Putting numbers in ascending order (whole
numbers & decimals)
1. Put them in groups according to
how many digits they have smallest to
biggest amount.
2. Then order each of those groups in
numbers according to the digits for example:
1,3,8,9 23,34,67,84, 100,135,654,879,
1134,2335,4657,7685
decimals: 1. group the numbers according to how
many zero's there are after the decimal point.
2. Than compare the numbers within the groups by looking at
the number after each last zero that is after the decimal point
and the number which is the smallest goes first as it's
asscanding order.
The most amount of zero's of decimal groups
is the smallest decimals so the smallest
amount or no amount of zero's after the
decimal point is the biggest number.
Adding and subtracting
decimals:
1. same as normal method expect the digits should
be lined to the decimal place
2. Once there all lined do the same way you would
either add or subract normally.
when subtracting put the biggest decimal above
first if it helps imagine the decimals as pounds.
2. multiplying decimals you must move the
decimal place which is already there and if the
decimal point moves places and there's no number
than you must add a zero.
multiplying other numbers like 300 split the number for
example you can divide by three than put a decimal at
the end of the number if it's not already a decimal and
move it two places to the right.
Dividing a number by ten you move the invisible decimal
one place to the left for decimals you divide using the
actual decimal which is VISIBLE andivide by moving it one
decimal to the left. for divide you do not need to keep the
zero if it's on the right hand side, on the left you must add a
zero to fill it in
2.when dividing with normal numbers that are not 100 than split the number and
repate the process however instead of adding two 0's move the decimal point
two places to the left. when it comes to decimals you must turn the number into a
whole number by x's it by 10 100 or 100's all numbers should be on the left than
divide how you would normally using the bus stop method and than add that
decimal place according how many digits there were on after the decimal point
for both of the decimal numbers that were used before.
1. To multiply by 10 you must add a single 0 on whole numbers with
two digits however you can also imagine a decimal point at the end
of the number and move the decimal point along one place to the
right the the same will apply if you're mulitplying by 100 0r 1000
expect you move it along two or three decimal point as there are two
or three zero's.
multiplying without a
calculator(CHINESE
METHOD)
Dividing without a calculator for
whole numbers and decimals
(BUS STOP METHOD)
1.Draw the bus stop method diagram and on the outside
write the divider even it has two digits than write the
number that's getting divided on the inside if a decimal
than decimal point on top where the answer will be and
also inside the diagram to.
2. than work it starting from the number closet to the divider our
if the number doesn't go into that particlar number than carry that
number to the other one to make a 2 digit number on the next one.
same goes to reminders carry them on.
3. place the numbers on top of the bus stop line that will be
you're answer. If there's a reminder on the last digit than just
carry it avove on top of the bus stop line and add it into you're
answer like you would for the addtion method. the above is you're
answer.
1. split the digits and put them in a grid make
sure to draw digonal lines.
2. Once you have done that from the bottom right
times each digit if the digit is a single digit than add a
zero ahead for example an 8 is 08
3. Once that is done you start from the bottom right using the digonal
lines as a guide. IF THE NUMBER ADDED HAS TWO DIGIT CARRY
ONE ON TO THE RIGHT the remaining numbers that you had addedis
you're answer.
for decimals just x the number so it turns to a whole number and than do the same
Chinese method and how ever much amount of digits there were after the decimal
point put a decimal point so that's how much digits there are, make sure to have the
same amount of digits from both number
approximates to one DP (decimal place)
& sp (significant place)
1. Rounding to one DP you have to: first find out
weather it's to one or two decmal place and circle
the 2nd or ist number after the decimal point
2. Look at the number next to the circle number that will be the decider. If the
decider is 5 or more than round it up one and if the decider is four or less
then round it one. you have to get rid of the remaining numbers after the 2
or 1 number that is mean;t to be rounded off. if the decider is 9 than
rounded of would be ten so than carry 10 to the digit ahead.
( 1 or... Significant place)
1. look at the digits whatever number that is after a zero or the first
number of th(this zero must in the beginning of the decimal and
not after a whole number digit)l if there isn't a 0. Than you look at
the number next to it on thr right that will be the decider weather
you round up or down. The remaining digits you get rid as you'll
only need the amount of digits it says in the question. If the
signifcant figure is the first digit of a whole number than fill in the
rest of the remaining digits in 0 also fill in the gaps of any decimal
points with a 0.
LCM & HCM
LCm: to find the lcm you must find the smallest
number that aill divide all the numbers you are
given to find this out you write the timetables of
the given numbers and look for the lowest mulitply
in all the timetables written likewise you do the
same for HCM however you look for the biggest
number rather than the smallest
Ratio
give the ratio in his simplist form well you have to look at both numbers
and see what they times by both should times by same number and
keep simplyfing until it cannot be done xample
dividing in a given ratio well you first add the two ratios
than you use that new number and divide the other
number and then you mulitply one part by the ratio to
get you're new ratio for example
Graphs
Shapes & area
Angles & geometry
Measures
statistics & probabilty
Algebra
square numbers: when you
square a number you multiply it
by itself. all square numbers
answers are positive
reguardless if you're doing two
minus whole numbers or not
Cube numbers: when you times a
number by itself than by itself again.
cube numbers can give posative and
negative answers
other powers: the littel number on the right of
a whole number or decimal can be any
number but you times it by that many times
like you would for sqaure or cube it's the
same method just diffrent numbers to multply it
with. the little number is called the power of
index. you read this as somethimg to power
of something 3 to the power of 5
Power rules: rule one when you multiply you add the powers. example
ruke two: when dividing you subtract the powers (the small
numbers on the top right of a normal number) example
rue 3: when raising (numbers in brackets) one
power to another you multiply.
rule 4: anything with the power 1 on a normal
number just keep the numbers the same,
anything to the power zero the answer
is always 1
if the big number is one than you just make
the answer one regardless what the power
maybe
Simplifying Terms
abc means a x b x c and 3a means
3xa
k x k x k x k means k4
(gn)2 g x g x n x n the brackets mean
both letters are squared, g x g x n x n
(-3) you do the ame -3 x-3= 9
collecting and simplyfing terms
= and + make a -
+ and a - makes -
= and = makes a +
+ and a + makes a +
1. circle individual terms
rembering to put a plus or
minuse infront of each
individual for all or as many as
you can an example
1. Now ithat it's a lot more clearer you
add up or take away the like terms to
make a similoar equation using the
like terms which are the letter that
repersent a number
expanding brackets
fitst you times what's outsside the brackets in the inside of
the brackets on each digits to make a new equation
then circle the new equations with the pkus or
minus in front and simplkyf if you can then
work oyt the answer example
watch out for minus
signs and collect like
terms at the end
factorings ( adding brackets in algerbnra equations)
inequalities and equalties
calculator methods to use in exam
Fractions
Equivilant fractions and simplyfing (cancelling down)
To simpligy you must 1. you must multiply
the numorter and demonitor to make the
even number which is asked in the
questions the top and bottom should be
timed same. you make a fracyion equvilant
so the denimontor is even and easier to
divide.
To simplyfy fractions you divide the top and botom till it can
longer be divided. an easier way to do this is look at the
denomintor and numonayor and look for the lowest common
factor that both can be divided and make that into the fraction in
nthe right order if the nu,bers are ecen then repeate the process
again until not completly dimplified. or you can go through the
first ten times tvle and think if it can be divided and the lowest
term will be the simplistexample
iconverting mixed fractions nto fractions look at the denominators of all the fractions than
1. you have to times the mixed number by the
demoniator then add the numerator that will be
you're new numerator the demoniator stays the
same only the numerator changes
Converting fractions to mixed numbers
divide top by bottom you write the whole number as the big number and
the reminder goes into the numerator
ordering fractions:
for all the fractions look at the
denominator and write down the
timetable for each and find the
LCM change all the demoniators
than times the same you did for the
bottpm on the top than order
remeber to put the orginal
fractioms in the answer not the
converted ones that's just to help
you line your's and the orginal
together to make it clearer to see
what ti write in the answer
adding and subtracting fractions
when nymbers on the bottom is
the same tjhan just add or
subtract tht top and keep the
nottom you havve yo cancrl thr
answer down if it can/
when numbers of a fractiomn the
denominators aere nit the same than you
must must find the denominators lowest
commen muliply and then do what you
did for the bottom top to the times than
continue normally as yiou would
remerbing ti cancelling down the answer if
you can/
when adding and subtracting with mixed
nymbers you must convert them into
normal fractiomns by getting the whole
number and times it by denominator and
than add the numerator to make the new
numerator and than proceed if the bottom
are not same number than find LCM and do
top as bottom and subtract or minuse if
you want to turn the answer back into a
mixed number than divide top my bottom
the reminder will be the whole number
mulitplying and dividing fractions:
when multiplying improper or normal fractions times
top and bottom to get you're answer. you can then
cancel down. if possibel cancel down the fractions in
teh sum first to find the answer
when having fraction of a number than you mist turn the number into a
fraction by putting the numerator as number and the denominator always as
1 than times as normal
when dividing you turn teh second
fraction upside down and tomes the two
fractions to get youre answer and simplyf if
asked.
when dividng with fractions and whole numbers do
the same do the numebr over 1 as a fraction and than
flip the second fraction and times normaaly but simply
the fractions first if ou can
qhen multiplying or dividing mix
numbers you must tur the mixed
number into a fraction and proceed
how you would.
percentage decimals and fractions
fraction - decimal top
divided by bottom gives
you a decimal
decimal to
percantage x by
100
percantage to decimal you
have to divide by 100
decimal to fractions
you must you
divide top by
bottom and than
you must decide if
you need to times
over 10 100 1000
you know by looking
at amount of digits
after the decimal
points if tehre's two
then you do 100
to find out the percantage of something
1. divide the percentage by 100 than
and then you will have a decimal get
that decimal than times it by the second
number that needs to be found the the
new decimal is you're answert exampke
increase or decrese of a
percentage
1. first you need work out 1% of something you need to
divide the whole number by 100 than you get a decimal that
you times on howver much perecnt needs to be time than
add or decerse that in the orginal number depending on waht
the questions asking yiou for example