Learn on PengiEureka Math, Grade 4Chapter 5: Multi-Digit Whole Number Subtraction

Lesson 1: Use place value understanding to decompose to smaller units once using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.

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

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.

1 hundred=10 tens1 \text{ hundred} = 10 \text{ tens}
1 ten=10 ones1 \text{ ten} = 10 \text{ ones}

Examples

Section 2

Standard Subtraction with Single Regrouping

Property

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.

Examples

Section 3

Checking Subtraction with Addition

Property

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).

a−b=c⇔c+b=aa - b = c \quad \Leftrightarrow \quad c + b = a

Examples

Book overview

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Chapter 5: Multi-Digit Whole Number Subtraction

  1. Lesson 1Current

    Lesson 1: Use place value understanding to decompose to smaller units once using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.

    LearnPractice
  2. Lesson 2

    Lesson 2: Use place value understanding to decompose to smaller units up to three times using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.

    LearnPractice
  3. Lesson 3

    Lesson 3: Use place value understanding to fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.

    LearnPractice
  4. Lesson 4

    Lesson 4: Solve two-step word problems using the standard subtraction algorithm fluently modeled with tape diagrams, and assess the reasonableness of answers using rounding.

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

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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.

1 hundred=10 tens1 \text{ hundred} = 10 \text{ tens}
1 ten=10 ones1 \text{ ten} = 10 \text{ ones}

Examples

Section 2

Standard Subtraction with Single Regrouping

Property

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.

Examples

Section 3

Checking Subtraction with Addition

Property

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).

a−b=c⇔c+b=aa - b = c \quad \Leftrightarrow \quad c + b = a

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 5: Multi-Digit Whole Number Subtraction

  1. Lesson 1Current

    Lesson 1: Use place value understanding to decompose to smaller units once using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.

    LearnPractice
  2. Lesson 2

    Lesson 2: Use place value understanding to decompose to smaller units up to three times using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.

    LearnPractice
  3. Lesson 3

    Lesson 3: Use place value understanding to fluently decompose to smaller units multiple times in any place using the standard subtraction algorithm, and apply the algorithm to solve word problems using tape diagrams.

    LearnPractice
  4. Lesson 4

    Lesson 4: Solve two-step word problems using the standard subtraction algorithm fluently modeled with tape diagrams, and assess the reasonableness of answers using rounding.

    LearnPractice