TCAP Grade 7 Ratios and Proportional Relationships Practice

Ratios and Proportional Relationships skills

7.RP.A.1 Compute unit rates associated with ratios of fractions

7.RP.A.2 Recognize and represent proportional relationships between quantities

7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems

Standards basis

Tennessee Academic Standards for Mathematics — Tennessee

How the TCAP reports it

TCAP math is Tennessee’s state assessment program and its blueprints are aligned to Tennessee Academic Standards, which closely mirror the Common Core content structure in grades 3-8 and the CCSS-style high school conceptual categories. The blueprint page lists the current 2025-26 assessment overviews, including Math Grade 2, Grades 3-5, Grades 6-8, and Math EOC. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Blueprint & weighting

Published TCAP math blueprints assign content emphasis by grade/course, but the exact percentage table was not recoverable from the accessible blueprint page in this session. The state blueprint landing page confirms the math overviews but did not expose the PDF links in the fetched page content. [Tennessee Department of Education](https://www.tn.gov/education/districts/lea-operations/assessment/tcap-blueprints.html)

Official sources

Tennessee Department of Education TCAP Blueprints
Tennessee Education Glossary (academic standards entry)

8 free questions · 0/0 correct

Practice playmedium

A bubble solution uses soap concentrate and water in a ratio of $5$ to $40$ . How many cups of soap concentrate should be added to $6$ gallons of water to make the solution in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)

Six gallons of water is $6 \times 16 = 96$ cups. With a $5$ to $40$ ratio, $\dfrac{5}{40} = \dfrac{x}{96}$ , so $40x = 480$ and $x = 12$ cups of concentrate.

Practice playeasy

A $\text{\char36}60$ shirt is on sale for $15\%$ off. What is the sale price?

Discount: $0.15 \times \text{\char36}60 = \text{\char36}9.0$ . Sale: $\text{\char36}60 - \text{\char36}9.0 = \text{\char36}51.0$ .

Practice playeasy

A customer buys a desk for $\text{\char36}250$ and pays $7\%$ sales tax on the purchase. How much is the sales tax, in dollars?

Tax $= 0.07 \times 250 = 17.50$ dollars.

Practice playmedium

Five identical printing presses can complete a job in $12$ hours. Working at the same rate, how many hours would it take $8$ of these presses to complete the same job?

Total work is fixed. Time with $8$ presses: $\dfrac{5 \times 12}{8} = \dfrac{60}{8} = 7.5$ hours.

Practice playeasy

Solve for $n$ : $\dfrac{2}{9} = \dfrac{n}{45}$ .

Cross-multiply: $9n = 90$ , so $n = 10$ .

Practice playeasy

Find the simple interest on $\text{\char36}200$ at $10\%$ per year for $2$ years.

$I = 200 \times 0.10 \times 2 = \$40$ .

Practice playmedium

At a fitness challenge, each completed attempt scores the points shown. How many points were scored in all?
$\begin{array}{l|c|c|c} \text{Station} & \text{Attempts} & \text{Percent completed} & \text{Points each} \\ \hline \text{Jump} & 20 & 80\% & 1 \\ \text{Sprint} & 15 & 60\% & 2 \\ \text{Throw} & 25 & 40\% & 3 \end{array}$

Jump: $20\cdot 0.80=16$ completed for $16\cdot 1=16$ points. Sprint: $15\cdot 0.60=9$ completed for $9\cdot 2=18$ points. Throw: $25\cdot 0.40=10$ completed for $10\cdot 3=30$ points. Total: $16+18+30=64$ points.

Practice playmedium

Iced tea is made with tea concentrate and water in a ratio of $3$ to $12$ . How many cups of tea concentrate should be added to $3$ quarts of water to make the tea in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)