Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/21/4 miles per hour, equivalently 2 miles per hour. 7.RP. A.2 Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. Represent proportional relationships by equations. For example, if total cost 𝑡𝑡 is proportional to the number 𝑛𝑛 of items purchased at a constant price 𝑝𝑝, the relationship between the total cost and the number of items can be expressed as 𝑡=𝑝𝑛. d. Explain what a point (𝑥,𝑦) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,𝑟), where 𝑟 is the unit rate. 7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. 7.EE.B.42 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?