Vocabulary
Associative Properties of Multiplication and Addition
Changing the grouping of addends or factors does not change the sum or product.
For example:
(3+2) +5 = (5+2) +3
Or (2 x 4) x 6 = (6 x 4) x 2
You are running a 4500-foot race. How much farther do you have to go after running 2000 feet?
4500 ft - 2000 ft = 2500 ft
Always label your units.
Write the expression for:
4 more than a number n
n + 4 or 4 + n
Name the property:
8 + (3 + 1) = (8 + 3) + 1
Associative Property of Addition
Discuss how to distribute this. What is the answer?
3 (4 + 5)
Discussion:
3 x 4 + 3 x 5
Answer:
12 + 15 = 27
Like Terms
Terms of an algebraic expression that have the same variables raised to the same exponents 4 and 8, 2x and 7x
A young rattlesnake grows at a rate of about 20 centimeters per year. How much does a young rattlesnake grow in 2 years?
2 years x 20 cm = 40 cm
Write the expression for:
the difference of a number m and 3
m − 3
Name the property:
12 × (6 × 2) = (12 × 6) × 2
Associative Property of Multiplicaiton
Distribute:
8(c - 4)
8c - 32
Identity Properties of Addition and Multiplication or the Properties of 0 and 1
The product of any number and 0 is 0.
The product of any number and 1 is that number.
The sum of any number and 0 is that number.
For example:
5 x 0 = 0
5 x 1 = 5
3 + 0 = 0
For lunch, you buy 5 sandwiches that cost $3 each. How much do you spend?
5 x $3 = $15
Write the expression for:
10 less than a number p
p − 10
Name the property:
5 + 8 = 8 + 5
Commutative Property of Addition
Distribute:
3(4 + r + 3)
3r + 21
Why?
12 + 3r + 9
Distributive Property
To multiply a sum or difference by a number, multiply each number in the sum or difference by the number outside the parentheses. Then evaluate.
For example:
3(4 + 10) = 3(4) + 3(10)
You have $60. You buy a pair of jeans and a shirt. The pair of jeans costs $27. You come home with $15. How much did you spend on the shirt?
$60 - $27 - $15 = $18
Write the expression for:
a number n divided by 3
n ÷ 3
Name the property:
a x b = b x a
Commutative Property of Mulitplication
Distribute:
11(x + 7)
11x + 77
Commutative Properties of Addition and Multiplication
Changing the order of addends or factors does not change the sum or product.
For example:
5 x 3 = 3 x 5
4 + 2 = 2 + 4
Write and solve a problem:
You Babysit for 3 hours. You receive 12 dollars. What is your hourly wage?
$12 divided by 3 hrs = $4 per hour
Write the expression for:
the quotient of 3 and a number
3 ÷ n
Which Statements are True? What Property explains each?
a. 3 + 5 = 5 + 3
b. 3 - 5 = 5 - 3
c. 12 x (6 x 2) = (12 x 6) x 2
d. 12 ÷ (6 ÷ 2) = (12 ÷ 6) ÷ 2
e. 3 x 1 = 3
f. 4 + 0 = 4
a: Commutative Property
c: Associative Property
e: Identity Property of Multiplication
f: Identity Property of Addition
b is subtraction and d is division. The properties only work for addition and multiplicaiton.
Distribute:
4(y + 3 + 5)
4y+12+20 = 4y + 32