MAST Grade 7 Ratios and Proportional Relationships Practice

Ratios and Proportional Relationships skills

Compute and identify unit rates from tables, graphs, and verbal descriptions.

Determine if a relationship is proportional and interpret points in context.

Standards: 7.RP.1, 7.RP.2, 7.RP.2.a, 7.RP.2.b, 7.RP.2.c, 7.RP.2.d

Standards basis

Montana PK-12 Mathematics Content Standards / Common Core State Standards for Mathematics (CCSS-M)-aligned Montana standards — Montana

How the MAST reports it

Montana’s MAST is a state-specific through-year assessment built by New Meridian and aligned to Montana’s academic content standards, not a Smarter Balanced-style claims/targets framework. The math blueprints organize content into grade-level strands/testlets that map directly to CCSS-M-derived Montana standards.

Blueprint & weighting

The blueprint publishes a through-year design of 12 strands/testlets per grade, with 1 strand per testlet, 2 reporting attributes per strand, and 9–13 items per testlet. It also specifies approximate item-type and DOK distributions, but does not publish percentage weighting by domain in the captured blueprint text.

Official sources

Montana OPI MontCAS
Montana OPI - MasteryGuide Mathematics Assessment Specifications and Blueprints
Montana OPI - Montana MAST Math Testlets

8 free questions · 0/0 correct

Practice playeasy

An engine coolant mixture uses antifreeze concentrate and water in a ratio of $8$ to $64$ . How many cups of antifreeze concentrate should be added to $4$ gallons of water to make the coolant in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)

Four gallons of water is $4 \times 16 = 64$ cups. With an $8$ to $64$ ratio, $\dfrac{8}{64} = \dfrac{x}{64}$ , so $x = 8$ cups of antifreeze concentrate.

Practice playmedium

A water tank held $12{,}500$ gallons of water. After leaking at a constant rate for $25$ minutes, the tank held $11{,}000$ gallons. How many gallons of water leaked from the tank each minute?

Water leaked: $12{,}500 - 11{,}000 = 1{,}500$ gallons in $25$ minutes. Rate: $\dfrac{1{,}500}{25} = 60$ gallons per minute.

Practice playeasy

A car travels $390$ miles in $6$ hours. What is the speed in miles per hour?

$390 \div 6 = 65$ miles per hour.

Practice playmedium

An herbicide spray uses concentrate and water in a ratio of $6$ to $24$ . How many cups of concentrate should be added to $2$ quarts of water to make the spray in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)

Two quarts of water is $2 \times 4 = 8$ cups. With a $6$ to $24$ ratio, $\dfrac{6}{24} = \dfrac{x}{8}$ , so $24x = 48$ and $x = 2$ cups of concentrate.

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 $y$ : $\dfrac{6}{4} = \dfrac{y}{24}$ .

Cross-multiply: $4y = 144$ , so $y = 36$ .

Practice playmedium

A pool treatment uses chlorine concentrate and water in a ratio of $9$ to $72$ . How many cups of chlorine concentrate should be added to $5$ gallons of water to make the treatment in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)

Five gallons of water is $5 \times 16 = 80$ cups. With a $9$ to $72$ ratio, $\dfrac{9}{72} = \dfrac{x}{80}$ , so $72x = 720$ and $x = 10$ cups of concentrate.

Practice playmedium

On a map, $1.5$ inches represents an actual distance of $36$ miles. At this scale, what is the actual distance, in miles, represented by $4$ inches on the map?