A reliable method
- Write the starting quantity with units.
- Choose a known equivalence.
- Put the unwanted unit opposite itself so it cancels.
- Check the resulting unit and whether the size should increase or decrease.
Example 1
Convert 2.4 liters to milliliters, using 1 liter = 1,000 milliliters.
- Write 2.4 liters.
- Multiply by 1,000 mL per liter so liters cancel.
- 2.4 times 1,000 is 2,400 mL.
Answer: \(2400\) mL
Example 2
A vehicle travels 150 miles in 3 hours at a constant speed. How far does it travel in 4.5 hours?
- Divide 150 miles by 3 hours to get 50 miles per hour.
- Multiply the speed by 4.5 hours.
- 50 times 4.5 is 225 miles.
Answer: \(225\) miles
Common mistakes
- A length conversion factor must be squared for area and cubed for volume.
- Clinical dosage decisions are outside this general math lesson.
Practice without the answer first
- Convert 135 minutes to hours.
- A map scale is 1 cm for 8 km. A route measures 6.5 cm on the map. Find the actual length.
- \(8\) identical items cost \(28\) dollars at a constant unit price. Find the cost of \(14\) items.
Answers and step-by-step explanations
Practice 1
- One hour contains 60 minutes.
- Divide 135 by 60.
- 135/60=9/4=2.25 hours.
Answer: \(9/4\) hours
Practice 2
- Use 8 km per map centimeter.
- Multiply 6.5 cm by 8 km/cm.
- Centimeters cancel and the result is 52 km.
Answer: \(52\) km
Practice 3
- Divide cost by count for the unit price, then multiply by the new count.
- Substitute the given values: \(28 \cdot \frac{1}{8} \cdot 14\).
- Calculate without premature rounding: \(49\) dollars.
- Check that the units and the size of the result match the quantity requested.
Answer: \(49\) dollars
These original skill exercises are not official exam questions or a score prediction. Use the coverage notes on your exam hub to choose relevant practice.
