IGCSE_Numbers.pptx ffffffffffffffffffffffgt5reds

Numbers: Calculations
Jean Paul VEGA
jpvega@ombrosa.fr

 Please Excuse My Dear Aunt Sally
 Parenthesis, Exponent , Multiply, Divide, Add, Subtract
 Be careful when using Calculator
Order of Operations Mnemonics
¿ 36 − 3 −2=31

Factors of 12 are : 1, 2, 3, 4, 6, 12
12 = 1x 3 x 4 or 12 = 2 x 6
Multiples of 12 are: 12, 24, 36
12 = 1 x 12
24 = 2 x 12
36 = 3 x 12
Factors and multiples

Prime number: its integer factors are only 1
and itself: 2, 3, 5, 7, 11, 13, 17, 19
19 = 19 x 1 prime
-19 = 19 x 1 x (-1) not prime
8 = 4 x 2 not prime
Decomposition in prime factors to find Highest
Common Factor HCF and Lowest Commen
Multiple
Prime numbers applications

Decomposition into prime factors
24 75

Decomposition into prime factors

5 square
= 125 5 cube or 5 to the power 3
square root of 25
or 
cube root of 125
cu. root of 1.953125
Power and Roots

(-2) x (-2) = +4 always positive
Cannot take square root of negative
number
cannot but OK
Power and Roots

HCF Highest common factor
The factors of 12, 18 are 1 and combinations of their prime factors
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 12: 1, 2, 3, 4, 6, 12 HCF = 6
12
2 6
2 3
3 1
12 = 2 x 2 x 3

HCF Highest common factor
= = =

LCM Lowest Common Multiple
Multiples of 18: 18, 36, 72, … LCM = 36
Take common prime factors 2 x 3
Factors of 12: 12, 24, 36, 48 Multiply with remaining factors: 2 x 3 x 2 x 3
LCM = 2 x 2 x 3 x 3 = 36 to get both numbers 12, 18
12
2 6
2 3
3 1
12 = 2 x 2 x 3

LCM Lowest Common Multiple
= = =



Reciprocal or inverse of a number

Fractions, Decimals
Percentages

1 or more units can be divided into equal
parts called fractions:
1 pizza cut into 6 equal slices and eat 3
slices
 and I eat 3 x =
Fractions

P
Im
Proper and Improper Fractions

24 is the largest multiple of 4 below 27
Mixed to Improper Fractions

Multiply and Divide Fractions
¿
1× 2×3
2×2×3
WRONG !!
OK

Multiply Fractions
2
3
× 18=
2
3
×
18
1
=
36
3
2
3
×
3
4
=
6
12
=
1
2

Add and Subtract Fractions
4 × 3
5 ×3
−
1× 5
3× 5
=
12
15
−
5
15
=
7
15
Put all fractions on the
same denominator

Exam: 69 marks out of 75
Percentages: denominator =100

Percentages Increase and Decrease
A phone price changes from $100 to $120
=
A phone price changes from $120 to $100
=

New Price =
100% + 12% = 1.12
More rigorous algebra:

Increase Value X by p% =
Decrease Value X by p% =
You buy a phone $150 before discount of 15%
and pay additional tax of 10%. What is the final
price?

Simple Interest
Interest in % is money earned on sums deposited by
customers in a bank account or money charged by
banks when customers borrow a sum called the
principal.
With logic, no need to memorize ear
for 1 year

Simple Interest
Alan invests $500 at 1.5%/year simple interest. After n
years, the total value of his investment is $612.5. Find n

Start F1 F2 F3 …. …. F11 F12
350

Start F1 F2 F3 …. …. F11 F12
350 350x(1.1) 350x 350x 350x
x(1+10%) x(1+10%)

Percentages, Ratios, Proportions

% Questions
92% 23
100% Total?
×
100
92
×
23
0.92
×
100
92
×
23

Percentages: of what?
Of the buying cost

Of the buying cost

Bottles Time
500 15
B? 90
×
90
15
×
90
15
×
500
15
×
500
15

Butter Flour Sugar Currants Cakes

Butter Flour Sugar Currants Cakes
150 500 50 100 18
3 10 1 2 0.36
600 2000 200 400 72
1000 120
×
1000
600 ×
1000
600
×
600
3
×
3
150

Inverse Proportions
People Days
8 6
12 4
×
12
8 ÷
12
8

Ratios
Red Blue White Green Total
Ratio 7 5 3 1 16
Cars 48000
×
48000
16

¿
1× 2×3
2×2×3
OK

¿
1× 2×3
2×2×3

Algebra, Factorizing…
WRONG !!

Solving simple linear equations

There are 32 Plastic cups and 96 Ceramic
cups. After some Ceramic cups were sold, the
number of Ceramic cups left were 3/7 of the
total number of cups left. How many were
sold?

10 years ago, a couple’s average age is 28 years
old. In 8 years’ time, the wife will be 44 years
old. How old is her husband now?

10 years ago, a couple’s average age is 28 years
old. In 8 years’ time, the wife will be 44 years
old. How old is her husband now?
10 y ago: total age = 28 x 2 = 56
In 8 years: Total = 56 + 10 + 10 + 8 + 8 = 92, 
Husband = 92 -44 =48
Now: Husband =48-8 =40 y

John’s age is 1/8 of his father’s age now. His
father will be 36 years old in 4 years’ time. How
old will John be when he is 3/5 of his father’s
age?

John’s age is 1/8 of his father’s age now. His
father will be 36 years old in 4 years’ time. How
old will John be when he is 3/5 of his father’s
age?
J=4 , Father = 32 now
4 + Y = 3/5( 32 + Y)
20 + 5Y = 96 + 3Y  Y=38
J=42 years old

Simultaneous equations: Elimination

Simultaneous equations: Substitution

Simultaneous equations
J + K =160
J = K + 8
K = 76 , J = 84 J : K  21 : 19

Wendy’s savings is $720 more than twice of
Tim’s savings. If Wendy has $1680 more than
Tim, how much should Tim give Wendy so that
she will have 5 times as much as Tim?

Wendy’s savings is $720 more than twice of
Tim’s savings. If Wendy has $1680 more than
Tim, how much should Tim give Wendy so that
she will have 5 times as much as Tim? T= $960,
W= $2640, Tim must give $360
W=720 + 2T
W=1680+T
(960-G)x5 = 2640 + G  G= 360

0.6 of the population of town P is equal to 1/4 of the
population in Town Q.
of the population of town P moved to Town Q. After
that there were 3575 more people in town Q than P.
Find the total population P+Q.

0.6 of the population of town P is equal to 1/4 of the
population in Town Q.
of the population of town P moved to Town Q. After
that there were 3575 more people in town Q than P.
Find the total population P+Q. P= 1625, Q= 3900
0.6 P = 0.25Q  Q= 2.4 P

Laws of Indices / Exponents
(𝑎
𝑚
𝑏
𝑛
𝑐
− 𝑝
𝑑
𝑞 )
𝑟
=
(𝑎
𝑚𝑟
𝑏
𝑛𝑟
𝑐
−𝑝 𝑟
𝑑
𝑞𝑟 )

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