Math.7.RP.1 7.RP.A.1 Math.7.RP.2a 7.RP.A.2.A Math.7.RP.2b 7.RP.A.2.B Math.7.RP.2c 7.RP.A.2.C Math.7.RP.2d 7.RP.A.2.D

Common Core Standards Interpret Proportional Relationships
Grade:	7th Grade
Standard:	Math.7.RP.1 or 7.RP.A.1
Description:	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 ^1/2/_1/4 miles per hour, equivalently 2 miles per hour.
Standard:	Math.7.RP.2a or 7.RP.A.2.A
Description:	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.
Standard:	Math.7.RP.2b or 7.RP.A.2.B
Description:	Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
Standard:	Math.7.RP.2c or 7.RP.A.2.C
Description:	Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
Standard:	Math.7.RP.2d or 7.RP.A.2.D
Description:	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.

7th Grade Math - Interpret Proportional Relationships Lesson

A rate is a ratio involving quantities, typically with different units.

A rate where the second quantity is 1 is called a unit rate.

The ratio is

\frac{1}{2}

pound of butter per

1 \frac{1}{2}

cups of flour.

To find the amount of butter per 1 cup of flour, or the unit rate, divide

\frac{1}{2}

pound of butter by

1 \frac{1}{2}

cups of flour.

Use the improper fraction

\frac{3}{2}

in place of the mixed number

1 \frac{1}{2}

\begin{array}{rcl} \frac{\frac{1}{2}}{\frac{3}{2}} & = & \frac{1}{2} \div \frac{3}{2} \\ = & \frac{1 \times 2}{2 \times 3} \\ = & \frac{2}{6} \\ = & \frac{1}{3} \end{array}

So,

\frac{1}{3}

pound of butter is needed for 1 cup of flour.

Common Core Standards