Simplify Formulas /maths formula
SIMPLIFICATION
what is simplify?
In the simplification of
sum involving operations
of +,- ,×,and ÷,, frist do
÷, ×,+ and in that order. We can
remember this order
as ODMAS where
O is of, D is divition, M is Multiplication, A is
addition ,S is Subtraction.
However ,, when bracket
are present in a simplification
sum, the order is know as
“BODMAS:”and we proced as
follows..
(a) Frist we
perform the operations within
the frist brackets , that is ( )
(b) Secondly wedo
the operations with the 2nd
brackets, that is {
}.
(c) Finaly we do the operations with
square brackets , that
is [ ]
NOTE ;Note
that ‘—‘ is also
used as bracket called
“vinculum”
(d) The rest of simplifications is done using ODMAS” rules
(e) In the brackets
also we must
follow the “ODMAS” rules .
( )
brackets are ooften called frist brackets , parentheses
or round brackets ,
{ }
brackets are called second
brackets , braces or curly brackets ,
second brackets often
enclose the frist
brackets .. [ ] brackets are called block
or square brackets, ‘—‘ is called
bar brackets or ‘’ vinculum’’
Example : Simplify: {(7+13) ÷5} ÷4-{(7×3) ×(2-2)
= {20 ÷ 5} ÷ 4-{21×0}
= 4 ÷ 4-0
=1-0
=0
ROUNDING NUMBER
*To round a number to the nearest 10, we use the nearest multiple of 10.
*To round a number to the nearest 100, we use the nearest multiple of 100.
* To round a number to the nearest 1000, we use the nearest multiple of 1000.
Example; Round 2,126 to the nearest 10,100 and 1000 respectively.
Solved; The multiples of 10 nearest to 2,126 are 2,120 and 2,130
2,126
_______________________________/______________________
Example; Round 2,126 to the nearest 10,100 and 1000 respectively.
Solved; The multiples of 10 nearest to 2,126 are 2,120 and 2,130
2,126
_______________________________/______________________
2,120 2,125 2,130
nearest 10 nearest 10 after 2,126
before 2,126
2,126 a can be seen is closer to 2,130 so it is rounded up to 2,130.
the short cut is as under .
Rule 1 ; For rounding to the nearest 10 check the digit at the ones place.
___Greater than 5 Round up: Since 6>5 add
/ 1 to digit at ten
2,126--- Replace by zero round up to 2,130 place ,replace the
/ one place by 0.
/
Increase to 3
Rule 2 ; To Round to the nearest 100, check the digit at the tens place.
__ Less than 5 Round down;
/ 2<5; No change in the
2,126--- repalce by zero Round down to 2,100 digit at the hundred place
/ replace digit at tens and
/ ones place by zero.
No change
Rule 3 ; To round to the nearest 1000, check the digit at the hundred place
___Less than 5 1<5; Round
/ down
2,126--- replace by zero Round down to 2,000
/
No change
Rounding off Large Numbers
nearest 10 nearest 10 after 2,126
before 2,126
2,126 a can be seen is closer to 2,130 so it is rounded up to 2,130.
the short cut is as under .
Rule 1 ; For rounding to the nearest 10 check the digit at the ones place.
___Greater than 5 Round up: Since 6>5 add
/ 1 to digit at ten
2,126--- Replace by zero round up to 2,130 place ,replace the
/ one place by 0.
/
Increase to 3
Rule 2 ; To Round to the nearest 100, check the digit at the tens place.
__ Less than 5 Round down;
/ 2<5; No change in the
2,126--- repalce by zero Round down to 2,100 digit at the hundred place
/ replace digit at tens and
/ ones place by zero.
No change
Rule 3 ; To round to the nearest 1000, check the digit at the hundred place
___Less than 5 1<5; Round
/ down
2,126--- replace by zero Round down to 2,000
/
No change
Rounding off Large Numbers
The same method as discussed above is applied to rounding off large numbers, The following example will be helpto understand it clearly.
Example; Round off each of the folloing numbers to the nearest ten thousand.
(a) 682437 (b) 4287532
(a)Solved; In the number 682437 the digit at the thousand place is 2 which is Less than 5 , therfore we do not make change in the digite 8 at the ten thousnd place and replace the digite 2,4,3 and 7 by zero.Hence rounded off to ten thousend, 682437= 680000.
(b)Solved; In the number 4287532 the digit at the thousand place is 7, which is greater than 5. Therefore ,we increase the digit 8 at the ten thousand place to 9 ,and replace the digit 7,5,3,2 by zero.Hence, rounded off ten-thousands place 4287532=4290000.
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