Page 310 - Theory and Problems of BEGINNING CHEMISTRY

APP.] SCIENTIFIC CALCULATIONS 299

The rules of precedence followed by the calculator are exactly the same as those for algebra and arithmetic,
exceptthatinalgebraandarithmetic,multiplicationisdonebeforedivision(multiplicationhasahigherprecedence
than division). Algebraically, ab/cd means that the product of a and b is divided by the product of c and d.On
the calculator, since multiplication and division have equal precedence, if the keys are pressed in the order

a × b ÷ c × d =

the quotient ab/c is multiplied by d. To get the correct algebraic result for ab/cd, the division key should be
pressed before the value of d is entered, or parentheses should be used around the denominator.

EXAMPLE A.12. What result will be obtained from pressing the following keys?
3 6 ÷ 9 × 2 =
Ans. The result is 8; first, 36 is divided by 9 and then the result (4) is multiplied by 2. If you want 36 divided by both 9
and 2, use either of the following keystroke sequences:

3 6 ÷ 9 ÷ 2 =

or 3 6 ÷ ( 9 × 2 ) =
EXAMPLE A.13. Solve:

9.3 9.3
(a) × 2.0 (b)
6.0 6.0 × 2.0
Ans. (a) The answer is 3.1. The keystrokes are
9 . 3 ÷ 6 . 0 × 2 . 0 =
(b) The answer is 0.775. The keystrokes used in part a do not carry out the calculations required for this part. The
correct keystroke sequence is

9 . 3 ÷ 6 . 0 ÷ 2 . 0 =

or 9 . 3 ÷ ( 6 . 0 × 2 . 0 ) =
Either divide by each number in the denominator, or use parentheses around the two numbers so that their product
will be divided into the numerator.

Division
In algebra, division is represented in any of the following ways, all of which mean the same thing:
a
a/b a ÷ b
b
Note that any operation in the numerator or in the denominator of a built-up fraction (a fraction written on two
lines), no matter what its precedence, is done before the division indicated by the fraction bar. For example, to
simplify the expression
a + b
c − d
the sum a +b is divided by the difference c−d. The addition and subtraction, despite being lower in precedence,
are done before the division. In the other forms of representation, this expression is written as

(a + b)/(c − d) or (a + b) ÷ (c − d)