CHAPTER 11: PERCENTAGES

11.4: Practical Examples

Ø  EXPLANATION:

·         If you buy something and sell it, the difference between the 2 prices is profit or a loss.

·         When you buy something you may be offered a discount.

This is a reduction in a price. It is usually given as a percentage.

·         If a bank helps you to buy an item, you may have to pay back more than you borrow. This is the interest that bank charges.

·         If you buy something the price may include a tax. This is called a purchased tax. When you earn money you may have to pay tax on what you earn. This is called income tax.

Ø  EXAMPLE:

A man earns $45 000 in a year

He can earn $16 000 without paying any tax.

He pays 24% tax on anything above $16 000.

a)   Work out how much tax he pays.

b)   What percentage of his income does he pay in income tax?

a)    45 000 – 16 000 = 29 000

24% of 29 000 = 6960

He pays $6960

b)   (6960 : 45 000) x 100% = 15.5%

 EXERCISE

1.    A woman bought an old chair for $240. She sold it for $300.

Work out the percentage profit.

2.    A man bought a car for $15 900. He sold it for $9500.

Work out the percentage loss.

A bottle of grape juice costs $6.50.

If you buy 6 bottles you can get 10% discount.

Work out how much you save if you buy 6 bottles.

CHAPTER 11: PERCENTAGES

11.3: Percentage Changes

Ø  EXPLANATION:

·         You can use percentages to describe a change in a quantity

It could be a increase or decrease.

·         A percentage change is always calculated as a percentage of the initial value.

·         The initial value is 100%. It is important to choose the correct value to be 100%

Ø  EXAMPLE:

In May, 800 people visited a museum.

In June, 900 people visited.

In July, the number was 800 again.

a)   The percentage increase  from May to June.

b)   The percentage decrease from June to July.

1.    100% = 800

The increase is 100 (from 800 to 900)

The percentage increase is (100 : 800) x 100% = 12.5%

2.    100% = 900

The decrease is 100 (from 900 to 800 again)

The percentage decrease is (100 : 900) x 100% = 11.1%

EXERCISE 

1.    Game $40

Alain increases the price by $10. Find the percentage increase.

ü  ($10 : $40) x 100% = $25

2.    Tebor weighed 84 kg. He went running every day and began to lose mass.

After 1 month his mass was 78 kg. What was the percentage decrease?

ü  84 – 78 = 6 kg

ü  (6kg : 84kg) x 100% = 7.14%

The price of a car was $20 000. In a sale, the price decreased by 4%. After the sale it increased by 4%. (The price after the sale is $20 000 again.) 

a)    What mistake has it made?

b)   What is the correct price after the sale?

CHAPTER 11: PERCENTAGES

11.2: Comparing Different Quantities

Ø  EXPLANATION:

·         You will often need to compare groups that are different sizes

·         à Suppose that, in 1 school, 85 students took an exam & 59 passed. In another school, 237 students took an exam & 147 passed.

Which school did better?

·         It is hard to say because each school had a different number of students.

·         The worked example below shows how to use percentages to help to answer questions like this.

Ø  EXAMPLE:

In school A, 85 students took a mathematics exam and 59 passed

In school B, 237 students took a mathematics exam and 147 passed.

Which school had a better pass rate?

ü  59 out of 85 = 59 : 85 = 69%

ü  147 out of 237 = 147 : 237 = 62%

è The pass rate in school B is better by 7 percentage points.

 There were 425 girls & 381 boys in a school. 31 girls & 48 boys are overweight.

Work out:

1.    The percentage of the girls that are overweight.

      à 31 out of 425 = 7.3%

2.    The percentage of all the students that are overweight.

           è 79 out of 806 = 9.8%

 

	Smoker	Non-smoker	Total
Men	12	64	76
Women	9	32	41

    a.    What percentage of men are smokers?

 ü  12 out of 76= 12 : 76 = 15.8%

CHAPTER 11: PERCENTAGES

11.1: Using Mental Methods

Ø  EXPLANATION:

·         Some percentages are easy to findà For Simple Fractions.

·         If you know 10%, you can find any multiple of 10%.

·         You can often do this quite easily. (Don’t always need a calculator)

Ø  EXAMPLE:

There are 4400 people in a stadium. 60% are males. How many is that?

ü  60% = 50% + 10%

ü  50% of 4400 = 2200

ü  10% of 4400 = 440

è 60% = 2200 + 440 = 2640

Work out:

ü  49% of 2300

ü  49% = 50% - 1%

ü  50% of 2300 = 1150

ü  1% of 2300 = 23

ü  49% = 1150 – 23 = 1127

ü  110% of 36

ü  110% = 100% + 10%

ü  100% of 36 = 36

ü  10% of 36 = 3.6

ü  110% = 36 + 3.6 = 39.6

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Show that 30% of 65 is the same as 65% of 30

 (30 : 100%) x 65 = 19.5

     (65 : 100%) x 30 = 19.5

Network Topology

Network topology is the arrangement of the various elements (links, nodes, etc.) of a computer network.Essentially, it is the topological structure of a network, and may be depicted physically or logically. Physical topology refers to the placement of the network's various components, including device location and cable installation, while logical topology shows how data flows within a network, regardless of its physical design. Distances between nodes, physical interconnections, transmission rates, and/or signal types may differ between two networks, yet their topologies may be identical.

A good example is a local area network (LAN): Any given node in the LAN has one or more physical links to other devices in the network; graphically mapping these links results in a geometric shape that can be used to describe the physical topology of the network. Conversely, mapping the data flow between the components determines the logical topology of the network.

Topologies remain an important part of network design theory. You can probably build a home or small business computer network without understanding the difference between a bus design and a star design, but becoming familiar with the standard topologies gives you a better understanding of important networking concepts like hubs, broadcasts, and routes.

In computer networking, topology refers to the layout of connected devices. This article introduces the standard topologies of networking.

Topology in Network Design

Think of a topology as a network's virtual shape or structure. This shape does not necessarily correspond to the actual physical layout of the devices on the network. For example, the computers on a home LAN may be arranged in a circle in a family room, but it would be highly unlikely to find a ring topology there.

Network topologies are categorized into the following basic types:

• bus
• ring
• star
• tree
• mesh

More complex networks can be built as hybrids of two or more of the above basic topologies.

Here are some explanations of the 2 types of Typology:

Tree Topology

Tree topologies integrate multiple star topologies together onto a bus. In its simplest form, only hub devices connect directly to the tree bus, and each hub functions as the root of a tree of devices. This bus/star hybrid approach supports future expandability of the network much better than a bus (limited in the number of devices due to the broadcast traffic it generates) or a star (limited by the number of hub connection points) alone.

Mesh Topology

Mesh topologies involve the concept of routes. Unlike each of the previous topologies, messages sent on a mesh network can take any of several possible paths from source to destination. (Recall that even in a ring, although two cable paths exist, messages can only travel in one direction.) Some WANs, most notably the Internet, employ mesh routing.

A mesh network in which every device connects to every other is called a full mesh. Partial mesh networks also exist in which some devices connect only indirectly to others.

Source: http://compnetworking.about.com/od/networkdesign/a/topologies.htm http://en.wikipedia.org/wiki/Network_topology