7.4.a 7.4.b 7.4.c MA.7.3.2

Proportional Relationships 7th Grade

Texas Essential Knowledge and Skills (TEKS): 7.4.a
represent constant rates of change in mathematical and real-world problems given pictorial, tabular, verbal, numeric, graphical, and algebraic representations, including d = rt;
Texas Essential Knowledge and Skills (TEKS): 7.4.b
calculate unit rates from rates in mathematical and real-world problems;
Texas Essential Knowledge and Skills (TEKS): 7.4.c
determine the constant of proportionality (k = y/x) within mathematical and real-world problems;
Florida - Benchmarks for Excellent Student Thinking: MA.7.3.2
Apply previous understanding of ratios to solve real-world problems involving proportions.

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.

Proportional Relationships