OSTP Grades 6-8 Ratios and Proportional Relationships Practice

Practice playmedium

A hiking sign lists the distance to a waterfall as $4{,}500$ meters. How many kilometers is that? ( $1$ kilometer $= 1{,}000$ meters)

Use a conversion factor with kilometers in the numerator so meters cancel: $4{,}500 \text{ m} \times \dfrac{1 \text{ km}}{1{,}000 \text{ m}} = 4.5 \text{ km}$ .

Practice playeasy

Write $5\%$ as a fraction in lowest terms.

$5\% = \dfrac{1}{20}$ .

Practice playeasy

A community center expects $80$ volunteers for a cleanup day. By $8$ a.m., $60\%$ of the volunteers have signed in. How many volunteers have signed in by $8$ a.m.?

Convert $60\%$ to a decimal and multiply: $0.60 \times 80 = 48$ volunteers.

Practice playeasy

A scrap shipment weighs $2$ tons. How many ounces is that? ( $1$ ton $= 2{,}000$ pounds and $1$ pound $= 16$ ounces)

Convert tons to pounds, then pounds to ounces: $2 \text{ tons} \times \dfrac{2{,}000 \text{ lb}}{1 \text{ ton}} \times \dfrac{16 \text{ oz}}{1 \text{ lb}} = 64{,}000 \text{ oz}$ .

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 playeasy

Sales tax is $10\%$ . What is the tax on a $\text{\char36}80$ purchase?

Tax: $0.1 \times \text{\char36}80 = \text{\char36}8.0$ .

Practice playmedium

The price of a laptop decreased from $\text{\char36}800$ to $\text{\char36}680$ . What is the percent decrease?

Decrease $= 800 - 680 = 120$ . Percent decrease $= \dfrac{120}{800} = 0.15 = 15\%$ .

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.

OSTP Grades 6-8 Ratios and Proportional Relationships. Practice it free.

Ratios and Proportional Relationships skills

unit rates

ratio tables

equivalent ratios

proportional relationships

percent problems

Topics mapped to this domain

Custom unit conversions

Fraction-decimal-percent conversion

Percent of a quantity

Two-step unit conversions

Fluid concentration ratios

Percent problems

Percent proportion word problems

Ratio, rate, and proportion word problems

Ratios, rates, and proportions

Simple interest

Table problems with percents and ratios (ACT)

8 free questions · 0/0 correct

Turn ratios and proportional relationships into game time.

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