Back to Exercise: Use units to solve problems

Exercises: Use Units as a Way to Understand Problems and to Guide the Solution of Multi-Step Problems

Work through each section in order. Show your work where indicated. Include units in every step of your calculations.

Grade 9·22 problems·~40 min·Common Core Math - HS Number and Quantity·standard·hsn-q-a-1

Printable layout

Recall / Warm-Up

A car travels at 55 miles per hour for 2 hours. Which unit does the answer (distance) have?

miles

miles per hour

hours

miles² per hour

A runner completes 3 laps around a track. Each lap is 400 meters. Which setup gives the total distance?

3 laps ÷ 400 meters/lap

3 laps × 400 meters/lap

400 meters/lap ÷ 3 laps

3 laps + 400 meters/lap

Using the formula $d = r \times t$ , a cyclist travels at $r = 12$ km/h for $t = 2.5$ hours. What is the distance in kilometers?

Fluency Practice

A printer prints 8 pages per minute. A document is 120 pages. Which expression correctly gives the printing time in minutes?

$120 \text{ pages} \times 8 \text{ pages/min}$

$120 \text{ pages} \div 8 \text{ pages/min}$

$8 \text{ pages/min} \div 120 \text{ pages}$

$120 \text{ pages} + 8 \text{ pages/min}$

A factory produces 150 widgets per hour. Each widget weighs 0.5 kg. The factory operates 8 hours per day. What is the total mass of widgets produced per day, in kilograms?

Convert 3 hours to seconds using dimensional analysis. Chain two conversion factors: hours → minutes → seconds. What is the answer in seconds?

Convert 45 miles per hour to meters per second. Use 1 mile = 1,609 meters and 1 hour = 3,600 seconds. Round your answer to one decimal place.

The simple interest formula is $I = P \times r \times t$ , where $P$ is in dollars, $r$ is in 1/year, and $t$ must be in years. If $P = 500$ dollars, $r = 0.06$ /year, and $t = 18$ months, first convert $t$ to years: $t =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ years. Then the interest $I =$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ dollars.

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