Quote:
Originally Posted by PorscheGAL
My son has a problem in his math book that has not shown itself in previous lessons and I was hoping someone here could help.
If a * b = a - 3b and a # b = 2a+3b, evaluate the expression (4 *3) # 5.
In a problem like this, what does # mean? He has several of these types of problems in the next few lessons and I want to make sure we understand it fully. I have looked in my teacher's book and it has a poor explanation.
TIA
|
This type of question has been commonly showing up on HS Introductory algebra tests for decades
the # and * are abstract operations which are
defined in the statement of the problem, other symbols, &,%,? etc. are commonly used as well,
* is not multiplication this is mistake one.
The object of the question is to determine if the student can follow the abstract rules
as presented w/o having any prior experience w/ them and then evaluate the resulting expression using the common math operations.
a * b = a - 3b is the definition of the * binary operator in terms of the usual subtraction binary operator and implicit binary multiplication using the variable values of a & b
similarly a # b = 2a+3b is the definition of the # binary operator in terms of the usual addition and implicit multiplication binary operators using the variable values of a & b.
the substitution principle, use of parenthesis and the use of the unary - operator are also involved in the solution.
starting w/ a=4, b =5 because it is inside parenthesis
a * b = a - 3b
becomes
4 * 3
4 - 3(3) per the def of * and substituting
4 - 9 regular arithmetic
-5
and then using the def of #
a # b = 2a+3b
(4 * 3) # 5 note that the current value of
a was derived in the previous step as
-5
(-5) # 5 implicit multiplication by 1 implies 1(-5) = -5
-5 # 5 the current value of a is -5 and the current value of b is 5
2(-5) +3(5) per the def of #
-10 + 15
5