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0:23 AM Math Concept----------- kashim | |
Without parentheses, without using a calculator
In a series of calculations without parentheses, the
calculations should be carried out in the following order:
first the square roots; then the powers (always starting with the one that is furthest left); next, the multiplications or divisions (always starting with the one that is furthest left); finally the additions or subtractions (always starting with the one that is furthest left). We say that the square roots take precedence over the powers, the powers take precedence over the multiplications and divisions, and that these have priority over the additions and subtractions.
Example: We want to calculate
A = 7 + 3 × 4² – 6.
First we carry out the power calculation:
A = 7 + 3 × 16 – 6.
Next the multiplications (or divisions):
A = 7 + 48 – 6.
And finally the additions or subtractions, from left to
right:
A = 55 – 6; A = 49.
Note: Remembering the correct order of operations
can be difficult. Therefore, the preferred approach is to use parentheses to
indicate the order of calculations, as described below.
B. With parentheses, without using a calculator
If there are parentheses, the calculations inside each
pair of parentheses are carried out according to the rules of precedence,
starting with the innermost parentheses.
Example: We want to calculate
B = (–3) + (4 + 5) × (7 – 12 × (5 – 2)).
We carry out the calculation beginning with the
innermost pair of parentheses:
B = (–3) + (4 + 5) × (7 – 12 × 3)
We apply the rules of the order of operations to the
inside of each pair of parentheses:
B = (–3) + 9 × (7 – 36) B = (–3) + 9 × (–29) B = (–3) + (–261) B = –264
Note: Pay attention to implied parentheses. The
following examples demonstrate how to interpret certain calculations.
Given
 . We should understand:  . We therefore have:  .
Given
 . We should understand:  . We therefore have:  .II. Calculating with a calculator
Take the preceding calculations A, B,
C, and D again with a scientific calculator.
A. Calculating A = 7 + 3 × 4² – 6
It is generally necessary to input the following
sequence (the drawings on the keys may be different!):
7
 3  4   6 
In general, the result given is: 49.
B. Calculating B = (–3) + (4 + 5) × (7 – 12 × (5 – 2))
Input the sequence:
3
 ( 4 5 ) ( 7 1 2 × ( 5 – 2 ) )
The result will be given: -264.
Note: It is important to distinguish the
subtraction key (press – ) and the +/– key (or (–) ), which allows you to
input a negative number or obtain the opposite of the number given.
C. Calculating
Input the sequence:
1 1
( 3 4 )  ( 1 3 5 )
Note that the order of precedence of operations will be
respected.
Depending on the calculator, the result will be given
as: 81/8 or 10.125. | |
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BASIC ENGLIS USAGE
