Convert Using Equivalent Ratios
Measurement unit conversion in 6th grade can be done using equivalent ratios. Write the known conversion rate as a fraction, then multiply or divide to find an equivalent ratio at your target value. To convert 7 feet to inches using 12 in/1 ft: multiply both by 7 to get 84 in/7 ft, so 7 feet = 84 inches. For smaller-to-larger conversions with remainders: 20 oz divided by 16 = 1 pound remainder 4 ounces. This method from Reveal Math, Course 1, Module 1 makes unit conversion systematic and error-resistant for 6th graders.
Key Concepts
To convert units, you can create an equivalent ratio by multiplying or dividing the numerator and denominator of a known conversion rate by the same number: $$\frac{a \text{ units} 1}{b \text{ units} 2} = \frac{a \times c \text{ units} 1}{b \times c \text{ units} 2}$$.
To convert from a larger unit to a smaller unit , multiply by the conversion factor. To convert from a smaller unit to a larger unit , divide by the conversion factor. If division results in a remainder, that amount stays in the original, smaller unit.
Common Questions
How do I convert units using equivalent ratios?
Write the conversion rate as a fraction. To convert to a smaller unit (multiply): scale up both numerator and denominator by the same factor. To convert to a larger unit (divide): divide both by the conversion factor.
Convert 9 feet to inches using equivalent ratios.
Use the rate 12 in/1 ft. Multiply both by 9: 108 in/9 ft. So 9 feet = 108 inches.
Convert 25 ounces to pounds and ounces.
1 pound = 16 ounces. Divide 25 by 16: 1 remainder 9. So 25 ounces = 1 pound and 9 ounces.
Why do remainders occur in some unit conversions?
Remainders occur when the smaller unit total does not divide evenly into the larger unit. The remainder stays as the original smaller unit.
How does equivalent ratio conversion compare to dimensional analysis?
Both methods use the same multiplication logic. Equivalent ratio conversion is a 6th grade approach that uses the ratio table framework; dimensional analysis is the more formal version used in higher grades.
When do 6th graders learn to convert units with equivalent ratios?
Module 1 of Reveal Math, Course 1 covers this in the Ratios and Rates unit.