ratio & proportion

RATIO & PROPORTIONSMPK PENABUR GS

DO NOW (not later):

• Compare the number of boys to girls in the class.

• The number of boys =

• The number of girls =

• If we compare boys to girls we get

___ boys to _____ girls.

What do we call a comparison between two or more quantities?

RATIOWe just found the RATIO of boys to girls.

Is the ratio of girls to boys the same ?

No, when writing a ratio, ORDER matters.

AIM:

What is a ratio?

DEFINITION OF RATIOA ratio is the comparison of two or more numbers (quantities).

A ratio has no units

Which ratio shows the ratio of 3 butterflies to 1 apple?

Three Ways to write a Ratio

The ratio of 3 boys to 5 girls can be written as:(i) 3 to 5(ii) 3 : 5(iii)

The ratio of a to b, can be written as:(i) a to b(ii) a : b(iii)

Three ways to write a ratio

Write A Ratio Rewrite into a ratio :a) 15 metre to 2 km 15 m : 2 km ( ratio no units, and km change to m ) 15 : 2000 ( write into simplest form )

3 : 400

b) 135 seconds : 1.5 minutes ( minute change to second ) 135 : 90 ( write into simplest form )

3 : 2

Write A Ratio If P : Q = 3 : 5, and Q : R = 2 : 1, find the ratio P : R !

P : Q : R(1) 3 : 5(2) 2 : 1

The value of Q are 5 and 2.So, we need to make it equal .Find LCM of 2 and 5 ! It is 10

Ratio becomes : P : Q : R

(1) 6 : 10(2) 10 : 5

So, the ratio of P : R = 6 : 5

WRITE A RATIO

In a new car dealer’s lot, there were 23 silver, 18 white, 2 maroon, 8 red, and 12 blue vehicles. Write the ratio of silver vehicles to total vehicles.

Write the ratio of white to blue vehicles.

silver

total

23

63

white

blue

18

12

3

2

Decrease and Increase in RatioIf the number of teachers in a college is increased from 50 to 60. Then the ratio of new staff and old staff is :

5

Numbers of new staff Number of old staff

60 50

6

We say that, number of teachershas beenincreased in ratio 6 : 5

In other words, number of new staff is times the number of old staff

RULE TO INCREASE OR DECREASE To increase a number “ X “ , we multiply X by

an improper fraction.

Ex. Increase Rp 500 in ratio 5 : 8 New value : Rp 500 x = Rp 800

Similarly, to decrease a number  “ X ”  we multiply “ X “  by an proper fraction.

Ex. Decrease 56 in ratio 7 : 8           New value = 56 x = 49

Improper fraction

Proper fraction

PROPORTION

Definition of Proportion• A proportion is an equation that says one ratio is equal to another.

4

352

39ratio ratio=

DIRECT PROPORTION Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

Understanding Direct Proportion Question :Price of 8 oranges Rp 2600. What is the price of 6 oranges ?

Calculation based on units

Price 8 oranges = Rp 2600Price 1 orange = Rp 2600 : 8

= Rp 325

Price 6 oranges = 6 x Rp 325= Rp 1950

Understanding Direct Proportion Price of 8 oranges Rp 2600. What is the price of 6 oranges ?

Calculation Based on ratio

Number of oranges Price ( Rp )

8

6

2600

X

X=6 x 26008

=𝐑𝐩𝟏𝟗𝟓𝟎

Understanding Direct Proportion

If you drive 90 miles in 2.5 hrs, how long should it take for you to complete the final 200 miles of a trip?

mile hour

90

200

2,5

X

X=2.5 x 20090

=𝟓 ,𝟓𝟔𝐡𝐨𝐮𝐫𝐬

Understanding Direct Proportion

Six identical CNC machines can produce 768 pistons in one day. If two of the CNC machines break down, how many pistons can be produced in a day?

Machine Piston

6 768

4 X

X=4 x7686

=𝟓𝟏𝟐𝐩𝐢𝐬𝐭𝐨𝐧𝐬

INVERSE PROPORTION

In the inverse proportion, if the quantity x increases, the quantity y decreases, or when the quantity x decreases, the quantity y increases.

Understanding Inverse ProportionSome candies are distributed to 15 kids and each kid gets 4 candies. If there are only 12 kids, how many candies does each kid get

Calculation based on the result of multiplication.

Kid candy

15 4

12 C

15 x 4 = 12 x C60 = 12 CC = 5 candies

Understanding Inverse Proportion 4 employees can complete a basic auto

interior restoration in 6 work days. If only two employees are available for a similar project, how long will it take?

Employee day

4 6

2 D

4 x 6 = 2 x D24 = 2 DC = 12 days

Understanding Inverse Proportion 6 childrens need 30 minutes time to

tidy up the books in their schools library. How many children must be added so that the job could be done in 20 minutes?

Children Minute

6 30

X 20

6 . 30 = X . 20180 = 20 XX = 9 childrens

Children must be added :9 – 6 = 3 students

Children Minute

6 30

X

MAPS & SCALE DRAWINGS

P

S R

P = Picture ( size on picture/map)

S = Scale ( in Ratio )

R = Real ( the real size of that object)

P = S . R

Example A design drawing has a scale 1 : 250a) Determine the actual distance ( in metre ) if the distance on the drawing is 3 cm.b) If the real distance is 12 m, determine the distance on the drawing.

SOLUTION !Given : Scale ( S ) = 1 : 250 or

a) P = 3 cm ,

R = 3 : R = 3 x 250 R = 750 cm R = 7,5 m

b) R = 12 m = 1200 cmP = S x RP = x 1200

P = 4, 8 cm

EXERCISE 39 PAGE 63 - 64