NH SAS Grade 7 Ratios and Proportional Relationships Practice

What the test measures

Ratios and Proportional Relationships skills

Compute unit rates associated with ratios of fractions
Recognize and represent proportional relationships between quantities
Use proportional relationships to solve multistep ratio and percent problems
Solve problems involving scale drawings

Standards basis

Common Core State Standards for Mathematics (CCSS-M) / New Hampshire mathematics standards — New Hampshire

How the NH SAS reports it

New Hampshire SAS is the state assessment system, but the official math reporting structure was not accessible from the state page in this session. In practice, New Hampshire’s math assessments are aligned to the state’s K-12 mathematics standards, which closely mirror Common Core grade-level domains and clusters.

Blueprint & weighting

Not published in the accessible source set used here.

Official sources

New Hampshire Department of Education – Assessments
Common Core State Standards for Mathematics
CCSS-M Grade 3 (Oregon ODE reprint)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playeasy

Similar triangles $MNO$ and $PQR$ have areas $4$ and $36\textsf{.}$ Side $MN$ corresponds to side $PQ\textsf{,}$ and $MN = 5\textsf{.}$ What is the length of $PQ\textsf{?}$

The area ratio is $\dfrac{36}{4} = 9 = k^{2}\textsf{,}$ so $k = 3\textsf{.}$ Then $PQ = 5 \cdot 3 = 15\textsf{.}$

Practice playeasy

A sports drink is made with syrup and water in a ratio of $5$ to $20$ . How many cups of syrup should be added to $1$ gallon of water to make the drink in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)

One gallon of water is $16$ cups. With a $5$ to $20$ ratio, $\dfrac{5}{20} = \dfrac{x}{16}$ , so $20x = 80$ and $x = 4$ cups of syrup.

Practice playeasy

$50$ is what percent of $100$ ?

$\frac{50}{100} = 0.5 = 50\%$ .

Practice playeasy

A restaurant bill is $\text{\char36}72$ . What is a $15\%$ tip, in dollars?

Tip $= 0.15 \times 72 = 10.80$ dollars.

Practice playeasy

A passenger train traveled $348$ miles in $4$ hours at a constant speed. What was the train's speed, in miles per hour?

Speed = distance $\div$ time: $\dfrac{348}{4} = 87$ miles per hour.

Practice playeasy

Given $a:b = 5:2$ and $a = 75$ , find $b$ .

$\dfrac{a}{b} = \dfrac{5}{2}$ . With $a = 75$ , $\dfrac{75}{b} = \dfrac{5}{2}$ , so $5b = 150$ and $b = 30$ .

Practice playeasy

Find the simple interest on $\text{\char36}400$ at $25\%$ per year for $1$ year.

$I = 400 \times 0.25 \times 1 = \$100$ .

Practice playmedium

The table shows two juice mixtures. For Mixture A, what decimal part of the total liquid is concentrate?
$\begin{array}{l|c|c} \text{Mixture} & \text{Concentrate (L)} & \text{Water (L)} \\ \hline \text{A} & 2 & 8 \\ \text{B} & 3 & 9 \end{array}$