Properties and Closure
Which property is shown here? 4+0=4
additive identity property
which property is shown here? 7+-7= 0
additive inverse property
what numbers are included in the set of rational numbers?
any number that can be written as a fraction- integers, whole, counting
an expression with exactly two terms
binomial
Solve the following problem- 8c+1= 7c-14-2c
c = -5
Which property is shown here? 6+5=5+6
commutative property of addition
write a justification. 2(x+3) = 20 2x+6= 20 2x = 14 x = 7
distributive property subtraction property of equality division property of equality
a statement containing two algebraic expressions joined with a sign of equality
equation
True or False? The set of whole numbers is closed under subtraction.
false
Change the following into their verbal form- 3-4 5(x+5) 5x+ 5 2(x-3)
four less than three five times a number less than five five times the sum of a number and five two times the difference of a number and three
What is the difference between justify and explain?
justify= math explain= words
terms with identical variables
like terms
an expression with exactly one term
monomial
Give three words that suggest multiplication and division.
multiplication- product, times, multiply by division- quotient, divided by, over
explain what no solution means.
no answer will ever work
Are the following examples of like terms? Why or why not? 4a and 4b 3/11 and .75
no- not same letter yes- same value
an expression with one or more terms
polynomial
what numbers are included in the set of integers?
(-1,0,1,2...)
what numbers are included in the set of whole numbers?
(0,1,2,3...)
what numbers are included in counting numbers?
(1,2,3...)
Combine like terms- (9x <2> + 5x <3>) - (12x <3> -5x)
-7x<3> +9x<2> + 5x
Change the following into algebraic/ symbolic form- two increased by seven the product of five and a number the sum of one and a number is ten
2+7 5x 1+x= 10
Which property is shown here? 1+(5+6)=(1+5)+6
Associative Property of Addition
Solve the following problem- 2(2x+6-4x)= 10-4
INFINITE SOLUTIONS
Solve the following problem- 4x+2(-2x+8)= 30
NO SOLUTION
Is the set of integers closed under division?
NO. INTEGERS ARE NOT FRACTIONS/ DECIMALS.
True or False? The set of rational numbers is closed under division by non-zero rational numbers.
True
give an example of the distributive property.
a(b+c)= ab+ac
Give an example of the multiplicative inverse property.
a* 1/a=1
Give an example of the associative property of multiplication.
a*(b*c)=(a*b)*c
give an example of the multiplicative identity property.
a*1=a
Give an example of the commutative property of multiplication.
a*b=b*a
Give three words that suggest addition and subtraction.
addition- sum, plus, increased subtraction- difference, minus, less than
the number that can replace the variable in the equation- the answer
root or solution
a number, a variable, or a product of numbers and variables; one piece of an expression
term
an expression with exactly three terms
trinomial
True or False? The set of integers is closed under addition, subtraction, and multiplication.
true
True or False? The set of whole numbers is closed under addition and multiplication.
true
explain what an infinite solution is.
when every answer will work
What does it mean for a set to be closed under an operation? Explain and give an example.
when using the operation on the set of numbers and performing it on any 2- you should get a number stil within the set example- counting numbers closed under addition? yes 1+4=5 6+10=16
ALGEBRAIC/SYMBOLIC
written with symbols
VERBAL
written with words
Solve the following problem- x-(12-x)= 38
x=25
Solve the following problem and then explain. : x+6=15
x=9: Subtraction Property of Equality
which property is shown here? 10*0=0
zero property of multiplication
