I have an ext. exam coming up tomorrow and I needed help with Equations with Fractions.
I looked up a tutorial and got this, which I do not understand:
How do they multiply the terms by 15?Multiply both sides of the equation -- every term -- by the LCMof denominators. Every denominator will then cancel. We will then have an equation without fractions.
+ x − 2
The LCM of 3 and 5 is 15. Therefore, multiply every term on both sides by 15:
Each denominator will now cancel into 15 -- that is the point -- and we have the following simple equation that has been "cleared" of fractions:
+ 15· x − 2
= 15· 6
5x + 3(x − 2) = 90.
Like how do they multiply 15 by x over 3?
This is confusing. :P
Thanks in advance!
It may be more convenient to break division into two operations: multiplication and reciprocal function. Thus, x / y would really mean x * (1 / y). This is, in fact, how it is done in higher mathematics.
As you know, multiplication obeys the following laws:
x * y = y * x (commutativity)
x * (y * z) = (x * y) * z (associativity)
= 15 * (x / 3) =
15 * (x * (1 / 3)) = (by definition of division)
15 * ((1 / 3) * x) = (by commutativity)
(15 * (1 / 3)) * x = (by associativity)
5 * x
because 15 * (1 / 3) = 15 / 3 = 5.
Think of as a brick, (or some other object if you prefer it).
divided by means that the brick is being divided into three pieces, is a third of a brick.
Now suppose that you have of these and that they could be stuck back together again. How many whole bricks could you make ?
Answer bricks. Algebraically,
For the next term, relate to some object.