Pre-Algebra: Chapter 5-5
Adding and Subtracting Unlike Fractions
To add or subtract unlike fraction, MAKE SURE that the denominators are converted to the same value. You may use the LCM/LCD technique, multiply both denominators together (sort of the like the LCD idea) or see of one denominator is a factor of the other. Remember too, that you can borrow whole units from the integer part of the fraction. You can convert the whole 1, into fractions like 5/5 to add where needed. See this link for GREAT EXAMPLES.
Algebra: Chapter 8-2
Substitution Method
You can solve 2 equations by solving 1 equation for 1 variable and then substituting that equivalent expression in the other linear equation. By doing this, you eliminate one variable. Solve for the remaining variable and then substitute its value in the original equation to find the first variable.
Here is an example, its easier that way:
x – 2y = 6 and 3x + 2y = 4
Solve the first equation for x, so … x = 6 + 2y
then substitute for x in the second equation which now looks like: 3(6 + 2y) + 2y = 4.
We must distribute the new equation in y, it now looks like: 18 + 6y + 2y = 4 or
combining like terms we have: 18 + 8y = 4 or
8y = 4 – 18 … or … 8y = -14 and y is finally = -14/8 or -7/4!
With y = -7/4, we can use the first equation to write:
x – 2(-7/4) = 6 … or …. x + 7/2 = 6 … or …. x = 5/2!
The solution is then (5/2, -7/4)!! Wow!!!!