Learn on PengiEureka Math, Grade 4Chapter 13: Division of Tens and Ones with Successive Remainders

Lesson 7: Solve division problems without remainders using the area model.

Grade 4 students learn to solve division problems without remainders using the area model, breaking apart a two-digit dividend into smaller parts that are easier to divide. In this Eureka Math lesson, students decompose dividends like 48 and 96 into tens and ones, use number bonds alongside partitioned rectangles to find unknown side lengths, and combine partial quotients to reach the full answer. The lesson builds on students' understanding of the distributive property and connects multiplication and division concepts introduced earlier in Chapter 13.

Section 1

Set Up the Area Model for Division

Property

A division problem can be visualized as finding the unknown length of a rectangle. The dividend represents the total area, the divisor represents the known width, and the quotient represents the unknown length.

Dividend÷Divisor=QuotientDividend \div Divisor = Quotient
Area÷width=lengthArea \div width = length

Section 2

Combining Parts: The Distributive Property in Division

Property

The total quotient is the sum of the partial quotients.
If a dividend is decomposed into parts, such as a+ba + b, the total quotient QQ for (a+b)÷c(a + b) \div c is the sum of the partial quotients from a÷ca \div c and b÷cb \div c.

Q=(a÷c)+(b÷c)Q = (a \div c) + (b \div c)

Examples

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Chapter 13: Division of Tens and Ones with Successive Remainders

  1. Lesson 1

    Lesson 1: Solve division word problems with remainders.

  2. Lesson 2

    Lesson 2: Understand and solve division problems with a remainder using the array and area models.

  3. Lesson 3

    Lesson 3: Understand and solve two-digit dividend division problems with a remainder in the ones place by using place value disks.

  4. Lesson 4

    Lesson 4: Represent and solve division problems requiring decomposing a remainder in the tens.

  5. Lesson 5

    Lesson 5: Find whole number quotients and remainders.

  6. Lesson 6

    Lesson 6: Explain remainders by using place value understanding and models.

  7. Lesson 7Current

    Lesson 7: Solve division problems without remainders using the area model.

  8. Lesson 8

    Lesson 8: Solve division problems with remainders using the area model.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Set Up the Area Model for Division

Property

A division problem can be visualized as finding the unknown length of a rectangle. The dividend represents the total area, the divisor represents the known width, and the quotient represents the unknown length.

Dividend÷Divisor=QuotientDividend \div Divisor = Quotient
Area÷width=lengthArea \div width = length

Section 2

Combining Parts: The Distributive Property in Division

Property

The total quotient is the sum of the partial quotients.
If a dividend is decomposed into parts, such as a+ba + b, the total quotient QQ for (a+b)÷c(a + b) \div c is the sum of the partial quotients from a÷ca \div c and b÷cb \div c.

Q=(a÷c)+(b÷c)Q = (a \div c) + (b \div c)

Examples

Book overview

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

Continue this chapter

Chapter 13: Division of Tens and Ones with Successive Remainders

  1. Lesson 1

    Lesson 1: Solve division word problems with remainders.

  2. Lesson 2

    Lesson 2: Understand and solve division problems with a remainder using the array and area models.

  3. Lesson 3

    Lesson 3: Understand and solve two-digit dividend division problems with a remainder in the ones place by using place value disks.

  4. Lesson 4

    Lesson 4: Represent and solve division problems requiring decomposing a remainder in the tens.

  5. Lesson 5

    Lesson 5: Find whole number quotients and remainders.

  6. Lesson 6

    Lesson 6: Explain remainders by using place value understanding and models.

  7. Lesson 7Current

    Lesson 7: Solve division problems without remainders using the area model.

  8. Lesson 8

    Lesson 8: Solve division problems with remainders using the area model.