RISE Grade 7 Ratios and Proportional Relationships Practice

Ratios and Proportional Relationships skills

Analyze proportional relationships and use them to solve real-world and mathematical problems

Standards basis

Utah Core Standards for Mathematics (CCSS-aligned Utah math standards) — Utah

How the RISE reports it

Utah’s RISE mathematics assessment is a state assessment aligned to Utah Core Standards rather than a separately branded national framework. The official Utah pages point to Utah Core standards resources and the RISE administration guidance, with no separate public math blueprint published on the assessment page itself.

Blueprint & weighting

RISE mathematics weighting by domain was not located on the official Utah assessment page; the official page only points to the RISE assessment overview/administration resources and the Utah Core Standards resources. Grade 6 administration guidance notes a two-segment math test with Segment 1 no calculator and Segment 2 calculator allowed, and the proctor guide states Mathematics has an expected testing time of 90 minutes for most students and 135 minutes for all students.

Official sources

Utah State Board of Education Assessments
Utah State Board of Education Learning Resources for Families
Utah State Board of Education Assessment Contacts PDF

8 free questions · 0/0 correct

Practice playeasy

Windshield washer fluid is mixed with concentrate and water in a ratio of $7$ to $56$ . How many cups of concentrate should be added to $3$ gallons of water to make the fluid in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)

Three gallons of water is $3 \times 16 = 48$ cups. With a $7$ to $56$ ratio, $\dfrac{7}{56} = \dfrac{x}{48}$ , so $56x = 336$ and $x = 6$ cups of concentrate.

Practice playeasy

A $\text{\char36}200$ shirt is on sale for $25\%$ off. What is the sale price?

Discount: $\frac{25}{100} \times \text{\char36}200 = \text{\char36}50$ . Sale: $\text{\char36}200 - \text{\char36}50 = \text{\char36}150$ .

Practice playmedium

A town's population increased from $12{,}000$ to $13{,}800$ . What is the percent increase?

Increase $= 13{,}800 - 12{,}000 = 1{,}800$ . Percent increase $= \dfrac{1{,}800}{12{,}000} = 0.15 = 15\%$ .

Practice playeasy

A paint mixture uses red and blue paint in a ratio of $4$ to $7$ . How many ounces of blue paint are needed to mix with $32$ ounces of red paint?

Scale the ratio: $32$ oz red is $8$ groups of $4$ , so blue paint = $8 \times 7 = 56$ ounces.

Practice playeasy

Solve for $x$ : $\dfrac{9}{63} = \dfrac{6}{x}$ .

Cross-multiply: $9 x = 63 \cdot 6 = 378$ . So $x = 42$ .

Practice playeasy

Find the simple interest on $\text{\char36}100$ at $5\%$ per year for $1$ year.

$I = 100 \times 0.05 \times 1 = \$5$ .

Practice playmedium

Three purchases are taxed at the rates shown. What is the total cost including tax?
$\begin{array}{l|c|c} \text{Item} & \text{Price} & \text{Sales tax} \\ \hline \text{Book} & \text{\char36}40 & 5\% \\ \text{Headphones} & \text{\char36}60 & 8\% \\ \text{Cable} & \text{\char36}20 & 10\% \end{array}$

Book: $40+0.05\cdot 40=42\textsf{.}$ Headphones: $60+0.08\cdot 60=64.80\textsf{.}$ Cable: $20+0.10\cdot 20=22\textsf{.}$ Total: $42+64.80+22=\text{\char36}128.80\textsf{.}$

Practice playeasy

A fabric dye bath uses dye concentrate and water in a ratio of $4$ to $32$ . How many cups of dye concentrate should be added to $2$ gallons of water to make the bath in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)