Lesson 7: Converting Measures

Property

A conversion factor is a fraction made from two equivalent measurements, such as $1 \text{ meter} = 100 \text{ centimeters}$.
Because the numerator and denominator are equal, the fraction's value is $1$.
Multiplying by a conversion factor changes the units of a measurement but not its value.

Examples

Property

The U.S. system of measurement uses units of inch, foot, yard, and mile to measure length and pound and ton to measure weight.
For capacity, the units used are cup, pint, quart, and gallons.
To convert between units, we use the identity property of multiplication, writing 1 as a fraction that helps convert the units, such as $\frac{1 \text{ foot}}{12 \text{ inches}}$.

Length
1 foot (ft.) = 12 inches (in.)
1 yard (yd.) = 3 feet (ft.)
1 mile (mi.) = 5,280 feet (ft.)

Weight
1 pound (lb.) = 16 ounces (oz.)
1 ton = 2000 pounds (lb.)

Property

To compare two lengths given in different units, you must first convert one or both lengths so they are expressed in the same unit.
Then, you can use the symbols $<$, $>$, or $=$ to compare their numerical values.

Examples

Property

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
When quantities are multiplied or divided, their units are also multiplied or divided.
For example, multiplying pace by speed gives a new rate:

Examples

• A runner's pace is 8 minutes per mile and their speed is 7.5 miles per hour. The product is $8 \times 7.5 = 60$. This means the runner travels for 60 minutes in one hour.
• A factory worker earns 4 dollars for each toy assembled and can assemble 5 toys per hour. The earning rate is $4 \times 5 = 20$ dollars per hour.
• A machine uses 0.5 liters of fuel per hour and runs for 8 hours. The total fuel used is $0.5 \times 8 = 4$ liters, as the 'hour' units cancel out.