Learn on PengiEureka Math, Grade 5Chapter 11: Mental Strategies for Multi-Digit Whole Number Division

Lesson 1: Use divide by 10 patterns for multi-digit whole number division.

Grade 5 students learn to use divide-by-10 patterns to solve multi-digit whole number division problems such as 420 ÷ 10 and 1,600 ÷ 100 by applying place value understanding and digit-shifting rules. This lesson from Eureka Math Grade 5, Chapter 11 builds fluency with dividing by multiples of 10 and 100 using place value disks and place value charts. Students practice recognizing that dividing a whole number by 10 shifts each digit one place to the right, and by 100 shifts digits two places to the right.

Section 1

Dividing Whole Numbers by 10, 100, and 1,000

Property

Dividing a whole number by $10$ shifts its digits one place to the right.
Dividing by $100$ shifts its digits two places to the right.
Dividing by $1,000$ shifts its digits three places to the right.

Examples

Section 2

Divide Using Unit Form

Property

To simplify division, express the dividend in a place value unit (e.g., hundreds, thousands). Then, divide the number of units by the divisor.

16 \text{ hundreds} \div 8 = (16 \div 8) \text{ hundreds} = 2 \text{ hundreds}

Section 3

Divide by Multiples of 10 by Decomposing the Divisor

Property

To divide by a number that is a multiple of a power of ten, you can decompose the divisor into its factors and divide sequentially. This can be expressed as:

a \div (b \times c) = (a \div b) \div c

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Dividing Whole Numbers by 10, 100, and 1,000

Property

Dividing a whole number by $10$ shifts its digits one place to the right.
Dividing by $100$ shifts its digits two places to the right.
Dividing by $1,000$ shifts its digits three places to the right.

Examples

Section 2

Divide Using Unit Form

Property

To simplify division, express the dividend in a place value unit (e.g., hundreds, thousands). Then, divide the number of units by the divisor.

16 \text{ hundreds} \div 8 = (16 \div 8) \text{ hundreds} = 2 \text{ hundreds}

Section 3

Divide by Multiples of 10 by Decomposing the Divisor

Property

To divide by a number that is a multiple of a power of ten, you can decompose the divisor into its factors and divide sequentially. This can be expressed as:

a \div (b \times c) = (a \div b) \div c

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Dividing Whole Numbers by 10, 100, and 1,000

Property

Dividing a whole number by $10$ shifts its digits one place to the right.
Dividing by $100$ shifts its digits two places to the right.
Dividing by $1,000$ shifts its digits three places to the right.

Examples

Section 2

Divide Using Unit Form

Property

To simplify division, express the dividend in a place value unit (e.g., hundreds, thousands). Then, divide the number of units by the divisor.

16 \text{ hundreds} \div 8 = (16 \div 8) \text{ hundreds} = 2 \text{ hundreds}

Section 3

Divide by Multiples of 10 by Decomposing the Divisor

Property

To divide by a number that is a multiple of a power of ten, you can decompose the divisor into its factors and divide sequentially. This can be expressed as:

a \div (b \times c) = (a \div b) \div c