Proportional Relationships
A relationship that passes through the origin and has a constant rate of change is called what?
Proportional relationship
Simplify: 3x + 2x
5x
What property says you can add numbers in any order?
Commutative property of addition
What do we call a math phrase with no equals sign?
Expression
What is the number multiplied by a variable called?
Coefficient
If a recipe uses 2 cups of sugar for 5 cups of flour, what is the unit rate of sugar per cup of flour?
0.4 cups per cup
Simplify: 7a + 4b + 3a
10a + 4b
What property says that (a × b) × c = a × (b × c)?
Associative property of multiplication
What’s the first step when simplifying expressions?
Combine like terms
What is a value that doesn’t change in an expression?
Constant
What is the constant of proportionality in the equation y = 3x?
3
Simplify: 2x + 3y – x + 4y
x + 7y
What property is shown: 5 × (2 + 3) = (5 × 2) + (5 × 3)?
Distributive property
Simplify: 6x + 3 – 2x + 7
4x + 10
What’s the difference between an equation and an expression?
An equation has an equals sign; an expression doesn’t.
A car travels 180 miles in 3 hours. Is the relationship between distance and time proportional?
Yes, constant speed is 60 mph
Simplify: 5m – 2n + 3m + 4n
8m + 2n
What property is shown: a + 0 = a?
Identity property of addition
Solve: 2x + 5 = 11
x = 3
What does it mean to simplify an expression?
Combine like terms and perform all operations.
Travis charges $30 to mow a lawn that takes 1.5 hours. The amount he charges, d, is proportional to the time it takes, h. Write an equation to represent this situation.
d=20h
Simplify: 4(2x + 3) + 3x
11x + 12
Name all properties used to simplify: 3(4 + x) = 12 + 3x
Distributive and commutative properties
Write an equation for: “A number increased by 8 is 20.”
x + 8 = 20
In the expression 4x+7y−3x+24x + 7y - 3x + 24x+7y−3x+2, identify all the terms, coefficients, and constants. Explain your reasoning.
Terms: 4x,7y,−3x,24x, 7y, -3x, 24x,7y,−3x,2
Coefficients: 4 (for 4x4x4x), 7 (for 7y7y7y), -3 (for −3x-3x−3x)
Constant: 2