There are 3 kinds of mathematicians….. those who can count and those who can't

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Objectives

• Understand basic mathematical calculations

• Application of simple mathematical functions in daily life

• Understanding the importance of these functions at work

• Removing the “number phobia”!!!

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Help Harold

• Write your suggestions to help him overcome the fear for Maths!!!

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Interesting!!!

• 9 times table on your hands!!!

• How much is a Google?

• What is a ‘Jiffy’ (“Ill be there in a jiffy”)

• What is Triskaidekaphobia?

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Numeracy cartoon 1 - catalog reference aba0036

Do Away With Number Phobia

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The Montapha Marathon

Your team is on an health retreat in Thailand

As part of your retreat in Thailand, you have decided to visit Mr. Kung Long, famous numerologist

However, Montapha is an ancient island and is inhabited by several tribal groups who do not appreciate having tourists on their Island.

The Thailand Tourism department has made a special arrangement with the heads of these tribal groups and thus you need to follow the below steps in order to reach this island.

You leave Thailand on the 7th of March’10.

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Signpost

The is the first the get back toThailand wins!!!

• Ensure you fill the appropriate columns of the table put up by your trainer

• You cannot move ahead until you write your numbers

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Date of Arrival

• Rent a Ship

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Date of Arrival

• Speed and Date

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Numerology Forecast Chart

• On calculation of the Date, collect Mr. Kung Long’s Numerology Forecast Chart

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Mr. Long’s Fee

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Your Learning’s

• _________________________________

• _________________________________

• _________________________________

• _________________________________

• _________________________________

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Roadmap

• Reading numbers with the Place Value Chart

• Fractions/Decimals/Percentages

• The BODMAS rule

• Measurement Tables

• Ratio & Proportions

• Average/Mean/Median/Mode

• Data Interpretation

• Simple calculations

Place Value System

Large numbers made easy!

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Place Value System

• It helps in:

– Reading numbers by showing us where they are placed

– Putting appropriate number of zeroes

– Easy conversion of fractions into decimals/percentages and vice versa.

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International Place System

PERIODSPERIODS BILLIONSBILLIONS MILLIONSMILLIONS THOUSANDSTHOUSANDS ONESONES

Place ValuesPlace Values

Hundred Hundred Billions Billions

(1000000(100000000000)00000)

Ten Ten Billions Billions

(10000000(10000000000)000)

Billions Billions (100000(100000

0000)0000)

Hundred Hundred Millions Millions

(10000000(100000000)0)

Ten Ten Million Million (100000(100000

00)00)

Millions Millions (100000(100000

0)0)

Hundred Hundred Thousand Thousand (100000)(100000)

Ten Ten ThousandThousand(10000)(10000)

Thousand Thousand (1000)(1000)

Hundred Hundred (100)(100)

Tens Tens (10)(10)

Ones Ones (1)(1)

No. of Zeroes 11 10 9 8 7 6 5 4 3 2 1 0

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Let’s Read Numbers

• International System – 254,885,235 – Two hundred and fifty four million, eight hundred

and eighty five thousand ,two hundred and thirty- five

• Decimal System– 46,667.256 – Forty six thousand ,six hundred and sixty seven

point two five six

Write down the following numbers as shown above:

1.58,70,0242.729,451,8943.99,213.305

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Currency Conversions

Keeping in sync with the fast growing world, it is beneficial to be well versed and aware of the currency exchange rates.

With the help of the table below, convert the value of the items in your currency:

CurrencyTo Egyptian

Pound

1 Australian Dollar LE 4.8974

1 British Pound LE 8.4591

1 U.S. Dollar LE 5.49

1. 1 Ltr of Milk (US) – $3.75 2. A Party Dress (US) - $373. 1 Kilo of Tomatoes (UK) - £3.754. A Newspaper (UK) - £1.255. A Packet of Chips (Australia) - $4.456. A Pair of Sneakers (Australia) - $ 87.50

Fractions/Percentages/Decimals

Different names of the same function

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Fractions

• A fraction is a part of a whole.

• If try to slice a pizza, we will get fractions:

1/2 1/4 3/8

(One-Half) (One-Quarter) (Three-Eighths)

 

• The number in fractions tells how many slices we have (Numerator) and the number in the denominator tells us the number of slices the pizza was cut into (Denominator).

• Solve: Ahmed gives 1/4th his salary to his mother and his salary is 5000 LE. Ahmed also deposits 1/2 of his remaining salary (after giving 1/4 th to his mother) in the bank, how much money does he have left?

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Percents

• In mathematics, we express something by percentage - expressing a number as a fractions of 100 (per cent meaning "per hundred").

• For example, 47% (read as "forty seven percent") equal to 47 / 100.

• Solve: Karim & Alia’s Report cards are given below. Calculate their percentage for each of the subject and their overall percentage. Who has scored the highest overall percentage?

StudentMath

(50marks)Science

(50marks)English

(50marks)Arabic

(50marks)

Karim 20 39 44 45

Alia 32 35 45 40

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Decimals

• Zero and the other countable numbers like (1,2,3,...) make up the set of whole numbers. • However every number is not a whole number. For e.g. 45,567.256

– Forty five thousand five hundred and sixty seven point two five six• Our decimal system allows us to express all types of numbers , using something called a

decimal point.

• Rounding Off: Rounding off to two digits: – if the number after the second digit (after the decimal) is 5 or greater than 5 then you add

1 to the second digit – However, if the number after the second digit (after the decimal) is less than 5 then you

leave it as it is– For example: 23.467 = 23.47 and 4456.3244 = 4456.32

• Solve: Calculate & round off to two digits:• 345/126 =• 9224/1705 =• 333.569/2=

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Fractions, Decimals and Percents

Operation Explanation Example

Convert a decimal to a percentMove the decimal point 2 places to the right

and add a percent (%) sign. .123 = 12.3%

Convert a percent to a decimalMove the decimal point 2 places to the left. 5% = .05

Convert a fraction to a decimalDivide the numerator by the denominator 1/8 = .125

Convert a percent to a fractionFirst turn the number into a decimal. Then

divide that by 10,100 or 1000 depending on the number of digits after the decimal

18% = .18 = 18/100 = 9/50

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More Examples

• Conversion of decimal to fractions

– 45.2 = 452/10 (because after decimal there is one digit)

– 45.25 = 4525/100 (because after decimal there are two digits)

– 45.256 = 45256/1000 (because after decimal there are three digits)

– 0.025 = 25/1000

• Conversion of Fraction to Decimal

– 456/10 = 45.6

– 2/10 = 0.2

– 456/100 = 4.56

– 2/100 = 0.02

– 456/1000 = 0.456

– 2/1000 = 0.002

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Help Harold – Math Paper I

Maths Test I - CLICK

BODMAS Rule

Tool to crack long calculations!

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BODMAS

• Think what is the answer to 2 + 3 x 5 is?

– Is it (2 + 3) x 5 = 5 x 5 = 25 ?– or 2 + (3 x 5) = 2 + 15 = 17 ?

• BODMAS is a rule which enables us to know exactly the right order of solving the mathematical question.

• If we follow the rule it gives us rules to follow so that we will always get to the right answer:

– B rackets– O rder – D ivision – M ultiplication– A ddition– S ubtraction

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BODMAS-Solved Examples

• Here's an example based on the BODMAS rule :

– The answer can be explained with a calculator which would give to the calculation 5 + 80/10 x (1 + 2)2 - 1 according to the BODMAS rules.

• Brackets gives 5 + 80/10 x (3)2 - 1

• Order gives 5 + 80/10 x 9 - 1

• Division gives 5 + 8 x 9 - 1

• Multiplication gives 5 + 72 - 1

• Addition gives 77 - 1

• Subtraction gives 76

• The answer is 76

Solve:

1. 7+5/10*(46-22)

2. 86/42-(96*7)+42

Measurement Tables

Now measure distance, time and quantity!

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Distance

1cm=10mm

1m=100cm

1km=1000m

1 feet=12 inches

1mile=1.6Km

1mm=1/10cm

1cm=1/100m

1m=1/1000Km

1 inch=1/12 feet

1Km=1/1.6 mile

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Quantity (Solid)

1gm=1000mg

1Kg=1000gm

1tonne=1000Kg

1mg=1/1000gm

1gm=1/1000Kg

1Kg=1/1000 tonne

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Quantity (Liquid)

1lts=1000ml

1Kl=1000lts

1ml=1/1000 lts

1lts=1/1000Kl

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Time

1min=60sec

1hour=60mins

1hour=3600secs

1week=7days

1year=12months

1sec=1/60 min

1min=1/60hour

1secs=1/3600hour

1day=1/7 week

1month=1/12 year

1day=1/365year

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Help Harold – Math Paper II

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Ratios & Proportions

Ratios:

• Ratios are used to make comparisons between two things/items. The number’s indicating the two things are separated using a “:” (colon).

For example:

• Comparing the number of circles to the number of triangles shown below, the ratio would be 4:3

 

• In 2001, 81 men enrolled in the English department at our university while 120 women enrolled. What is ratio of men is to women enrollment?

  Men: women = 81:120, which can be further simplified to (81/108) – 3/4 or 3:4

However, though the ratio is 3:4 , the original numbers are larger and this must be kept in mind when dealing with ratios

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Proportions

• Proportions or Equal Ratios:

Ratios are in proportion when the corresponding fractions are equal

To check if two ratios are equal, divide the numerator by the denominator for each ratio. If the quotients are equal, then the ratios are equal.

• Is the ratio 5:15 equal to the ratio 25:100? Divide both, the quotients are not equal. Therefore, these two ratios are not equal.

• Example of equal ratios: 4:20 = 2:10 = 20:100 = 1:5

• Example - Let us make an addition to the ratio example. In 2002, 159 men enrolled in the English department and if the ratio of men to women was the same is the year 2001, how many women enrolled?

2001 - Men: women ratio in = 3:4

2002 – Men: women = 3:4 = 159: x

3/4 = 159/x

Cross multiply the two fractions, 3x = 159*4

x = 636/3 = 212 Thus the number of women who enrolled in 2001 was 212

 

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Tips to solve questions

• Question – Find out Nishath & Rizwan’s division of ancestral money of LE 2000, in a ratio of 3:2

Solution:

1. add the numbers in the ratio

2. find the value of 1 part,

3. Calculate by multiplying the 1 part value with appropriate number in the ratio

Let us apply it to the question above:

1. Add - 3 + 2 = 5

2. Value of 1 part = LE 2000/5 = LE 400

3. Nishath’s Share = 3 * 400 = LE1200 &

Rizwan’s Share = 2 * 400 = LE 800 (A quick check, sum of their share is LE 2000

• Question – The price of 10 g Vanilla is 50 Piastras & 50 g is LE 2.50, are they proportional?

Solution – Write the ratio for each comparison: 10g:50P & 50g:LE 2.50

Convert the units to equate: 10g:50P & 50g: 250 P (100P = LE 1)

Ratio for each: 10:50 & 50:250

Simplify: 1:5 & 1:5, since they are equal – They are proportional

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Help Harold – Math Paper III

Average/Mean/Median/Mode

For Data Interpretation

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Average/Mean

• X = Sum of items/ No. of items

–Example•Marks of 5 students are 28,36,45,85,96•Sum = 28+36+45+85+96=290•No. of items = 5 (5 numbers are added)•X = 290/5 = 58•Average = 58

• Solve:• Calculate the average viewership of the listed TV programs , based on the viewership in all the listed

cities

City American IdolSo You Think

You Can Dance

Apprentice

City A 2467 3342 1364City B 3400 1245 2340City C 7804 1423 745City D 6329 4990 2551

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Median

• The median is the middle of a number distribution: half the scores are above the median and half are below the median.

• Computation of Median– Arrange the given data in ascending (increasing) or descending (decreasing) order– When the data set is odd, the median is simply the middle number. For example, the

median of 2, 4, and 7 is 4. – When the data set is even, the median is the mean of the two middle numbers. For

example: The median of : 1,2,6,8, is (2+6)/2=4

• Solve: Calculate the median of the following data:

1. 22,56,26,34,42,38,46,52

2. 101,123,111,113,125,107,109

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Mode

• The mode is the value that occurs the most frequently in a data set.

• Computation of Mode– Example:15,20,26,22,18,20,21,20,25,24,20,18,17,20,14,20,18

• 14 – 1 time• 15 – 1 time• 17 – 1 time• 18 – 3 times• 20 – 6 times• 21,22,24,25,26 – 1 time each

– Mode = 20 (highest number of repetitions)

Solve: Find the mode in the below data:

1.11,13,13,15,17,23,11,13,28,29,13,11,13,27,28,2315

2.1,7,2,2,3,6,7,1,9,4,4,1,1,7,1,9,3,5,1,2,8,9,1,2,1,9,1,4

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Selling Price/Cost Price/Profit & Loss

• Cost Price – the price at which one buys the item

• Selling Price – the price at which one sells the item

• Profit – If the selling price is greater than the cost price, profit is made

Profit = S.P – C.P

• Loss – If the cost price is greater than the selling price, loss is made

Loss = C.P – S.P

• Loss or Profit Percentage is calculated on the Cost Price:

     Profit Percentage = (profit /C.P) * 100

• Loss Percentage = (loss / C.P) * 100

 

• The cost price of a lamp is LE 500 and sold for LE 650. What is the Profit or Loss Percentage ?

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Help Harold - Math Paper IV

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THANK YOU