number patterns and sequences(form 1)
TRANSCRIPT
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A number sequence is a set of numbers arranged according to a
a certain pattern.This pattern is known as number
pattern.
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EXAMPLE 1Describe the pattern of the followingnumber sequence. 4, 8, 16, 32, 64, 128, …
Solution: x2 x2 x2 x2 x2 4 8 16 32 64 128
The pattern of the sequence is to multiplythe previous number by 2.
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EXAMPLE 2
Complete the following sequence. 38 880, , 1080, , 30, 5
Solution:
38 880, , 1080, , 30, 5 ÷6 ÷ 6 ÷ 6 ÷ 6 ÷ 6
The pattern is to divide the previous numberby 6.
1806480
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ODD AND EVEN NUMBERS
ODD NUMBERS
EVEN NUMBERS
Whole numbers which cannot be divided
exactly by 2.Example : 1, 3, 5, 7, …
Whole numbers which can be divided exactly by 2.
Example : 2, 4, 6, 8, …
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EXAMPLE 3
List all the odd numbers between 80 and 100.
Solution:
81, 83, 85, 87, 89, 91, 93, 95, 97 and 99
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PRIME NUMBERS
PRIME NUMBERS
A whole number that can only be divided
exactly by itselfand the number 1
Example : 2, 3, 5, 7, 11, …
REMEMBER…1 is not a
prime number
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EXAMPLE 4
List all the prime numbers that are lessthan 20.
Solution:
2, 3, 5, 7, 11, 13, 17 and 19
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FACTORS
A FACTOR Can divides exactly thewhole number
REMEMBER• 1 is a factor for
all numbers• A whole number has the number itself as a factor
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EXAMPLE 5
Find the factors of 14.
Solution:
14 can be divided exactly by 1, 2, 7 and 14.Factors of 14 are 1, 2, 7 and 14.
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EXAMPLE 6
Determine if 8 is a factor of 103.
Solution:
103 ÷ 8 = 12 remainder 7103 cannot be divided by 8 without anyremainder.Thus, 8 is not a factor of 103.
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PRIME FACTORS
PRIME FACTORS Factors of a given whole numbers which are prime
numbers
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EXAMPLE 7
Find the prime factors of 12.
Solution:
Factors of 12 = 1, 2, 3, 4, 6, 12Prime factors of 12 = 2 and 3
Among the factors, 2 and 3
are prime numbers
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EXAMPLE 8
Determine whether 19 is a prime factor of 418.
Solution:
418 ÷19 = 2219 is a factor of 418 and it also a prime number. Therefore, 19 is a prime factor of 418.
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MULTIPLES
MULTIPLES Product of the number andanother whole number other
than zero.
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EXAMPLE 9
(a) List the first five multiples of 6.
Solution:
6x1 6x2 6x3 6x4 6x5
6, 12, 18, 24, 30
(b) Determine whether 110 is a multiple of 13.
Solution:
110÷13 = 8 remainder 6Therefore, 110 is not amultiple of 13.
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COMMON MUTIPLES AND LOWEST COMMON MULTIPLES (LCM)
COMMON MULTIPLES
Multiples of two or more whole numbers
Example: 6 is a multiple of 2 and 3. Therefore, the
common multiple of 2 and 3is 6.
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EXAMPLE 10
(a)Find the first two common multiples of 3 and 5.(b)Determine whether 102 is a common multiple of 6 and 8.
Solution:
(a)Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, … Multiples of 5 = 5, 10, 15, 20, 25, 30, … Therefore, the first two common multiples of 3 and 5 are 15 and 30.
(b) 102 ÷ 6 = 17 102 ÷ 8 = 12 remainder 6. 102 is a multiple of 6 but is not a multiple of 8. Therefore, 102 is not a common multiple of 6 and 8.
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LOWEST COMMON MULTIPLES (LCM)
Smallest common multiple of two or
more numbers
There are three methods used to find
the LCM of whole numbers.
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EXAMPLE 11
Find the lowest common multiple of 3, 4 and 6.Solution:
Method 1: Listing allthe multiples
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