Ratios Rates Proportional Relationships and Units Pattern - Unit Conversion

Unit Conversion

This pattern gives you a quantity in one unit and asks you to convert it to another. Every conversion follows the same principle: multiply by a conversion factor that equals $1$. The key is setting up the factor so the unwanted unit cancels out.

The Core Method

To convert, multiply by a fraction where the old unit is in the denominator and the new unit is in the numerator:

$\text{quantity in old units} \times \dfrac{\text{new units}}{\text{old units}} = \text{quantity in new units}$

Worked Examples

Example 1. A recipe uses $48$ ounces of flour. How many pounds is that? ($1$ pound $= 16$ ounces)

A) $768$
B) $3$
C) $32$
D) $64$

$48 \text{ oz} \times \dfrac{1 \text{ lb}}{16 \text{ oz}} = \dfrac{48}{16} = 3 \text{ lb}$
Gotcha: Option A multiplies instead of dividing ($48 \times 16 = 768$). When converting from a smaller unit to a larger unit, you divide. When converting from larger to smaller, you multiply.
The answer is B.

Example 2. A file is $3{,}200$ kilobytes. How many megabytes is that? ($1$ MB $= 1{,}000$ KB)

$3{,}200 \text{ KB} \times \dfrac{1 \text{ MB}}{1{,}000 \text{ KB}} = 3.2 \text{ MB}$

Example 3. A car travels $55$ miles per hour. How many miles does it travel per minute?

$55 \dfrac{\text{mi}}{\text{hr}} \times \dfrac{1 \text{ hr}}{60 \text{ min}} = \dfrac{55}{60} = \dfrac{11}{12} \approx 0.917 \text{ mi/min}$
Gotcha: When the unit being converted is in the denominator (per hour → per minute), flip the conversion factor so "hours" cancels.

Example 4. A tank holds $5$ gallons. How many cups is that? ($1$ gallon $= 4$ quarts, $1$ quart $= 4$ cups)

Chain two conversions:
$5 \text{ gal} \times \dfrac{4 \text{ qt}}{1 \text{ gal}} \times \dfrac{4 \text{ cups}}{1 \text{ qt}} = 5 \times 4 \times 4 = 80 \text{ cups}$

Example 5. A currency exchange rate is $1$ dollar $= 1.15$ euros. How many dollars is $230$ euros?

$230 \text{ euros} \times \dfrac{1 \text{ dollar}}{1.15 \text{ euros}} = \dfrac{230}{1.15} = 200 \text{ dollars}$

What to Do on Test Day

• Set up the fraction so units cancel. If you're converting FROM ounces, put ounces in the denominator.
• Smaller → larger unit = divide. Larger → smaller unit = multiply.
• Chain conversions when no single conversion factor is given. Multiply by multiple fractions.
• "Per" units: If converting miles per hour to miles per minute, convert the denominator unit (hours → minutes).
• Double-check direction. If the answer is bigger than the original and you converted to a larger unit, something's wrong.