Using unit multipliers to convert measures
Using unit multipliers to convert measures in Grade 8 Saxon Math Course 3 is a systematic method where students multiply a measurement by a fraction equal to 1 to change its units. The unit multiplier is set up so that the original unit appears in the denominator, allowing it to cancel out and leaving only the desired unit. This approach is reliable for both single-step and multi-step unit conversions.
Key Concepts
Property A unit multiplier is a ratio in which the numerator and denominator are equivalent measures but different units. Because the measures are equivalent, the ratio is equal to 1. For the relationship between feet and inches, we can write two unit multipliers: $$\frac{12 \text{ in.}}{1 \text{ ft}} \quad \text{and} \quad \frac{1 \text{ ft}}{12 \text{ in.}}$$.
Examples Convert 72 inches to feet: $72 \text{ in.} \times \frac{1 \text{ ft}}{12 \text{ in.}} = \frac{72}{12} \text{ ft} = 6 \text{ ft}$ Convert 180 minutes to hours: $180 \text{ min} \times \frac{1 \text{ hr}}{60 \text{ min}} = \frac{180}{60} \text{ hr} = 3 \text{ hr}$ Convert 12 quarts to gallons: $12 \text{ qt} \times \frac{1 \text{ gal}}{4 \text{ qt}} = \frac{12}{4} \text{ gal} = 3 \text{ gal}$.
Explanation Think of a unit multiplier as a clever form of '1'. You're not changing the value, just swapping units! Pick the fraction that puts the unit you want to ditch on the bottom, so it cancels out and leaves you with the unit you need. It’s like a magic trick for measurements.
Common Questions
What is a unit multiplier?
A unit multiplier is a fraction equal to 1 formed by a unit equivalency, such as (12 inches / 1 foot). Multiplying by it changes the unit without changing the value.
How do you set up a unit multiplier for conversion?
Write the desired unit in the numerator and the unit to be eliminated in the denominator of the fraction. The unit in the denominator will cancel with the original measurement unit.
How do you convert 5 feet to inches using a unit multiplier?
5 feet x (12 inches / 1 foot) = 60 inches. The feet units cancel, leaving inches.
Can you use multiple unit multipliers in one conversion?
Yes. For multi-step conversions, multiply by successive unit multipliers until the desired unit is achieved. All intermediate units cancel out.
Why does Saxon Math Course 3 use unit multipliers?
Unit multipliers provide a systematic, error-resistant method for unit conversion that scales easily to complex multi-step problems and reinforces the concept of mathematical equivalency.