 or or taken why

Make sure to remember your password. If you forget it there is no way for StudyStack to send you a reset link. You would need to create a new account.

Enter the associated with your account, and we'll email you a link to reset your password.
Don't know
Know
remaining cards
Save
0:01
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size     Small Size show me how

# Ch 4: Fr., Fa. & Ex.

### Chapter 4 - Pre-Algebra 2: Fractions, Factors, and Exponents

Rules for divisibility 2 - ends in an even number - 0, 2, 4, 6, or 8 3 - the sum of the digits can be divided by 3 evenly 4 - the last two digits can be evenly divided by 4 5 - ends in 0 or 5 6 - if divisible by 2 and 3 8 - last 3 digits can be divided by 8 evenl
Rules for divisibility (continued) 9 - the sum of the digits can be divided by 9 evenly 10 - ends in 0
Factors Any number that can be evenly divided into another number.
Order of operations PEMDAS 1. Parentheses 2. Exponents 3. Multiply 4. Divide 5. Add 6. Subtract Sentence: *Please Excuse My Dear Aunt Sally.* *Multiply and divide, add and subtract left to right.*
Exponent A number written to a power where the power (exponent) tell us how many times to multiply the number by itself.
Base Example: 2^3 2 is the base.
Power Example: 2^3 3 is the power, or exponent.
(-3)^2 means (-3)^2 means (-3)x(-3), which would equal 9.
-3^2 means -3^2 means 3x3, which would equal -9 because you add the - sign to the answer once you have completed the problem, no matter what the number(s) is/are.
Prime Numbers Numbers with only 2 factors; 1 and itself. Example: 5=5x1
Composite Numbers Numbers with 3 or more factors. Example: 18=1, 2, 3, 6, and 9
GCF Greatest Common Factor The greatest number that is divisible into a group of numbers.
Variable GCF Example: x^2y^5,xy^3 The answer is xy^3. RULE: *Smallest power of common factors.*
Prime Factorization Example: 120 2x60 2X30 2x15 5x3 The prime factorization would be 2^3x3x5. *Hint: Use prime numbers in tree to determine prime factorization.*
Finding prime factorization using GCF Example: 78 and 124 78 2x39 3x13 The prime factorization for 78 would be 2x3x13. 124 2x62 2x31 The prime factorization for 124 would be 2^2x31. You then need to find what the two prime factorizations have in common with each oth
Finding prime factorization using GCF (continued) FINAL ANSWER: The final answer is 2, because you must use the smallest power of common factors, which is 2, not 2^2.
What is the rule for solving problems involving the Greatest Common Factor of 2 or more numbers? Always use the smallest power of common factors.
Simplifying Variable expressions Example: 12x^2y^5 __________ 8x^4y^2 The answer would be: 3y^3 _ 2x^2 You are simplifying what is already there.
What is the rule for simplifying variable expressions? When you are simplifying variables with exponents, you subtract the smaller power from the larger power, and whatever that power is, that will be the power for your variables in your final answer.
Rational Numbers Any number that can be written in the form a - b where b ≠ (is not equal to) 0.
Examples of rational numbers -2 - 8, 8 - 8, and -0.5. Pi, or 3.14, (π) is not a rational number.
Negative Rational Numbers - how do you write If the numerator is a positive number and the denominator is negative number, you make the numerator a negative number and the denominator a positive number; then, you simplify or reduce to the simplest (most simplified) term.
Negative Rational Numbers - how do you write (continued) If both the numerator and the denominator are negative numbers, you make the entire fraction or term positive.
Multiplying exponent rule Rule: Multiplying powers with the same base: a^m x a^n = a^m+n and a^4 x a^7 = a^4+7.
Multiplying exponent rule Example Example: 4x^3y^5 x 3x^2yz^2 12 x^3+2 y^5+1 z^2 Your final answer is: 12 x^5 y^6 z^2.
Power of Power rule Rule: When multiplying a power of a power: (a^m)^n = a^mxn => (x^6)^4 = x^6x4 = x^24.
Power of Power rule Example Example: (x^3y^5)^4 x^3x4 y^5x4 Your final answer is: x^12 y^20.
Zero exponent rule Any number written to the zero power is 1.
Zero exponent rule Example Example: x^0 = 1.
Negative exponent rule Negative exponents are the reciprocal of the positive exponents. Numerator = Denominator Denominator = Numerator (Swap negative numbers)
Negative exponent rule Example Example: x^-3 = 1 --- x^3.
Write without negative exponents (example) Example: x^-3 y^2 -------- a^2 b^-3 Swap negatives! The final answer is: y^2 b^3 ------- x^3 a^2.
Rewrite without a fraction bar The number and variables with powers on the top (numerator{s}) remain the same. The numbers and variables with powers on the bottom (denominator{s}) are the opposite of themselves and are last in the fraction without a bar; (equation).
Rewrite without a fraction bar Example Example: x^3 y^2 ------- a^2 b^3 Your final answer would be: x^3 y^2 a^-2 b^-3, as you kept the numerator(s) the same and made the denominator(s) the opposite (the numbers) of themselves.
Rewrite without zero or negative exponents and simplify If there a variable with a zero exponent, you would never include it in your final answer. Anything with a zero exponent equals 1, and the number 1 is never necessary to be included in our final answer.
Rewrite without zero or negative exponents and simplify (continued) This also applies for a variable by itself with no power/exponent by itself.
Rewrite without zero or negative exponents and simplify Example Example: x^-3 y^2 z^0 ------------ x^-2 y^-3 Rewrite: y^2 x^2 y^3 ----------- x^3-2 Your final answer would be: y^5 over x.
Rewrite without zero or negative exponents and simplify Example (Continued) BE SURE TO WRITE WITH A FRACTION (OVER)! You would not include z^0 or x^1; instead, you would include just x, as x^1 is equal to x.
Rewrite without zero or negative exponents and simplify STEPS: 1) Rewrite without zero or negative exponents 2) Simplify
Austin O'Keefe Period 2
Created by: okeefeaustin