Learn on PengiEureka Math, Grade 5Chapter 12: Partial Quotients and Multi-Digit Whole Number Division

Lesson 5: Divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value.

In this Grade 5 Eureka Math lesson, students learn to divide three- and four-digit dividends by two-digit divisors to produce two- and three-digit quotients, focusing on how successive remainders are decomposed across place values. Students practice the long division algorithm using estimation strategies, such as rounding to compatible numbers, to determine each digit of the quotient. Real-world word problems involving area, perimeter, and equal sharing reinforce the skill in applied contexts.

Section 1

Dividing Four-Digit Numbers Using the Standard Algorithm

Property

The standard algorithm for division is a systematic process based on the relationship: Dividend = (Divisor ×\times Quotient) + Remainder.

The process involves repeatedly dividing into the largest place values of the dividend first.
Any remainder from one step is decomposed and combined with the digit in the next smaller place value to continue dividing.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Dividing Four-Digit Numbers Using the Standard Algorithm

Property

The standard algorithm for division is a systematic process based on the relationship: Dividend = (Divisor ×\times Quotient) + Remainder.

The process involves repeatedly dividing into the largest place values of the dividend first.
Any remainder from one step is decomposed and combined with the digit in the next smaller place value to continue dividing.