Unit multipliers
Unit multipliers are fractions equal to 1 that are used to convert between units of measurement. For the equivalence 1 foot = 12 inches, the two unit multipliers are 12 inches/1 foot and 1 foot/12 inches. You choose the multiplier that cancels the unwanted unit, leaving only the desired unit in the answer. This method is taught in Chapter 5 of Saxon Math Course 2 and provides 7th grade students with a systematic approach to unit conversion that they will use throughout science and math.
Key Concepts
Property Because these fractions have units and are equal to 1, we call them unit multipliers . For an equivalent measure like $1 \text{ foot} = 12 \text{ inches}$, the two unit multipliers are: $$\frac{12 \text{ inches}}{1 \text{ foot}} \quad \text{and} \quad \frac{1 \text{ foot}}{12 \text{ inches}}$$.
Examples Two unit multipliers for $3 \text{ ft} = 1 \text{ yd}$ are: $$\frac{3 \text{ ft}}{1 \text{ yd}} \quad \text{and} \quad \frac{1 \text{ yd}}{3 \text{ ft}}$$ Two unit multipliers for $16 \text{ oz} = 1 \text{ lb}$ are: $$\frac{16 \text{ oz}}{1 \text{ lb}} \quad \text{and} \quad \frac{1 \text{ lb}}{16 \text{ oz}}$$.
Explanation Unit multipliers are like secret identity changers for your numbers! Since they always equal 1, multiplying by them doesn’t change a value, just its name (or unit). You just need to pick the right one to switch from feet to inches, or ounces to pounds. Presto change o!
Common Questions
What are unit multipliers?
Unit multipliers are fractions made from equivalent measurements that equal 1. For example, since 3 feet = 1 yard, both 3ft/1yd and 1yd/3ft are unit multipliers.
How do you choose the right unit multiplier?
Pick the multiplier that places the unit you want to cancel in the opposite position (numerator vs denominator) from where it appears in your given measurement. The unwanted unit cancels, leaving only the desired unit.
How do you convert 240 yards to feet using unit multipliers?
Multiply: 240 yd x (3 ft / 1 yd) = 720 ft. The yard units cancel, leaving feet.
Why are unit multipliers equal to 1?
Because the numerator and denominator represent the same quantity in different units. Since they are equal, the fraction equals 1, and multiplying by 1 does not change the value.
What are common mistakes with unit multipliers?
The most common mistake is using the wrong multiplier, which squares the original unit instead of canceling it. Always check that the unwanted unit appears in both the numerator and denominator.
Is unit conversion with multipliers part of 7th grade math?
Yes. Saxon Math Course 2 teaches unit multipliers in Chapter 5, giving students a reliable method for all measurement conversions.