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# czCh. 4 Fac.Frac.Ex.

Rules for Divisibility With 2, the number has to end in 0, 2 ,4, 6, 8. With 3, the number has to be divisible by 3. 4, the last 2 numbers have to be divisible by 4. 5, it has to end in 0 or 5. 6 it has to be divisible by 2 and 3. 8, last 3. 10 ends in 0.
Factors A number or quantity that when multiplied with another produces a given number or expression.
Order of Operations PEMDAS.
Exponent a quantity representing the power to which a given number or expression is to be raised.
Base the number that will be multiplied by itself when dealing with powers.
Power the number of times a certain number is to be multiplied by itself: 2 to the power of 4 equals 16.
(-3)^2 means The number, 9, will be positive because you multiply everything in the parenthesis
-3^2 means the number, 9, will be negative because you multiply 3 by 3 then add the negative sign.
Prime numbers Numbers that have only two factors, 1 and itself.
Composite numbers Numbers that have three or more factors.
GCF Greatest common factor: greatest number that is divisible into a group of numbers.
Variable GCF (ex. x^2y^5, xy^3) Finding the GCF of both of the same variables.
Prime factorization (ex. 120) Simplifying the numbers until the numbers are all prime.
Finding prime factorization using GCF (ex. 78 & 124) Use a tree chart to find the GCF of the numbers.
Simplifying Variable expressions (ex. 12x^2y^5 over 8x^4y^2) Simplify the numbers, then subtract the exponents of like terms so the answer would be 3y^3 over 2x^2
Rational numbers Any number that can be written in the form a/b where b doesn't equal 0.
Negative rational numbers- how do you write them If the negative sign is on the bottom when you solve, you have to put it to the top. If both are negative and you still have to simplify, the fraction will be positive.
Multiplying exponent rule (ex. 4x^3y^5 x 3x^2yz^2) So you would do x^3 times x^2, 4 x 3, y^5 x y.
Power of power rule (ex. (x^3y^5)^4) You multiply the exponent in the parenthesis by the exponent outside it.
Zero exponent rule (ex. x^0) Means that when there is a zero exponent, the number or variable turns into 1
Negative exponent rule (ex. x^-3) Rewrite with the reciprocal (ex. 1 over x^3)
Write without negative exponents (ex. x^-3y^2 over a^2b^-3) Reciprocal, unless the exponent is already positive.
Rewrite without a fraction bar (ex. x^3y^2 over a^2b^3) You would write the reciprocal of the numbers in the denominator.
Rewrite without zero or negative exponents and simplify (ex. x^-3y^2z^0 over x^-2y^-3) Write the reciprocal of the negative numbers and keep the positive ones positive. With the zero powers you would make it 1.
Colleen Zadoo period 2