Fraction Operations (How-To)
What is the FIRST thing you should do before doing any operations?
FACTOR all the parts of the fractions!
Look at the index! (the baby number on the root)
What operation "undoes" an exponent?
A root with an index that matches the exponent.
What is the base of a common log (log)?
10
What can you NOT take the log of?
When MULTIPLYING fractions, you...
Multiply all terms straight across the top and straight across the bottom.
When simplifying radicals, how do you simplify variables/exponents?
Option 2: Write out appropriate number of variables and create groups of them based on the index.
What operation "undoes" a radical?
An exponent that is the same as the index.
e
When do you need to check your answers when solving?
When your problem begins with multiple logs.
When ADDING or SUBTRACTING fractions, you need...
Common Denominators!
When ADDING or SUBTRACTING radicals, you first need...
Like-Radicals (the radicals need to match!)
When taking an EVEN root, how many answers should you get?
Change to exponential form: log(3x)=7
107=3x
Solve: log(x+1)=3
x=999
When DIVIDING fractions, you...
Keep, change, flip!
(Keep first fraction the same, change operation to multiplication, and flip the 2nd fraction)
When adding like radicals, what numbers change? (Ex: the coefficients, the indexes, the numbers under the root, etc)
ONLY the coefficients change!
Can you take the ODD root of a negative number? (Ex: cube root of -64)
YES! Check in your calc!
Expand Completely: ln(2x2y7)5
5ln2 + 10lnx + 35lny
OR
ln32 + 10lnx + 35lny
Solve: ln(3x+2) = ln(4x-5)
x = 7
When SOLVING an equation with multiple fractions, you need to...
Get common denominators and then they cancel out when solving!
When MULTIPLYING radicals:
A. Do you need like radicals?
B. Which numbers do you combine?
A. You do NOT need like radicals to multiply.
B. Multiply all coefficients together AND multiply all numbers under the root together. Simplify the root afterwards.
Solve: 2(x-3)2=18
x=6, 0
Condense completely: log2 - 6logx + 9logy - logz
log (2y9)/(x6z)
Solve: log(x) + log (4x) = 2
x = 5
1.Condense logs.
2.Change forms
3. Solve for x.
4. Check answers.