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Ch4 Fac, Frac, Exp
Study for test
| Question | Answer |
|---|---|
| Rules for divisibility | 2: Ends with an even # (0,2,4,6,8) 3: Sum of the digits are divisible by 3 (2+4+6=12) is divisible by 3 4: The last two #'s are divisible by 4 (2/48) 4 and 8 are divisible by 4 5: Ends in a 5 or 0 6: Divisible by 2&3 8: The last 3 #'s are divisible |
| Rules for divisibility | 9: Sum of digits are divisible by 9 10: Ends in 0 |
| Order of operations | The mathematical rules that determine the correct order for solving any sequence of math operations. Powers and roots are solved before multiplication and division, which in turn are solved before addition and subtraction. |
| Exponent | An Exponent is a mathematical notation that implies the number of times a number is to be multiplied by itself. Example: In 24, 4 is the exponent. It indicates that 2 is to be multiplied by itself 4 times. 24 = 2 × 2 × 2 × 2 = 16 |
| Base | In an expression of the form xy, x is the base. The base x is a factor that repeats y times. Example: In 34, 3 is the base. The factor 3 would repeat 4 times, i.e. 3 × 3 × 3 × 3 |
| Power | Power or Exponent tells how many times a number is multiplied by itself. Example: In 35, 5 is the power or exponent and 3 is the base |
| (-3)² means | Means that it is negative |
| -3² means | Means the opposite of negative so it is positive |
| Prime Numbers | A prime number that has exactly two factors, 1 and the number itself. Example: 2, 3, 5, 7, 11, 13, 17, 19, etc. are all prime numbers. There are infinitely many prime numbers. |
| Composite Numbers | A whole number that has factors other than 1 and the number itself is a Composite Number. Example: 4, 6, 9, 15, 32, 45 |
| GCF | Greatest common factor is the greatest number that is a factor of each of two or more given numbers. Example: the GFC of 24 and 15 is 3 |
| Variable GCF | Variables are (usually) letters or other symbols that represent unknown numbers or values. Example: 2x + 5 = 10, x is the variable |
| Example: X² Y⁵ XY³ | X³ Y⁸ |
| Prime Factorization | Prime factorization is to write a composite number as a product of its prime factors. Example: 48 is 2 × 2 × 2 × 2 × 3 = 24 × 3. |
| Example: 120 | 2*2*2*3*5=24 x 5 |
| Finding Prime factorization using GCF | You have to find factors that appear in both factorizations and multiply them together to get the greatest common factor. Use factor trees. |
| Example: 78 and 124 | 2 |
| Simplifying variable expressions | Like terms are those terms which contain the same powers of same variables. They can have different coefficients, but that is the only difference |
| 12x³ y⁵/8x⁴ y² | 96 x¹² y¹⁰ |
| Rational Numbers | Any number that can be written in the form A/B where B doesn't equal 0 any number that can be written into a fraction |
| Give examples of rational numbers | 3/5, 10.3 ,0.6, 12/5, 3/5 |
| Negative Rational Numbers | if the denominator and numerator are negative they turn positive and only the top number can be negative |
| How do you write | ??????? |
| Multiplying exponent rule | Multiplying powers write the same base |
| 4x³y⁵Times 3x² yz² | 12 x⁶ y¹⁰ |
| Power of power rule | multiplying powers with the same base by multiplying the exponents to the power, combine exponents together, ( aᴹ) ᴺ = a ᴹ*ᴺ (x⁴)⁶ = x ⁴*⁶ = x²⁴ |
| ( x³ y⁵)⁴ | x¹² y²⁰ |
| Zero exponent rule | Any number written to the zero power - the answer is one |
| x⁰ | = 1 |
| Negative exponent rule | Rewrite as its reciprocal with a positive power |
| x⁻³ | 1/x³ |
| Write without negative exponents | you move the numbers that are negative, to the opposite side that they were on and if they are positive they stay where they are, |
| x⁻³y²/a²b³ | y² / x³ a² b³ |
| rewrite without zero or negative exponents and simplify | you take the negative numbers and move them up to the top of the fraction bar and they become positive then add variable together |
| x⁻³y²z⁰/x⁻²y⁻³ | x² y² y² z⁰/ x³= y⁴ /x¹ |
Created by:
honermadison
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