Properties of Zero and One
What is 9 x 0?
0!
The multiplication property of zero states that anything times zero is zero.
Is this an example of the Associative or the Commutative Property?
Commutative!
It's commutative because I've just changed the orders of the numbers. I haven't changed groupings (adding parentheses), which would be Associative.
What operation (addition, subtraction, multiplication or division) do you do when a number is right against the parentheses?
e.g.: 7(3)
Multiplication
Factor the expression. Use the method for finding common factors that works best for you!
(12+8)
4(3+2)
4 is the GCF of 12 and 8. 4x3 equals 12 and 4x2 equals 8
Factor the expression using the GCF: 24p - 18.
6(4p - 3).
The variable goes inside the parentheses because if it was outside 6p(4 -3), and you simplified, you would get an incorrect answer of 24p - 18p.
What is 0 + 3?
3! The addition property of zero tells you that anything plus zero is just itself.
4 x (3 x 5) = (4 x 3) x 5
Is this Associative or commutative?
Associative!
It's Associative, because I've changed the groupings (who the numbers associate with/which numbers are in parentheses), but I haven't altered the order at all.
Simplify the expression using the distributive property:
7(3+y)
21 + 7y.
Remember, the number outside the parentheses has to multiply everything within the parentheses.
Factor the expression using the GCF: 27 - 18.
9(3 - 2).
9 is the GCF of 27 and 18. 9x3 equals 27 and 9x2 equals 18
Factor the expression using the GCF:
10i - 25y.
5(2i - 5y).
What is 8 x 1?
8!
This is the multiplication property of 1. Anything times 1 is itself.
4 x (3 x 2) = 4 x (2 x 3)
Is this associative or commutative?
It's commutative!
I haven't changed what numbers are in the parentheses--4 is still on the outside. I've just changed the order within the parentheses.
Simplify the expression:
8(2+4)
16+32 = 48
Factor the expression using the GCF:
38 - 22.
2(19 - 11).
All even numbers can be divided by 2 and it's the GCF of 38 and 22. Order is very important with subtraction, so you have to keep the original order of the problem.
Factor the expression using the GCF:
16m + 40
8(2m + 5)
What is the solution to the expression?
(a x 0) x 3
0!
Anything times zero is zero, so even though you don't know what a is, you can solve that portion--it's zero! Then, 0 x 3 will again be zero.
(b + 4) +3 = b + (4 + 3)
Is this associative or commutative?
Associative!
It's Associative because I've changed what's in the parentheses and what's not--the groupings have changed. The process is the same when you have a variable as when there are only numbers.
Simplify using the distributive property.
7(q-4)
7q - 28
When you have a number times a variable (and you haven't been told what the variable is equal to), you just attach the two together. 7x4 is 28.
The order is very important in subtraction--keep it the way that the problem writes it!
Factor the expression using the GCF: 35 + 49 - 14.
7(5+7-2). The GCF of all the numbers is 7. Order with subtraction is important, so keep it at the end!
Factor the expression using the GCF:
27 - 45c
9(3 - 5c).
What is the solution to the expression?
(17 x 1) + (p x 0)
17!
The multiplication property of 0 tells you that p x 0 is zero (even though you don't know p). The multiplication property of 1 tells you that 17 x 1 is still 17. The addition property of zero tells you that any number plus zero is just itself--so 17 plus zero is just 17.
4 x T x 3 = 4 x 3 x T
Is this associative or commutative?
It's commutative! I've only changed the order, I haven't altered groupings.
Simplify using the distributive property:
9(3+R-1)
27 + 9R - 9 = 9R+27 - 9 = 9R + 18.
Elsa is a 6th grade math student. She was asked to factor the expression, 24 + 12 using the GCF. Her factored expression was 4(6+3). Was Susie correct?
Susie is incorrect. While she used factors of 24 and 12, she did not use the GCF--which is 12. The correct factored expression using the GCF would be 12(2+1).
Belle is a sixth grader and was asked to factor an expression using the GCF. The expression she needed to factor was 5e + 40. Her factored expression answer was 5(1e + 8). Was Belle correct?
Yes! 5 is a prime number and is also a factor of 40, so the factored expression would be 5(1e+8). Another equally correct way of writing it would be 5(e+8).