7.3.B 7.4.D MA.7.AR.3.1

Problem Solving with Ratios & Percents 7th Grade

Texas Essential Knowledge and Skills (TEKS): 7.3.B
apply and extend previous understandings of operations to solve problems using addition, subtraction, multiplication, and division of rational numbers.
Texas Essential Knowledge and Skills (TEKS): 7.4.D
solve problems involving ratios, rates, and percents, including multi-step problems involving percent increase and percent decrease, and financial literacy problems; and
Florida - Benchmarks for Excellent Student Thinking: MA.7.AR.3.1
Apply previous understanding of percentages and ratios to solve multi-step real-world percent problems

A proportion is an equation indicating two ratios are equal.

If a is to b as c is to d, then

\frac{a}{b} = \frac{c}{d}

\frac{a}{b} = \frac{c}{d}

, then, using cross multiplication,

a d = b c

Set up a proportion to represent the situation.
Use a variable to represent the unknown value.

\frac{16 passengers}{2 cars} = \frac{p}{5 cars}

Cross multiply, then solve.

\begin{array}{rcl} (16 passengers) (5 cars) & = & (p) (2 cars) \\ 80 passengers · cars & = & 2 p cars \\ 40 passengers & = & p \end{array}

Problem Solving with Ratios & Percents