MATHS Flashcards
What are natural numbers?
All the positive numbers 1; 2; 3; 4; … are called the set of natural numbers
What are whole numbers?
Natural numbers including 0
What is often used to make calculation easier.
rounding off
Addition means….
finding the sum (adding the numbers together)
What is a factor?
A factor is a number that divides exactly into a whole number and leaves no
remainder.
What is a prime number?
Prime numbers are numbers that have only two factors, themselves and 1. T
What is a composite number?
Numbers with more than two factors are called composite numbers
Is the number 1 a prime number or a composite number?
The number 1 is neither a prime number nor a composite number
What does ‘ascending’ mean?
Smallest to biggest
What does ‘descending’ mean?
Biggest to smallest
< means
less than
> means
more than
What is the inverse operation of multiplication?
Division
What is the inverse operation of addition?
Subtraction
Adding numbers is called finding the….
Sum
Subtracting numbers is called finding the….
Difference
Multiplying numbers is called finding the….
Product
Dividing numbers is called finding the ….
Quotient
What is the commutative property of 2+7?
7+2
What is the commutative property of 3x6
6x3
What is the commutative property for 9 divided by 3?
Commutative property does not work with division
What is the commutative property of 8 - 4?
Commutative property does not work with subtraction
What is the associative property of 5 + ( 2 + 3)
(5 + 2) +3
What is the associative property of 6 - (1 + 3 )
(6 - 1 ) +3
What is the associative property of 4 x (2 x 2)
(4 x2) x 2
What is 54 x 100
5400
What is the identity element for subtraction and addition?
0
Whether you add or subtract 0 from a number, the number never changes
What is the identity element of multiplication and division?
1
Whether you multiply or divide a number by 1, the number never changes
What are odd numbers?
Numbers that cannot be divided by 2
What are even numbers?
Numbers that can be divided by 2
What are the first 5 counting numbers? (Whole numbers)
0 1 2 3 4
What are the first 5 natural numbers?
1 2 3 4 5
What are the first 6 multiples of 10?
10
20
30
40
50
60
What are the factors of 10?
1, 2, 5, 10
What are the prime factors of 12?
2, 3,
Round off 171 643 to the nearest thousand
172 000
Round off 166.16 to the nearest whole number
166
Use your knowledge about distributive property to solve:
29 x 4 + 29 x 7 + 29 x 10
(30 x 4 - 4) + (30 x 7 - 7) + (30 x 10 - 10)
116 + 203 + 290
500 + 100 + 9
609
Use your knowledge about distributive property to solve:
450 ÷ 10 + 680 ÷ 10
450 / 10 + 680 / 10
= (450 + 680) /10
= 1130 / 10
= 113
Use your knowledge about distributive property to solve:
50 x 369
50 x 369
= (100 x 369) / 2
= 36900 / 2
= 15 000 + 3000 + 450
= 18 450
True or false?
8 + 7 = 7 + 8
True
True or False?
10 x (7 +3 +4) = (10 x 7) + (10 x 3) + (10 x 4)
True
True or False?
(2 500 ÷ 20) ÷ 5 = 2 500 ÷ (20 ÷ 5)
False
(2500 / 20) / 5 = 125 / 5 = 25
2500 / (20/5) = 2500 / 4 = 625
A grocer buys 480 trays of oranges. He has to share the oranges equally
between 20 clients.
What is your equation?
480 / 20
480 / 10 / 2
48 / 2
24
Mr Padaychee owns a clothing shop. He has 25 designer tops which he sells for
R69 each. Assuming Mr Padaychee sells all of the tops,
What is your equation?
25 x 69
25 x 70 - 25
25 x 10 x 7 -25
250 x 7 - 25
250 x 10 - (250 x 3) - 25
2500 - 750 - 25
2500 - 775
2000 - 275
R 1725.00
Use the HORIZONTAL METHOD.
a) 456 +350 + 239
400 + 300 + 200 +50 + 50 + 30 + 6 + 9
900 + 100 + 30 + 10 + 5
1045
Use the HORIZONTAL METHOD.
a) 1 226 x 82
(1000 x 80) + (200 x 80) + (20x 80) + (6 x 80) + 2000 + 400 + 40 + 10 + 2
80 000 + 10 000 + 6000 + 1000 + 600 + 400 + 80 + 2000 + 400 +40 +10 + 2
90 000 + 9000 + 1000 + 400 + 100 + 30 + 2
100 532
What is the order of operations?
Brackets
Operations
Division
Multiplication
Addition
Subtraction
Calculate the following:
2(5 + 2) - (3 / 3) x 2 - 4 + 3 x 2 x 10 / (6 - 1)
(2 x 7) - (1 x 2) - 4 + (3 x 2 x 10 ) / 5
14 - 2 - 4 + (60 / 5)
8 + 12
20
True or False?
16 + 4 x 5 = 100
False
16 + 4 x5
= 16 + (4 x 5)
= 16 + 20
= 36
What is the product of 3 and 2?
6
What does HCF stand for?
Highest Common Factor
What does LCM stand for?
Lowest Common Multiple
What is the HCF of 12 and 20
Factors of 12 are: 1, 2, 3, 4, 6, 12
Factors of 20 are: 1, 2, 4, 5, 10, 20
HCF is 4
What is the LCM of 6 and 8?
Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42…..
Multiples of 8 are: 8, 16, 24…..
LCM is 24
A comparison between two numbers or two quantities that are measured in the
same units. For example: The ratio of the original price of the coat for the sale price is
R300: R210. We simplify this to 10 : 7
What is this called?
The Ratio
What is the Ratio for 250ml of juice concentrate for every litre of water?
250ml : 1L
= 250ml : 1000ml
= 25 : 100
= 5 : 20
= 1 : 4
What do we call the difference between the selling price added and the cost price of an
article.
The Profit
If It costs me R 20 to make a dozen cupcakes and I sell each cup cake for R5
What is my profit?
(5 x 12) - 20
= 60 - 20
= 40
My profit is R40
What is the equation to work out profit?
Selling Price - Cost Price = Profit
or
Selling Price - Expenses = Profit
What is an easier way to work out the HCF of bigger numbers?
Using Prime Factorization
Using Prime Factorization, work out the HCF of 60 and 72
60 = 3 x 20 = 3 x 5 x 4 = 3 x 5 x 2 x 2
72 = 2 x 36 = 2 x 3 x 12 = 2 x 3 x 3 x 4 = 2 x 3 x 3 x 2 x 2
2 x 2 x 3 x 5
2 x 2 x 2 x 3 x 3
2 x 2 x 3 = 12
The HCF is 12
What is an easier to work out what the LCM of bigger numbers is?
By Multiplying all the Prime factors that either each number has.
Using Prime Factorization, work out the LCM of 60 and 72
60 = 2 x 30 = 2 x 2 x 15 = 2 x 2 x 3 x 5
72 = 2 x 36 = 2 x 2 x 18 = 2 x 2 x 2 x 9 = 2 x 2 x 2 x 3 x 3
60 = 2 x 2 x 3 x 5
72 = 2 x 2 x 2 x 3 x 3
2 x 2 x 2 x 3 x 3 x 5
= 8 x 9 x 5
= 72 x 5
= 360
Two lighthouses can be seen from the top of a hill.
The first flashes once every 8 seconds, and the other flashes once every 15 seconds.
If they flash at the same time, how long will it be until they flash at the same time
again?
Find the LCM of 8 and 15
8 = 2 x 4 = 2 x 2 x 2
15 = 3 x 5
2 x 2 x 2 x 3 x 5
= 8 x 3 x 5
= 24 x 5
= 120
They will at the same time after 120 seconds / 2 minutes
Find the HCF of 30 and 24 using Prime Factorization
30 = 2 x 15 = 2 x 3 x 5
24 = 2 x 12 = 2 x 3 x 4 = 2 x 3 x 2 x 2
2 x 3 x 5
2 x 2 x 2 x 3
2 x 3 = 6
HCF = 6
Using Prime Factorization, find the LCM of 50 and 60
50 = 2 x 25 = 2 x 5 x 5
60 = 3 x 20 = 3 x 5 x 4 = 3 x 5 x 2 x 2
2 x 5 x 5 x 3 x 2
= 10 x 15 x 2
= 300
The LCM is 300
Using Prime Factorization, find the HCF of 26 and 45
26 = 2 x 13
45 = 5 x 9 = 5 x 3 x 3
26 and 45 have no prime factors in common
so
The HCF is 1
Using Prime Factorization, find the LCM of 26 and 45
26 = 2 x 13
45 = 5 x 9 = 5 x 3 x 3
2 x 13
3 x 3 x 5
2 x 3 x 3 x 5 x 13
= 18 x 5 x 13
= 90 x 13
= 1170
A number that shows how many times a base is used as a factor is called an….
Exponent
What are the first 5 square numbers?
1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16
5 x 5 = 25
The first 5 square numbers are:
1, 4, 9, 16, 25
What are the first 5 cube numbers?
1 x 1 x 1 = 1
2 x 2 x 2 = 8
3 x 3 x 3 = 27
4 x 4 x 4 = 64
5 x 5 x 5 = 125
The first 5 cube numbers are:
1, 8, 27, 64, 125
A base together with an exponent is called a …..
Power
What is 2 to the power of 5?
2 x 2 x 2 x 2 x 2
= 4 x 4 x 2
= 16 x 2
= 32
the inverse operation of squaring a number is called….
The square root
What is the square root of 25?
5 x 5 = 25
so the square root of 25
is 5
√9 =
=3
because 3 x 3 = 9
What is the cube root of 8?
= 2
because 2 x 2 x 2 = 8
If you multiply a number by itself the answer is …….
a square number
If you multiply a number by itself two times the answer is ……
a cube number
Write 8 in exponent form
2 (cubed) *write it down correctly
Write 9 in exponent form
2 (squared) *write it down correctly
5 squared is read as …
and calculated as …..
5 to the power of 2
5 x 5 = 25
5 cubed is read as….
and calculated as….
5 to the power of 3
5 x 5 x 5 = 125
A base together with a power is called….
An exponent
Write the following in exponential form
2x2x2x2
2 to the power of 4
Write it down correctly
What is the square of 5?
25
(5 x 5 = 25)
What is the cube root of 8000?
20
(20 x 20 x 20 = 8000)
What is the cube of 1?
1
(1 x 1 x 1 =1)