Simplification
BODMAS acronym: Brackets ( Parts of a calculation inside brackets always come first )
Orders ( Numbers involving powers or square roots )
Division
Multiplication
Addition
Subtraction
Brackets: Start with anything inside the brackets, going from left to right.
Example sum 5*(3+2)=?
You need to do the operation, or sum, inside the brackets first, 3 + 2, then multiply the answer by 5
3+2=5
5*5 = 25
If you ignored the brackets and did the sum 5 + 2 you would get 17.
You can see how the brackets make a difference to the answer.
Orders: Do anything involving a power or a square root next ( these are also known as orders ), again working from left to right if there
is more than one.
Example sum 2^2+ 3 = ?
You need to do the power first, before you can add 3.
Division and Multiplication Once you have done any parts of the sum involving brackets or powers the next step is division and multiplication.
Multiplication and division rank equally, so you go from left to right in the sum, doing each operation in the order in which it appears.
Example sum
3*5/3+7=?
You need to do division and multiplication first, but you have one of each. Start from the left and work across to the right, which means that you start with 3 *5=15
Then do the division, 15 / 3 = 5
Only then do you move to the addition: 5 +7=12
The answer is 12
Addition and Subtraction
The final step is to calculate any addition or subtraction. Again, subtraction and
addition rank equally, and you simply move from left to right.
Example sum
5+7-8+4=?
You simply start on the left and work your way across.
5+7=12
12-8=4
4+4=8
The answer is 8.
To Find Greater Value Between Fractions
Example sum Find greater value between fractions without calculating their decimal values of (11 / 10) and (7 / 9)
Consider (11 / 10) and (7 / 9)
Cross multiply the numerator and denominator of both the fractions.
11*9=99
7*10=70
99 > 70 so the fraction carrying 11 as the numerator is greater.
i.e. (11 / 10) > (7 / 9)
You can use this method when you are asked to find out the greatest or smallest among the given fractions.
