Section 1 - Number Flashcards
What’s an integer
It’s another name for a whole number - either s positive or negative number or 0
What are rational numbers
They can be written in 3 forms
Integers
Fractions
Terminating or recurring decimals
What are irrational
They can’t be written as fractions - they are never ending, non repeating decimals. Square roots of positive integers are either integers or irrational eg square root of 3 is irrational but square root of 4 is 2 and so is rational
Pi is irrational
What does bodmas stand for
Brackets Other Division Multiplication Addition Subtraction
Tells you the order which operations should be done
What’s the reciprocal
The reciprocal of a number is just 1 divided by the number eg 1/8
What are the multiples of a number
Just it’s time table we some multiples of 8 are 16,32
What are factors
Factors of a number are all the numbers that divide into it
Eg factors of 12 are 1, 12, 6, 3, 4
What’s a prime number
A number that’s only factors are itself and 1 - only exception is one which is not a prime number
How do you find the prime factors of a number
Can be broken down into a string of prime factors all multiplied together - called prime factor decomposition or prime factorisation
How do you make a prime factor tree
Start with the number at the top and split the number into factors
Every time you get a prime number ring it
Just keep factorising the numbers, then write out the primers in numerical order and if there’s more than one the same - put it as a power
Eg prime numbers are 2 X 2 X 3 X 5
Do 2^2 X 3 X 5
What’s the LCM
Least common multiple
The smallest number that will divide by all the numbers in the question
so LCM of 12 and 15 is 60
Lowest common MULTIPLE
What’s the HCF
The biggest number that will divide into all the numbers in the question
Eg the HCF of 36 and 54 is 18
How do you cancel down
To cancel down or simplify a fraction, divide top and bottom by the same number until you can’t
What’s a mixed number
With an integer and a fraction part .
What’s an improper fraction
Where the top number is larger than the bottom number - need to be able to convert mixed numbers to improper fractions and other way around
How do you multiply fractions
You can cross cancel then just multiply the numerators by the denomenators
How do you divide fractions
Flip the second fraction and multiply
Dividing fractions easy as pi, flip the second and multiply
What’s a common denominator
A denominator that can fit into all the fractions in a question
Easiest way to find it is to find the LCM bad there it, then multiply up to that denominator so all fractions have the same denominator
Tell me how to add and subtract fractions
Rewrite the mixer numbers as fractions
Find a common denominator
Combine the top lines and subtract numerators or add them
How do you work out fractions of something
Eg 9/20 of £360
Of means multiply the something by the top of the fraction and divide it by the bottom
Eg 360 divided by 20 X 9 = £162
How do you express numbers as fractions
Eg write 180 as a fraction of 80 so then just write 180/80 and cancel down
How is proportion represented
Expressed in fractions, decimals and percentages
How do you convert fractions, decimals and percentages
Fraction -> divide -> decimal -> X 100 -> percentage
Percentages -> divide by 100 -> decimal
To convert decimals to fractions it’s awkward
For terminating decimals, the digits after the decimal point go on top and a power of 10 on bottom - same number of 0s as there were decimal places
For recurring decimals to fractions see next questions
How do you turn recurring decimals into fractions
So name the decimal - eg r
R= 0.234 recurring
The multiply until the recurring part is in interfere and fully repeated so
1000r = 234.234 recurring
Now subtract to get rid of decimal part
1000r = 234.234 - R=0.234 = 999r = 234
So r = 234/999 = 26/111
Tell me how to turn recurring decimals into fractions - the difficult way
Eg write 0.16 recurring as a decimal
Name decimal r = 0.16 recurring
Multiply to move non recurring part of decimal past decimal point
So 10r = 1.6 recurring
Now multiply again to move full repeated Lump past decimal point
100r = 16.6 recurring
Subtract to get rid of decimal part
100r = 16.6 - 10r = 1.6
= 90r = 15
r = 15/90 = 1/6
How do you put fractions into recurring decimals
8/33 as a recurring decimal
2 methods
Find an equivalent fraction with all nines on bottom and number on top is the recurring part so 24/99 = 0.24 recurring
Or divide if you have a calculator 8 divided by 33
How do you round numbers to decimal places
Identify the position of the last digit from the number of decimal places - look at next digit to the right and round - must be no more digits after the last digit you want
Eg to round 7.4748 to 2 decimal places
7 is last digit and the 4 on the right is the decider so it’s 7.47
How do you round numbers to significant figures
The 1st significant figure of any number is the first digit not a 0
2nd, 3rd etc significant figures follow on immediately after the 1st regardless of being 0s or not 0s
What is estimating
Taking a look at numbers and making them easier to do calculations- won’t need to be as accurate as the real thing
How do you estimate calculations
Round numbers to easier one usually 1 or 2 sf and do calculation
Use special swirly equals signs
How do you estimate square roots
Find 2 square numbers, one either side of number given
Decide which is closest to and make a sensible estimate of the digit after the decimal point
What’s a bound
When a measurement is rounded to a given unit, the actual measurement Can be up to half a unit bigger or smaller
The lower bond is the smallest a measurement can be and the upper bound is the largest
You can work out intervals
- difference between them
Eg is greater than or equal to the lower bound but less than the upper bound
What’s truncated
When a measurement is truncated to a given unit, the actual measurement can be up to a whole unit bigger but no smaller
How do you calculate the maximum and minimum values for calculations
You need to calculate the lower and upper bounds for measurements and use them
What’s standard form for
Useful for writing very big or very small numbers
What are the 3 rules of standard rules
The front number must always be between 1 and 10
The power of 10, n, is how far the decimal point moves
N is positive for big number and negative for small numbers
How do you multiply powers
Rearrange front numbers and powers of 10 together
Multiply or divide front numbers and multiply or divide powers of ten (add or subtract powers)
Make sure answer is still in standard form
How do you add or subtract powers
Make sure the powers of 10 are the same and add or subtract the front numbers
Convert the answer to standard form is necessary
