Summary Grade 9 Numbers, operations and relationships.pdf

Whole numbers
THE NUMBER SYSTEM

rational numbers

integers
whole numbers
irrational
numbers

1,1 m k it

0 1 2 3
r
3 22 40

315 1.37 21.6

Imaginethitstobetupperwears
stacked
together when you pick up yellow
you pick up orange and red too

i
Integers are also whole and natural
numbers

exercise
Tick the correct boxes
number natural whole integer rational irrational

591
12T

, MULTIPLES
Natural numbers that are multiplied by another natural number

4
16 94 2,56 1,024
4 4 4 4

lowest common multiple LCM
write out multiples of each number and spot lowest common


ia
lowest common multiple 20

factors
natural numbers that can divide into another number without
remainders
1 factors of 48 I 2 3 4 6 8 12 16 24 48



11 41
highest common factor HCF
write out factors of each number and spot the common

1 factors of 30 I 2 3 4 6 10 15 30
2 factors of 40 I 2 4 5 8 10 20 40

highest common factor 10

prime factors
numbers with only 2 factors I itself
1 prime numbers 2 3 5 7 11 13 17 19 23

1 is not prime only has one factor

, PRIME
Ladder method
FACTORIZATION
write 80 as a product of its prime factors

2 300
2 150
keep dividing 300 22 3 52
3 75
by the prime

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heh 9m'T
number


find the LCM
1 make each number a product of its prime factors

eg Find the LCM of 6 and 8 by means of prime factorisation

prime factors
2 2

1 LCM 23 3 24

find the HCF
I write each number as a product of its prime factors

eg fhffort.gg f of 30 3 40 by means of prime

prime factors 3 ÉE 5
common factors

2 5 10

, exercise
1 Find the factors of
a 49


b 64

C 108


2 Find the multiples of
a 7


b 12

C 24


3 Find the HCF of
a 4 3 14


b 18 3 22


C 45 390

4 Find the CCM of
a 18 3 22


b 35 48