MOCA: Math
Variable - answer - A non-numeric symbol used to represent an unknown quantity - Often represented by letters of the English alphabet such as x or n
Coefficient - answer - A number multiplied with a variable - Writen in front of the variable
Variable Expression - answer - Consist of at least one variable, a coefficient, and sometimes a power or operation - Ex: 10.2x
Constant - answer - A number with no variable multiplied with it - Ex: In the expression 3x + 4, 4 is the constant
Algebraic Terms - answer - Numbers, variables, or products of numbers and variables that are separated from other terms by addition and or subtraction signs - Variable expressions can have a single term or multiple terms - Ex: The expression 7x + 3x has two terms
Reflexive Property of Equality - answer - A quantity is always equal to itself - Ex: a=a
Transitive Property of Equality - answer - It two quantities are equal to the same quantity, then they must be equal to each other - Ex: if a = b and b = c, then a = c
Symmetric Property of Equality - answer - It two quantities are equal, then it does not
matter which quantity is written on the left-hand side of the equal sign and which is written on the right-hand side - Ex: if a = b, then b = a
Closure for Addition - answer - If two real numbers are added, then their sum will also be a real number
Closure for multiplication - answer - If two real number are multiplied, then their product will also be a real number
Substitution Property for Equality - answer - If two quantities are equal, one may replace the other in a true statement and the statement will remain true - Ex: if a + b = c and a = x, then x + b= c Addition Property of Equality - answer - If the quantities on each side of an equal sign are both added by the same amount, the resulting statement will still be equal
- Ex: if a = b, then a + c = b + c
Subtraction Property of Equality - answer - If the quantities on each side of an equal sign are both subtracted by the same amount, the resulting statement will still be equal - Ex: if a = b, then a-c = b-c
Multiplication Property of Equality - answer - If the quantities on each side of an equal sign are both multiplied by the same amount, the resulting statement will still be equal - Ex: if a = b, then ac = bc
Division Property of Equality - answer - If the quantities on each side of an equal sign
are both divided by the same amount, the resulting statement will still be equal - Ex: if a = b and b = a, then a/c = b/c
Commutative Property of Addition - answer - If the order of the addends changes in a statement of addition, then the sum will stay the same - Ex: a + b= b + a
Commutative Property of Multiplication - answer - If the order of the factors changes in a statement of multiplication, then the product will stay the same - Ex: ab=ba
Associative Property of Addition - answer - If the placement or the grouping symbols of a set of addends changes, then the sum will stay the same - Ex: a + (b + c) = (a + b) + c
Associative Property of Multiplication - answer - If the placement or the grouping symbols of a set of factors changes, then the product will stay the same - Ex: a(bc)= (ab)c
Identity Property of Addition - answer - A value added by zero will yield a sum equal to the original value - Ex: a + 0= a
Identity Property of Multiplication - answer - A value multplied by one will yield a product equal to the original value - Ex: a x 1= a
Additive Inverse Property - answer - A value added by its inverse or opposite will have a sum of zero - Ex: a + -a= 0 Multiplication Inverse Property - answer - A value multiplied by its reciprocal will have
a product of 1 - Ex: a x 1/a = 1
Distributive Property of Multiplication over Addition - answer - The product of a factor
with a sum is the same as the sum of the products made by that factor and each number involved in the addition or subtraction - Ex: a(b+c)= ab + ac
Zero Product Property - answer - If values are multiplied to yield a product of zero, then at least one of those factors must be zero - Ex: if ab=0, then a or b must be 0
Like terms - answer - Must have the same variable and must be raised to the same power
- Can be added and subtracted to each other - The coefficients are added or subtracted and the variable parts remain unchanged
Unlike terms - answer - Cannot be added or subtracted - Can be multiplied and divided
Polynomial - answer - An expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication
- Must have terms that have different variables and are raised to different powers - Binomial= 2 terms - Trinomial= 3 terms
How do you determine the degree of a monomial expression? - answer - Add all the powers of the variables in the term together
How do you determine the degree of a polynomial expression? - answer - Look at the degree of each term in the polynomial and then report the highest degree - Ex: 7x + 2 has a degree of 1
Ratio - answer - The comparison of one part to another
- When two ratios are equal then a proportion is formed
How do you solve proportions? - answer - Cross multiplication
Inequality Solving - answer - Very similar to solving regular algebraic equations - There are two major differences when solving these types of problems 1. The direction of the inequality sign will change after some operations are performed 2. A finished final answer generally requires the variable to be written on the left
When does an inequality sign reverse in a problem? - answer - When a negative number is multiplied or divided across the entire inequality statement
Variable - answer - A non-numeric symbol used to represent an unknown quantity - Often represented by letters of the English alphabet such as x or n
Coefficient - answer - A number multiplied with a variable - Writen in front of the variable
Variable Expression - answer - Consist of at least one variable, a coefficient, and sometimes a power or operation - Ex: 10.2x
Constant - answer - A number with no variable multiplied with it - Ex: In the expression 3x + 4, 4 is the constant
Algebraic Terms - answer - Numbers, variables, or products of numbers and variables that are separated from other terms by addition and or subtraction signs - Variable expressions can have a single term or multiple terms - Ex: The expression 7x + 3x has two terms
Reflexive Property of Equality - answer - A quantity is always equal to itself - Ex: a=a
Transitive Property of Equality - answer - It two quantities are equal to the same quantity, then they must be equal to each other - Ex: if a = b and b = c, then a = c
Symmetric Property of Equality - answer - It two quantities are equal, then it does not
matter which quantity is written on the left-hand side of the equal sign and which is written on the right-hand side - Ex: if a = b, then b = a
Closure for Addition - answer - If two real numbers are added, then their sum will also be a real number
Closure for multiplication - answer - If two real number are multiplied, then their product will also be a real number
Substitution Property for Equality - answer - If two quantities are equal, one may replace the other in a true statement and the statement will remain true - Ex: if a + b = c and a = x, then x + b= c Addition Property of Equality - answer - If the quantities on each side of an equal sign are both added by the same amount, the resulting statement will still be equal
- Ex: if a = b, then a + c = b + c
Subtraction Property of Equality - answer - If the quantities on each side of an equal sign are both subtracted by the same amount, the resulting statement will still be equal - Ex: if a = b, then a-c = b-c
Multiplication Property of Equality - answer - If the quantities on each side of an equal sign are both multiplied by the same amount, the resulting statement will still be equal - Ex: if a = b, then ac = bc
Division Property of Equality - answer - If the quantities on each side of an equal sign
are both divided by the same amount, the resulting statement will still be equal - Ex: if a = b and b = a, then a/c = b/c
Commutative Property of Addition - answer - If the order of the addends changes in a statement of addition, then the sum will stay the same - Ex: a + b= b + a
Commutative Property of Multiplication - answer - If the order of the factors changes in a statement of multiplication, then the product will stay the same - Ex: ab=ba
Associative Property of Addition - answer - If the placement or the grouping symbols of a set of addends changes, then the sum will stay the same - Ex: a + (b + c) = (a + b) + c
Associative Property of Multiplication - answer - If the placement or the grouping symbols of a set of factors changes, then the product will stay the same - Ex: a(bc)= (ab)c
Identity Property of Addition - answer - A value added by zero will yield a sum equal to the original value - Ex: a + 0= a
Identity Property of Multiplication - answer - A value multplied by one will yield a product equal to the original value - Ex: a x 1= a
Additive Inverse Property - answer - A value added by its inverse or opposite will have a sum of zero - Ex: a + -a= 0 Multiplication Inverse Property - answer - A value multiplied by its reciprocal will have
a product of 1 - Ex: a x 1/a = 1
Distributive Property of Multiplication over Addition - answer - The product of a factor
with a sum is the same as the sum of the products made by that factor and each number involved in the addition or subtraction - Ex: a(b+c)= ab + ac
Zero Product Property - answer - If values are multiplied to yield a product of zero, then at least one of those factors must be zero - Ex: if ab=0, then a or b must be 0
Like terms - answer - Must have the same variable and must be raised to the same power
- Can be added and subtracted to each other - The coefficients are added or subtracted and the variable parts remain unchanged
Unlike terms - answer - Cannot be added or subtracted - Can be multiplied and divided
Polynomial - answer - An expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication
- Must have terms that have different variables and are raised to different powers - Binomial= 2 terms - Trinomial= 3 terms
How do you determine the degree of a monomial expression? - answer - Add all the powers of the variables in the term together
How do you determine the degree of a polynomial expression? - answer - Look at the degree of each term in the polynomial and then report the highest degree - Ex: 7x + 2 has a degree of 1
Ratio - answer - The comparison of one part to another
- When two ratios are equal then a proportion is formed
How do you solve proportions? - answer - Cross multiplication
Inequality Solving - answer - Very similar to solving regular algebraic equations - There are two major differences when solving these types of problems 1. The direction of the inequality sign will change after some operations are performed 2. A finished final answer generally requires the variable to be written on the left
When does an inequality sign reverse in a problem? - answer - When a negative number is multiplied or divided across the entire inequality statement
