 2 (35 mm ﬁ lm)

9 Real / STEM Although not as visible, cars use gears in the same way

iii 8 : 5 (computer screen)

iv 4 : 3 (cathode ray tube TV)

as bikes. Different gear ratios (number of turns in the engine : number

v 37 : 20 (US widescreen)

vi 12 : 5 (cinema widescreen)

of turns in the wheels) make the wheels travel different distances for

Q9 Literacy hint

b Which of these ratios shows the widest picture?

each revolution in the engine.

A revolution is a full rotation of 360° .

In a typical car each revolution of the wheels is about 2 m.

Real / STEM Engine performance can be compared by looking at the

Q6 hint

ratio of power to weight. A high power-to-weight ratio means a car will

power

______

Gear

Turns in the engine : turns in the wheels

Use a calculator to work out

weight

accelerate (or perform) well.

1st

2.97 : 1

and round to a whole number.

Find the ratio of power to weight for each of these cars as a unit ratio.

2nd

2.07 : 1

Car

Power (kW)

Weight (tonne)

Power : weight (unit ratio)

3rd

1.43 : 1

Chevrolet Corvette

476

1.51

315 : 1

4th

1 : 1

Caparo T1

429

0.47

5th

0.84 : 1

Caterham Superlight R500

196

0.51

6th

0.56 : 1

Ariel Atom 500

373

0.55

a Explain why 6th gear is the fastest gear.

Ferrari F12

544

1.63

b How many revolutions of the engine does it take to travel 1 km

Porsche GT2RS

456

1.37

in 6th gear?

Discussion Which car has the best performance?

10 Real / Problem-solving Clocks and watches with hands also have

7 Real / STEM Most modern bikes have a variety of

Key point

gears.

gears, with a number of different-sized cogs.

What is the gear ratio of the minute hand to the second hand?

A road-racing bike has a front cog at the pedals with

53 teeth and a choice of 5 cogs at the rear.

Explore How do mountain bikes get up steep hills?

Is it easier to explore this question now you have completed the lesson?

rear cog

What further information do you need to be able to answer this?

26 teeth

front cog

52 teeth

In engineering, gears are used to change speeds.

12 Reﬂ ect In this lesson you answered lots of real problem-solving

These two cogs are connected by a chain and have

questions. This is different from some other lessons in this unit where

equal sized teeth. Each turn of the large cog makes

pedal

you worked out lots of calculations (as in lesson 6.2).

the small cog turn twice, because 1 × 52 = 2 × 26.

One turn of the pedals turns the front cog once.

Which type of lesson do you like best? Explain.

Copy and complete the table to work out the number of

turns the rear wheel will make when the pedals are

turned once for different gears.

Front cog teeth

Gear

Rear cog teeth

Ratio of front teeth to rear teeth

53 : 32

Unit ratio

1.66 : 1

Number of rear wheel turns per

1.66

turn of the pedals

147

Unit 6 Decimals and ratio

148

Theta 2, Section 6.5

Decimals And Ratio Worksheet Page 7

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