Section One - Number Flashcards
What is an integer?
An integer is a whole number. It can be positive, negative or zero.
Integer examples: -365, 0, 1, 17, 989
Numbers can fall into two different categories. What are they?
There are Rational and Irrational numbers.
What are the 3 different forms rational numbers can come in?
Rational numbers can come in the following forms:
Integer form e.g 4 (=4/1), -5 (=-5/1), -12 (=-12/1)
Fraction form e.g p/q where p and q are non-zero integers - 1/4, -1/2, 7/4
Terminating or recurring decimals e.g 0.125 (=1/8), 0.3333 = 1/3, 0.143 = 143/999
How can we define irrational numbers?
Irrational numbers are messy.
They CANNOT be written as fractions
They are never-ending, non-repeating decimals
What can we say about positive square roots?
Positive square roots can be integers or irrational numbers
e.g the square root of 2 is irrational however the square root of 4 is an integer
What are surds?
Surds are numbers or expressions containing irrational roots.
π is also irrational
What does B I D M A S stand for?
B = Brackets
I = Indices
D = Division
M = Multiplication
A = Addition
S = Subtraction
What are multiples?
What is a factor?
Multiples of a number are just its times table.
Factors of a number are all the numbers that divide into it.
What method should we use to find all the factors of a number?
Try finding all the factors of 24 as an example.
Step one - start off by listing the number times 1 then times 2, then 3 and so on listing pairs in rows
Step two - try each one in turn. cross out the row if it does not divide exactly
Step three - eventually when you get a number repeated, stop
Step four - The numbers in the rows that you have not crossed out make up all the factors of that number
So the factors of 24 are the following: 1, 2, 3, 4, 6, 8, 12, 24
What is a prime number?
A prime number is a number that is only divisible by 1 and itself.
The only exception is the number 1 which is NOT a prime number.
What are prime factors and how do we set about finding them?
What is the process of breaking down numbers into prime factors referred to as?
All numbers are made up of prime factors.
We can use a factor tree to find the prime factors of a number.
The process of finding the prime factors of a number is referred to as prime factor decomposition or prime factorisation.
Please express the number 420 as a product of prime factors?
Using a factor tree we can find that the prime factorisation of 420 is the following:
420 = 2 * 2 * 3 * 5 * 7
420 = 22 * 3 * 5 * 7
What does LCM stand for and what does it mean?
LCM stands for LEAST COMMON MULTIPLE
Definition: The SMALLEST number that will divide by all the numbers in question.
What methods can we employ to find the LCM of a number?
Method One: List the multiples of all numbers and find the smallest that is in both lists.
Method Two: If you know the prime factors of the numbers you can use this method instead
Step one - List all the prime factors that appear in either number
Step two - If a factor appears more than once in one of the numbers list it that many times
Step three - Multiple these numbers together to give the LCM
Please find the LCM of 18 and 30
First, let’s start by performing prime factorisation on both 18 and 30.
We can do this by using a factor tree
18
6 x 3
2 x 3
18 = 2 x 3 x 3 or 2 x 32
30
3 x 10
2 x 5
30 = 2 x 3 x 5
Now we have the prime factors we can work out the least common multiple by looking for the repeating factors in both numbers
2 x 3 x 3 x 5 = 90
So the LCM of 18 and 30 is 90
What does HCF stand for and what does it mean?
HCF stands for Highest Common Factor.
Definition: The biggest number that will divide into all the numbers in question.
What method do we use to find the HCF of numbers?
We list the factors of both numbers and find the biggest one that’s in both lists.
Try and find the HCF of 180 and 84
What are the two methods by which we can do this?
Method One - Just list the factors of both numbers and find the biggest one that is in both lists.
Method Two - Find the prime factors of both numbers. Then list all the prime factors that appear in both numbers.
Multiply these numbers together to find the HCF
If all your working is correct then your answer should be
2 x 2 x 3 = 12
Therefore the HCF of 180 and 84 is 12.
This is a fraction
18/24
What do we call the top number?
What do we call the bottom number?
How would we set about simplifying or cancelling down 18/24?
What is 18/24 simplified?
The number on the top of the fraction is called the numerator.
The number on the bottom of the fraction is called the denominator.
Cancel down in a series of steps until you cannot cancel anymore.
18/24 = 6/8 = 3/4
So the simplified form of 18/24 is 3/4
What are mixed numbers?
What are improper fractions?
Mixed numbers are things like 3 and 1/3 - a mix between an integer part and a fraction part.
Improper fractionsare fractions where thenumeratoris larger than thedenominator. e.g 14/3
What method do we use to convert mixed numbers to improper fractions?
Try and convert 4 and 2/3rds to an improper fraction.
Step one - Think of a mixed number as an addition. 4 and 2/3 becomes 4 + 2/3
Step two - turn the integer part into a fraction.
4 + 2/3 = 12/3 + 2/3 = 12+2 / 3 = 14/3
That means 4 and 2/3 converted to an improper fraction becomes 14/3
How do we convert an improper fraction to a mixed number?
Try and convert 31/4 to a mixed number
Divide the top number by the bottom number.
The answer gives the whole number part
the remainder goes on top of the fraction
so 31/4 is 7 remainder 3 giving us the answer of 7 and 3/4
