PROPORTIONALITY · 2019. 8. 2. · Steps for solving problems of proportionality 1st) Identify the...

PROPORTIONALITY

www.matematicasalmudena.com Almudena Casares Fernández

MEANING OF PROPORTIONALITY

The ratio between two amounts A and B, is a

number meaning the quotient of them.

A proportion is an equality between two ratios.

A

B

A C

B D


DIRECTLY PROPORTIONAL MAGNITUDES

If two quantities are directly proportional, as one

increases, the other increases by the same ratio.

PROPERTY: The ratio between two respective

amounts is constant. This constant is called

constant of proportionality.

A= Number

of bottles1 2 3 4

B= Litres 2 4 6 8


INVERSELY PROPORTIONAL MAGNITUDES

If two quantities are inversely proportional, as

one increases, the other decreases by the

inverse ratio.

PROPERTY: Product between two respective

amounts is constant.

A= Number of

painters10 5 20 15

B= Worked

days6 12 3 4


SOLVING PROPORTIONAL PROBLEMS

FIRST METHOD: How much is the unit?

Solution:

- How much does one sweet cost?

- How much do 7 cost?

Example: If three sweets cost 15p, how much

do 7 cost?



SECOND METHOD: RULE OF THREEThe rule of three is a mechanical method for solving proportions

where you know three numbers a, b, c and want to find the

fourth, x.

Steps for solving problems of proportionality

1st) Identify the magnitudes.

2nd) Place the data and the unknown.

3rd) Decide if they are directly or inversely proportional.

4th) Use the property.

a

cbx

x

c

b

a ·



Solution:

Example 1: Carlos makes £25 in 4 hours. How much

will he make in 2 hours?



Solution:

Example 2: If 4 workers can do a job in 7 hours,

how long will 8 workers take to do that job?


PERCENTAGES

VIDEO

http://www.bbc.co.uk/skillswise/topic/percentages

Per cent means “out of 100” so, a percentage is a

fraction whose denominator is 100.

We can solve percentage problems by directly

proportional problems because each amount is

directly proportional to its respective percentage.

55%

100


http://www.bbc.co.uk/skillswise/topic/percentages

PERCENTAGES: EXAMPLE 1 (FIND THE PART)

Solution:

There are 250 boats in a harbour. 46% of the boats are

yachts. How many yachts are there in the harbour?

TOTAL PART


PERCENTAGES: EXAMPLE 2 (FIND THE TOTAL)

Solution:

In a flock, there are 80 black sheep, that is 20% of the flock.

How many sheep does the flock have?

TOTAL PART


PERCENTAGES: EXAMPLE 3 (FIND THE PERCENTAGE)

Solution:

In a flock, there are 900 sheep, 45 of them are black. What

is the percentage of black sheep?

TOTAL PART


SPECIAL PERCENTAGES

Percentage Fraction Decimal

50% 1/2 0.5

25% 1/4 0.25

75% 3/4 0.75

20% 1/5 0.20

10% 1/10 0.10


PERCENT INCREASE AND DECREASE

Two important questions:

How much is the increase or decrease?

How much is the final amount?

Final amount = initial amount + increase

Final amount = initial amount - decrease



Solution:

1st) Reduction

2nd) Final price

Example (Finding the final amount): A store reduced all

normal prices by 15% in a two-days sale. Work out the sale

price of a drill with a normal price of £14.



Solution:

Example (Finding the final amount): A store reduced all

normal prices by 15% in a two-days sale. Work out the sale

price of a drill with a normal price of £14.

Initial amount Final amount



Solution:

Example (Finding the initial amount): Jean has 205

stamps after she gave 18% of all her stamps to her sister.

How many stamps did Jean have originally?




Solution:

Solution:

Example (Finding percentage increase o decrease):

24800 people went to the beach for swimming in August.

And the number of visitors for the beach decrease to 23300.

What was the percentage decrease in the number of visitors

for the beach?



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PROPORTIONALITY · 2019. 8. 2. · Steps for solving problems of proportionality 1st) Identify the...

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