 # Linear Expressions with Rational Coefficients

Related Topics:
Common Core for Mathematics

Videos, solutions, examples, and lessons to help Grade 7 students learn how to apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Common Core: 7.EE.1

### Suggested Learning Targets

• I can simplify algebraic expressions by using distributive property.
• I can apply properties of real numbers (add, subtract and expand linear expressions).
• I can apply properties of real numbers (factor).
• I can simplify algebraic expressions by combining like terms.
• I can create a new equivalent expression when given a factored expression and a fully expanded expression ex. Given y(3+x+k) & 3y + xy

How to work with expressions?
Examples:
1. Identify the coefficients, constant terms, and like terms of the expression
a) x + 4 - 2x - 10
b) 5(w - 4) + w + 8
2. A rectangular soccer field is 30 yards longer than it is wide. Write and simplify an expression for the perimeter of the field in terms of the width, w. Expanding and Factoring Expressions
Examples:
1. Expand the expression 4(7x - 2).
2. Expand the expression 4/9(2/5x - 3/8).
3. Factor the expression 8x + 12 completely.
4. Factor the expression 15x + 21 completely.
5. Factor the expression 8/12 x + 12/21 completely.
3. Factor the expression 6/45 - 8/63 y completely.
Distributive Property
How the distributive property works with integers and with algebra?
Examples:
Use the distributive property:
3(5x + 2)
-4(x + 2)
-(4m - 5)

Distributive Property (7.EE.A.1)
How to simplify and rewrite expressions using the distributive property?
How to combine like terms?
Examples:
1. Simplify -2[-(3z + 4y) + 10z]
2. Simplify 4(3b) - 2(3b + 1)
3. Simplify -[-2(4x + 2y) + 7x]
Equivalent Expressions
Examples:
1. Write the expression for each figure below.
a) Write an expression for the area of this rectangle.
b) Write an expression for the perimeter of this rectangle.

2. Use the expression 14 + 2b - 18.
a) Write the expression in standard form.
b) Write the expression in factored form.
c) Add 9b + 11 to the expression and then simplify.
3. Which expression is equivalent to the expression -3(4x - 2) - 2x?

4. Ms. Offerdahl simplified the expression 2 - (3x - 5) with the following steps:
Step 1: 2 - (3x - 5)
Step 2: 2 - 3x - 5
Step 3: -3x - 3
On which step did Ms. Offerdahl make an error?
Fix her error below and write the final simplified expression.

5. Which expression is not equivalent to the other three?
A. 2(1 + 2b + 3a)
B. 2(1 + 2a) + 2(a + 2b)
C. 6a + 2 + 4b
D. 2(3a + 1) + 4b + 1
7.ee.1 Combining Like Terms
Examples:
1. Each envelope contains an amount of quadrilaterals and an amount of pentagons. You do not know how many of each are in the envelope. Write an expression to determine the total number of sides in each envelope. Explain your expression.
2. Each white envelope has the same amount of quadrilaterals and pentagons in them. Write an expression that repesents the toral number of sides in all the white envelopes.

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