ppt

1. CHAPTER 1 :
Fundamental Operation
of Arithmetic
1.1 Fraction
1.2 Ratio and Proportion
1.3 Percentage

2.  Two numbers separated by a horizontal or
sloping line.
 E.g. Two seventh = 2/7 =
7
2
Types of fraction
Types Definition Examples
Proper fraction Numerator < denominator
Improper fraction Numerator = or >
denominator
Mixed fractions Whole number + common
fraction
Equivalent fractions Two fractions that have
equals values
1.1 FRACTION WHAT IS
FRACTION?
Denominator, D
Numerator, N

3. MIXED
Multiply the whole number by D,
add N. Place the total over N.
IMPROPER
Divide N by D as far as possible
and express remainder as a proper fraction
1.1 FRACTION Conversion
improper to
mixed

4. 1. ADDITION & SUBTRACTION
Same Denominators
 Just add / minus the numerator
Different Denominators
 Find a common denominator, then add / minus and
simplified the answer to the lowest term.
 Example: Evaluate the followings;
5
2
5
4
3
2
d)
3
2
5
2
c)
5
1
7
3
b)
5
6
5
3
5
1
a)
+
−
+
+
+
1.1 FRACTION
OPERATION ON FRACTIONS

5. 1. Add together :
5
1
3
3
1
4
2
1
5
e)
5
3
4
3
2
3
d)
3
1
5
2
8
3
c)
9
1
8
5
b)
5
1
3
2
a)
+
+
+
+
+
+
+
PRACTICE 1
5
3
3
2
1
7
e)
4
3
2
3
1
5
d)
3
1
3
16
7
5
c)
5
2
4
3
b)
4
1
3
2
a)
−
−
−
−
−
2. Subtract the following:

6. 1.1 FRACTION
OPERATION ON FRACTIONS
s
q
r
p
s
r
q
p
×
×
=
×
r
q
s
p
r
s
q
p
s
r
q
p
×
×
=
×
=
÷
2. MULTIPLICATION
 Product of the numerators
divide by the product of the
denominators.
 Can be simplified if possible
before multiplying.
 Mixed fractions have to be
converted into improper
fractions before multiply.
3. DIVISION
 Invert the divisor and
change the division sign to
multiplication.

7. Calculate each of the following:
PRACTICE 2
4
3
8
7
5)
8
5
4
3
1
4)
5
3
4
1
3)
3
2
6
5
2)
7
4
8
5
1)
÷
×
×
÷
×
5
4
5
5
1
1
3
2
2
10)
2
1
4
1
3
2
5
2
)
9
5
2
3
5
2
2
8
7
1
8)
5
2
8
1
1
4
1
7)
4
3
8
1
1
6)
÷






+
+






−
×
−






×






×
÷
÷

8. 1.1 FRACTION
OPERATION ON FRACTIONS
n
n
n
b
a
b
a
=






9
4
81
16
81
16
=
=
b
a
b
a
=
4. POWERS
 Raise both the numerator &
the denominator to that
power.
 Example;
5. SQUARE ROOTS
 Invert the divisor and
change the division sign to
multiplication.
 Example;
125
8
5
2
5
2
3
3
3
=
=







9. 1.1 FRACTION
OPERATION ON FRACTIONS
with.
start
to
3.60
RM
had
girl
The
cents
360
90
4
1
cents
90
4
1
4
3
1
∴
=
×
=
=
=
−
20
7
20
13
20
20
13
1
Drink
)
2
=
−
=
−
=
6. PRACTICAL APPLICATION
 A girl spends 3/4 of her pocket money and has 90cents left. How
much did she have to start with?
20
13
20
5
8
4
1
5
2
Food
)
1
=
+
=
+
=
 A group, of school children went to a hamburger bar, 2/5 of them bought
hamburgers only, 1/4 bought chips only and the remainder bought drinks only
 What fraction bought food?
 What fraction bought drinks?

10. 1. Jane takes 5 ¾ minutes to iron a blouse. How
many blouses can she iron in 23 minutes?
2. The profit of a business are RM 29 000. It is
shared between two partners A & B. If A
receives 9/20 of the profits, how much money
does B receive?
3. A man sells his car for RM 16 200 and as a
result, loses one tenth of the price he paid for it.
What price did he pay for it?
4. 5/8 of a fence has been built. If there is still 40
feet to be built, how long will the fence be?
5. A man left three eight of his money to his wife &
half the remainder to his son. The rest was
divided equally between his five daughters.
Determine what fraction of the money each
daughter received.
PRACTICE 3

11.  Comparison of 2 numbers or quantities as quotient.
 Represent by x/y or x : y.
 Generally reduced to lowest terms like fraction (by
dividing the HCF of the numbers).
 Derived from quantities measured in the same units
 Its just number, don’t have unit.
 Its express the relationship between 2 or more
factors (or numbers)
1.2 RATIO &
PROPORTION
WHAT IS
RATIO ?

12.  E.g. Simplify the ratio 200g : 1 kg (different units)
= 200g : 1000g
= 1 : 5
 Example: Expressed the following ratio to the lowest
term;
1.2 RATIO &
PROPORTION
WHAT IS
RATIO ?
2
2
mm
10
:
cm
10
d)
13
8
to
13
12
c)
8
3
:
8
5
b)
2
3
52
78
52
:
78
a)
=
=
=

13.  The equality of 2 ratios
 E.g. 5 : 2 = 25 : 10
 To solve problems dealing with proportion, we use
cross multiplication.
 Types of proportion:
1.2 RATIO &
PROPORTION
WHAT IS
PROPORTION ?
1. Direct proportion
 If increase or decrease at the
same rate.
 E.g. If we buy rice at RM 2 for 2
kg, then we expect to pay RM 4
for 4 kg.
2. Inverse proportion
 If an increase (decrease) in one
quantity produces a decrease
(increase) in a second quantity
in the same time.
 E.g. 5 men building a wall take
20 days. If 4 men, it will take
only 25 days.

14.  Examples:
1. Find the value of x for 5 : 25 = 3 : x.
2. If a : b = 5 : 3, find
a. b : a
b. a : (a – b)
c. b : (a + b)
d. (a – b) : (a + b)
1. If a : c = 3 : 4, and a : b = 4 : 5, find b : c
15
75
5
3
25
5
=
=
⇒
=
x
x
x
1.2 RATIO &
PROPORTION
WHAT IS
PROPORTION ?

15.  Express a quantity as the number of parts in 100 parts.
 Written as fraction, e.g. 20 percent = 20 % = 20/100 = 0.20
 Conversion:
Fractions Percentage Decimal
x 100% ÷ 100%
x 100%
÷ 100%
Then move dec. point
2 places to the left
Then move dec. point
2 places to the right
1.3 PERCENTAGE WHAT IS
PERCENTAGE
?

16.  Example: Express each number as a fraction, decimal
and percent.
a. 86% b. 5.6%
c. 8 ½% d. 0.025
e. 1.5 f. 9/8
g. 17/1000
1.3 PERCENTAGE