Section 1
Decomposing Place Value Units
Property
Decomposing a place value unit means trading it for 10 of the next smaller unit. This is done when you don't have enough in a place value to subtract.
In this Grade 4 Eureka Math lesson from Chapter 5, students learn to use place value understanding to regroup across columns — such as unbundling 1 hundred into 10 tens — to apply the standard subtraction algorithm with multi-digit whole numbers. Using place value disks, charts, and tape diagrams, students work through problems like 4,259 − 2,171 to practice identifying when regrouping is needed and recording the renamed values in the algorithm. The lesson also connects subtraction to real-world word problems, reinforcing how tape diagrams model the relationship between the whole and its parts.
Section 1
Decomposing Place Value Units
Decomposing a place value unit means trading it for 10 of the next smaller unit. This is done when you don't have enough in a place value to subtract.
Section 2
Standard Subtraction with Single Regrouping
When subtracting vertically, if a digit in the top number (minuend) is smaller than the digit below it (subtrahend), you must regroup. To regroup, you decompose 1 from the next higher place value to the left and add 10 to the current place value. For example, 1 hundred becomes 10 tens, or 1 ten becomes 10 ones.
Section 3
Checking Subtraction with Addition
Addition and subtraction are inverse operations. To check a subtraction problem, add the difference (the answer) to the subtrahend (the number being subtracted). The sum must equal the minuend (the number you started with).
Expand to review the lesson summary and core properties.
Section 1
Decomposing Place Value Units
Decomposing a place value unit means trading it for 10 of the next smaller unit. This is done when you don't have enough in a place value to subtract.
Section 2
Standard Subtraction with Single Regrouping
When subtracting vertically, if a digit in the top number (minuend) is smaller than the digit below it (subtrahend), you must regroup. To regroup, you decompose 1 from the next higher place value to the left and add 10 to the current place value. For example, 1 hundred becomes 10 tens, or 1 ten becomes 10 ones.
Section 3
Checking Subtraction with Addition
Addition and subtraction are inverse operations. To check a subtraction problem, add the difference (the answer) to the subtrahend (the number being subtracted). The sum must equal the minuend (the number you started with).