Expressions and Equations

7.EE

Use properties of operations to generate equivalent expressions.

  1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
  2. Understand  that  rewriting  an  expression  in  different  forms  in  a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

  1. Solve multi-step  real-life  and  mathematical  problems  posed  with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with  numbers  in  any  form;  convert  between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
  2. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

            a. Solve word  problems leading to equations of the form px + q = r  and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic

                solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

            b. Solve word  problems leading to inequalities of the form px + q > r    or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality  and  interpret  it  in  the  context  of the problem. For

                 example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.