Terms, Coefficients, Constants (TCC)
What is a Constant?
A fixed number, that is not attached to a variable.
Translate from a verbal to algebraic expression:
"15 times a number"
15x ("A number" means a variable, a letter in place of an unknown number)
2 x 4 + 5 x 3
23
What is the Commutative Property of Addition
a + b = b + a
(Changing the order to addition does not change the result)
What is a Coefficient?
A number that is attached to a variable through multiplication. (Ex: 3x, -8y)
Translate from verbal to an algebraic expression
"Twice a number decreased by 5"
2d - 5
Solve 13 + (16 - 4^2)
13
What is the Associative Property of Multiplication?
(a x b) x c = a x (b x c)
(Regrouping the order of multiplication does not change the answer)
What is a Term?
A number, a variable, or a number and variable multiplied together. Separated by addition and subtraction. [Ex: 4y - 2x + 9 (4y, -2x, 9 are all terms)]
What is the difference between verbal expressions and algebraic expressions?
Verbal: Written expressions, math translated to english
Algebraic: Consists of numbers, variables. It is a "math sentence"
32/4 + 2^3 - 3
13
What is the Identity Property of Addition
a + 0 = a
(If you add zero to a number, the answer is the original number)
Solve: (5x - 2y + 3) + (27x +17y - 23)
32x + 15y - 20
Translate from verbal to an algebraic expression
" Half a number increased by nine "
c/2 +9
(15 - 4)^2 - (5 + 16)
100
What is the Distributive Property?
a(b + c) = ab + ac
(Whats outside the parentheses multiplies to everything inside the parentheses)
Solve (2x^2 + 3x - 4) - (x^2 + 2x - 9)
(x^2 + x + 5)
Translate from verbal to algebraic expression:
" Twelve less than a number squared "
x^2 - 12
2(3^2) + (9-7)^2 + (21/3)
29
What is the Substitution Property?
If a=b, then "a" can replace "b" in any expression or equation