Add and Subtract Mixed Units by Regrouping
Adding and subtracting mixed units by regrouping is a Grade 4 math skill from Eureka Math where students operate on like units separately, then regroup when necessary: for addition, convert excess small units to large units (e.g., 15 inches = 1 ft 3 in); for subtraction, borrow a large unit and convert it to small units when there are not enough small units to subtract from. For example, 4 ft 3 in - 1 ft 9 in requires borrowing 1 ft as 12 in: 3 ft 15 in - 1 ft 9 in = 2 ft 6 in. Covered in Chapter 35 of Eureka Math Grade 4, this general strategy applies to any measurement system with non-decimal conversion factors.
Key Concepts
To add or subtract mixed units, operate on like units separately. For addition, regroup the sum of the smaller units into larger units when possible (e.g., $12 \text{ inches} = 1 \text{ foot}$). For subtraction, decompose a larger unit into smaller units when the subtrahend's smaller unit is greater than the minuend's (e.g., $1 \text{ yard} = 3 \text{ feet}$).
Common Questions
How do you add mixed units with regrouping?
Add like units separately. If the sum of the smaller units equals or exceeds the conversion factor, convert the excess to the larger unit and add it to the larger-unit column. For example, 5 ft 8 in + 2 ft 7 in = 7 ft 15 in = 8 ft 3 in.
How do you subtract mixed units with regrouping?
Subtract like units. If the smaller units in the top number are not enough, borrow 1 of the larger unit from its column, convert it to the equivalent number of smaller units, and add those to the existing smaller units. Then subtract.
What grade adds and subtracts mixed units by regrouping?
This skill is a 4th grade math topic from Chapter 35 of Eureka Math Grade 4 on Problem Solving with Measurement.
What measurement conversions are used for regrouping in grade 4?
Common ones include 1 foot = 12 inches, 1 yard = 3 feet, 1 pound = 16 ounces, 1 hour = 60 minutes, 1 liter = 1,000 milliliters, and 1 kilogram = 1,000 grams.
What are common mistakes when adding and subtracting mixed units?
Using the wrong conversion factor is the most common error, especially confusing metric (multiples of 10 or 1,000) with customary (12 inches per foot, 16 ounces per pound). Always identify the correct conversion before regrouping.
How does mixed-unit regrouping connect to multi-digit arithmetic?
The structure is identical: add or subtract in each column separately, then regroup across columns. The only difference is the conversion rate between columns, which varies by measurement unit rather than always being 10.