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FOREWORD

Assalamualaikum Warahmatullahi Wabarakatuh.

Praise author prayed to Almighty God for this book can finally be resolved. The

authors present book as a guide for students in learning mathematics.

Today, mathematics is one of the subjects that are still considered difficult to

understand and apply, but after studying the material in this book, the authors

hope that students are able to understand the material presented easily.

Beside that in this book also contain case of real life that related to concept of

the material, so student can fell the use of the material and its hoped can grow up

students motivation in studying.

Finally, the author would like to thank all those who have helped the realiza-

tion of this book. Hopefully, this book is useful and can be used as a guide in the

study of mathematics.

Jember, April 2014

Writter

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MAIN COMPETENCE

Main Competence 1

Appreciate and practice the teachings of their religion.

Main Competence 2

Respect and appreciate the honest behavior, discipline, responsibility, caring (tolerance,

mutual assistance), polite, confident, in interacting effectively with the social and natural

environment in a range of socially and presence.

Main Competence 3

Understand and apply knowledge (factual, conceptual, and procedural) based on his cu-

riosity about science, technology, arts, culture and events related phenomena seem eye

Main Competence 4

Rework, Serve, and reasoning in the realm of concrete (using, parse, compose, modify,

and create) and the realm of the abstract (writing, reading, counting, drawing, and fabri-

cated) according to the learned in schools and other sources in the same viewpoint /

theory

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INSTRUCTION FOR USING THE BOOK

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CONTENT

Cover ...........................................................................................................................

Foreword .....................................................................................................................

Instruction for Using the Book ......................................................................................

Main Competence .......................................................................................................

Table of Content ..........................................................................................................

Chapter V Ratio and Scale ............................................................................................

Basic Competence and Learning Experience ...........................................................

Mapping Concept .................................................................................................

Learning Material ..................................................................................................

5.3 Scale as a Ratio ............................................................................................

A. Scale Concept ..........................................................................................

B. Numerical Operation by Using Ratio and Scale ..........................................

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Word to the Wish

Never-ending Job is a

Job that never Started

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Chapter V

Ratio and Scale

Basic Competence and Learning Experience

Basic Competence

Through learning process of ratio and scale, students are able to :

use the concept of comparison to solve real problems with using tables and graphs.

Learning Experience

Through learning process of ratio and scale, students have a learning experience:

Are able to find a concept of scale as a ratio.

Are able to solve a problem that related to concept of ratio and scale.

Key Word : Ratio

Scale

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B. Mapping Concept

Ratio

Scale

Distance in Real

Distance in Figure

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5.3 Scale as a Ratio

A. Concept of Scale

The picture above is a picture of Java Island as a whole, but the picture above is not

displayed in detail about what is on the Java Island in fact, the picture above is a represen-

tation of the actual situation presented in the form of small images that use the concept

of scale. On the scale it says 1: 4,000,000, it means that 1 cm on the map equals 4,000,000

centimeters on the actual conditions, so that we get a concept of scale, namely:

Example 5.1

At the map in figure 5.31 the distance from Banyuwangi to Surabaya is 3,4 cm and on that

map written 1 : 1.000.000. What is the real distance between both city?

Scale = distance in a map / distance in real

Figure 5.31

Scale = distance in a map / distance in real

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Distance from Banyuwangi to Surabaya in map = 3,4 cm

Scale of the map = 1 : 1.000.000. Its mean that 1 cm in map is equal to 1.000.000 cm in

real.

What is the real distance between both city?

Distance between both city in map 3,4 cm = 3,4 x 1.000.000 = 3.400.000 cm in real

The real distance between both city is 3.400.000 cm = 34 km

Alternative Solution :

Scale = distance in a map / distance in real

So, the distance from Banyuwangi to Surabaya is 34 km.

= 34 km

Given

Ask

Answer

SOLUTION

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In other case a carpenter or photographer also use a concept of scale as a ratio, we

know about maket that use by an architecture, concept of maket almost the same with

scale, namely :

Scale concept also can be find when we want to print a photo, we know the measure-

ment of photo, such as 3x4, 4x6, etc.’

Example 5.2 :

Mr. John and family want to make a photo. The distance between Mr. John and his child

is 1,3 m and the photographer use a photo with a scale 1:10. What is the distance be-

tween Mr. John and his child in photo?

The real distance between Mr. John an his child = 1,3 m

Scale = 1:10. Its mean that 1 cm in photo is equal to 10 cm in real.

What is the distance between Mr. John and his child in photo?

SOLUTION

Given

Ask

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1 cm in photo = 10 cm in real

1 cm in real = 1/10 cm in photo

Distance between Mr. John and his child in real is 1,3 m = 130 cm

Distance between Mr. John and his child in photo is 130 x 1/10 = 13 cm

Activity 1.

The figure beside is a building in Australia

Figure 1 have measurement 2x3 cm, and

Figure 2 have measurement 4x6 cm.

a What is the ratio between length in fugure-1

and figure 2?

b What is the ratio between width in figure-1

and figure 2?

c What is the ratio between area in figure-1

and figure 2?

d What is the ratio between Circumference

In figure-1 and figure 2?

e. Is the ratio between length same to

the ratio between width of both figure?

Answer

Individual Activity :

Make a group contain 3-4 person. Do activity 1, explain your result in front of class.

Figure 2

Figure 1

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B. Numerical Operation by Using Ratio and Scale

There are so many example in daily life that relate to concept of ratio and scale, in

sub material before there are ratio in map, maket, and photographer. And in this sub

material there is a different example of application of ratio and scale, it can be found in

conversion in temperature, etc.

Figure 5.32

Case 2

Mr. John is getting fever, and its temperature shows 40o C.

a. What is the temperature in

Reamure?

b. What is the temperature in

Fahrenheit?

Scale between some temperature :

C : R : F : K = 1000 : 800 : 1800 : 1000

= 5 : 4 : 9 : 5

Scale Conversion from Celcius to Fahrenheit

F = C + 320

Info :

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Mr. John Temperature = 400 C.

a. Mr. John temperature in Reaumur (R) ?

b Mr. John temperature in Fahrenheit (F) ?

a. C : R = 5 : 4

Then, 400 C= 4/5 x 400 = (4 x 400)/5 = 1600 / 5 = 320 R

So, Mr. John temperature is 320 R.

b. C : F = 5 : 9

Then, 400 C= (9/5 x 400) + 320=(9 x 400)/5=(3600 / 5)+ 320 = 720 + 320 = 1040 R

So, Mr. John temperature is 1040 R.

Given

Ask

Answer

SOLUTION

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a. By using a ruler measure the distance between watuulo beach (number 1) to

bande alit beach (number 4)!

b. What is the real distance between both beach?

c. What is the scale of the map above?

d. If the distance between patemon swimming pool (number 11) and tancak water

fall (number 6) is 2,5 cm, than there is some one want to go to tancak water fall

from patemon swimming pool at 08.00 by riding a motor cycle with the velocity is

40km/hour. What time he will arrive to tancak?

Group Discussion and Activity 2 :

Make a group contain 3-4 person. Do activity 1, compare your result with other groups

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