Hi,
I found out that I keep getting confused about some equations, like the following:
Say A - B = C
As practice I compare this to 15 - 5 = 10.
So that would be:
B = A - C (10 = 15 - 5)
But, let's say you know A and C and would to calculate B, then:
-B = C - A (-5 = 10 - 15)
and NOT
B = A - C
Correct: B = - 5
Incorrect: B = 5
But what do you personally used as a 'bridge' / reminder to approach it the right way at once?
(most of the item I end up trying B = A - C and get it wrong)
-B = C - A (-5 = 10 - 15)
and NOT
B = A - C
Err, why NOT??
From
A - B = C
both forms
-B = C - A ((A subtracted on both sides))
and
B = A - C ((B added and C subtracted on both sides))
are equivalent, because you just need to multiply one of the equations by -1 to yield in the other equation.
But what do you personally used as a 'bridge' / reminder to approach it the right way at once?
(most of the item I end up trying B = A - C and get it wrong)
I don't understand. I make equivalence transformations until the unknown variable is isolated (or else I do not know how to continue). In the given example I'm interested in B, not in -1 times B.
B = 5 is the correct answer. The variable is B and not -B.
15 - B = 10 <=>
-B = 10 - 15 = -5 <=>
-B = -5 <=>
B = (-)-5 = 5
My usual order of operations when doing it in the head is to isolate the variable I'm trying to solve for so that it's positive:
A - B = C <=>
A = C + B <=>
B + C = A <=>
B = A - C
I think you made an error substituting the variables with your values:
The first case:
A - B = C -> 15 - 5 = 10
thus:
A = 15
B = 5
C = 10
The second case:
B = A - C -> 10 = 15 - 5)
thus:
A = 15
B = 10
C = 5
Can't make any sense! ;)
Draw a circle, divide it in half vertically, and divide the lower portion in 2 horizontally.
Since F is the product of mass and acceleration, it takes the top spot, and the factors take the lower 2 spots.
F
-----
M | A
To solve for mass, cover it up, leaving F over A or F/A. to solve for acceleration, you cover up A, leaving F/M.
the same can be done for addition/subtraction as long as you remember the one permutation of the formula.
since you know a-b = c, then A is the sum of b+c and goes on top, with b and c taking the lower left and right respectively.
A
------
B | C
To solve for something other than A, cover what you want to solve up, and examine the relation between the 2 remaining values.
B = a-c, c=a-b
I use this to introduce formulas to trade students and they seem to grasp it much faster than a crash course in algebra.
I like to think of algebra problems like this almost as proofs. An equation is a statement that has a truth value. Our objective is to transform the statement into one that is logically equivalent, but more useful. "A - B = C" is logically equivalent to "A = C + B", "-B = C - A", "B = A - C", "2A - 2B = 2C", and an infinite variety of other statements, but only some of those are ever going to be useful. So, when you see a problem that boils down to "solve for x", what that's really saying is: an equation of the form x = '...' is more useful, so we need to apply a sequence of transformations to get the equation into that form while preserving its truth value/equivalence to the previous statements. Much like a logic proof, where you take a set of axioms and theorems and derive new theorems.
