Converting With Unit Multipliers
Converting with unit multipliers is a systematic method for changing one unit of measurement to another by multiplying by fractions equal to 1, where the numerator and denominator are equivalent measurements in different units. To convert 72 inches to feet, multiply by the unit multiplier 1 ft/12 in: 72 in x (1 ft/12 in) = 6 ft. This Grade 7 math skill from Saxon Math, Course 2 provides a reliable, algebra-based technique for unit conversion that scales to multi-step conversions in science, engineering, and everyday practical math.
Key Concepts
Property When we set up unit conversion problems, we will write the numbers in this order: $$\text{Given measure} \times \text{Unit multiplier} = \text{Converted measure}$$.
Examples Convert 240 yards to feet: $$240 \text{ yd} \cdot \frac{3 \text{ ft}}{1 \text{ yd}} = 720 \text{ ft}$$ Convert 240 feet to yards: $$240 \text{ ft} \cdot \frac{1 \text{ yd}}{3 \text{ ft}} = 80 \text{ yd}$$ Convert 100 meters to yards ($1 \text{ m} \approx 1.1 \text{ yd}$): $$100 \text{ m} \cdot \frac{1.1 \text{ yd}}{1 \text{ m}} \approx 110 \text{ yd}$$.
Explanation This is a simple matching game! To switch units, pick the unit multiplier that puts the unit you want on top and the unit you are getting rid of on the bottom. The old unit gets canceled out, leaving you with the shiny new unit you wanted. It's a guaranteed win!
Common Questions
What is a unit multiplier?
A unit multiplier is a fraction equal to 1, where the numerator and denominator are equivalent measurements. For example, 1 ft/12 in = 1 because 1 foot and 12 inches are the same length.
How do I use unit multipliers to convert units?
Multiply your measurement by a unit multiplier so the unwanted unit cancels. To convert 5 yards to feet, multiply by 3 ft/1 yd: 5 yd x (3 ft/1 yd) = 15 ft.
Why do unit multipliers work?
Multiplying by a fraction equal to 1 does not change the value — only the units. When the original unit cancels from numerator and denominator, you are left with the new unit.
How do I convert using multiple unit multipliers?
Chain the multipliers together. To convert 10 yards to inches: 10 yd x (3 ft/1 yd) x (12 in/1 ft) = 360 in. Each multiplier cancels one unit and introduces the next.
When do students learn unit multiplier conversions?
Unit multiplier conversions are introduced in Grade 7. Saxon Math, Course 2 covers them in Chapter 9 as a structured approach to both customary and metric unit conversions.
What are common mistakes with unit multipliers?
Placing the unit fractions upside down is the most common error — the unit you want to cancel must be in the denominator of the multiplier, not the numerator.
How does unit multiplier conversion connect to dimensional analysis?
Unit multipliers are the core of dimensional analysis, the scientific method for tracking units through calculations. Every physics and chemistry unit conversion uses exactly this technique.