Every pair of units makes a ratio: 1 foot : 12 inches, 1 hour : 60 minutes, 1 kilogram : 1,000 grams. In Grade 5 you converted with these facts. Now treat each one as a rate and scale it like any ratio.
Idea clave
Use the ratio between the units. Going to a smaller unit, multiply (you need more of them). Going to a larger unit, divide (you need fewer).
Por qué funciona
Since 1 foot : 12 inches is a ratio, it scales: 3 feet : 36 inches, 4.5 feet : 54 inches. Another way to see it: the fraction $\frac{12 \text{ inches}}{1 \text{ foot}}$ is equal to 1, because its top and bottom are the same length. Multiplying by 1 never changes an amount; it only changes the units we use to name it.
Ejemplo resuelto: To a larger unit
Convert 54 inches to feet.
- Feet are bigger than inches, so there will be fewer of them: divide.
- $54 \div 12 = 4.5$.
Respuesta: 4.5 feet (4 feet 6 inches).
Ejemplo resuelto: To a smaller unit
Convert 2.5 hours to minutes.
- Minutes are smaller, so there will be more of them: multiply.
- $2.5 \times 60 = 150$.
Respuesta: 150 minutes.
Ejemplo resuelto: Multiply by a fraction worth 1
How many inches are in 3 yards?
- $3 \text{ yd} \times \frac{3 \text{ ft}}{1 \text{ yd}} = 9$ feet.
- $9 \text{ ft} \times \frac{12 \text{ in}}{1 \text{ ft}} = 108$ inches.
Respuesta: 108 inches.
Error común
Multiplying when you should divide. Changing 54 inches to feet by multiplying gives 648 "feet", longer than a city block. Quick check before you compute: which unit is bigger? A bigger unit needs a smaller number, so feet must come out less than the number of inches.