Learn on PengienVision, Mathematics, Grade 5Chapter 6: Use Models and Strategies to Divide Decimals

Lesson 1: Patterns for Dividing with Decimals

In this Grade 5 enVision Mathematics lesson, students learn how to divide decimals by powers of 10 using place value patterns and mental math. The lesson focuses on understanding how dividing by 10, 100, or 1,000 shifts each digit one place to the right, which is equivalent to moving the decimal point to the left. Students practice applying these patterns to solve problems with expressions such as 89.5 ÷ 10¹ and explore the relationship between multiplying by decimals and dividing by powers of 10.

Section 1

Dividing by 10 by Unbundling Units

Property

Dividing a number by 10 is equivalent to unbundling each of its place value units into 10 units of the next smaller place value. This causes each digit to shift one place to the right, making its value 10 times smaller.

1 \text{ larger unit} = 10 \text{ smaller units to the right}

(\text{Value}) \div 10 = \text{Value shifted one place to the right}

Examples

Section 2

Divide Decimals by 10 Using a Place Value Chart

Property

Dividing a decimal by 10 shifts each digit one place to the right on the place value chart. This means the value of each digit becomes one-tenth of its original value.
For example, $5.2 \div 10 = 0.52$ .

Examples

To solve $4.5 \div 10$ on a place value chart, the 4 in the ones place moves to the tenths place, and the 5 in the tenths place moves to the hundredths place. The result is $0.45$ .
To solve $3.0 \div 10$ on a place value chart, the 3 in the ones place moves to the tenths place. The result is $0.3$ .
To solve $27.6 \div 10$ on a place value chart, the 2 in the tens place moves to the ones place, the 7 in the ones place moves to the tenths place, and the 6 in the tenths place moves to the hundredths place. The result is $2.76$ .

Explanation

A place value chart visually represents the value of each digit in a number. When you divide a number by 10, you are making it 10 times smaller. This is shown on the chart by moving every digit one column to the right. For example, a digit in the ones place moves to the tenths place, and a digit in the tenths place moves to the hundredths place.

Section 3

Procedure: Dividing by Powers of 10 with Exponents

Property

To divide a decimal by a power of 10, $10^n$ , move the decimal point $n$ places to the left.

Examples

Section 4

Dividing by 10⁰

Property

Dividing a number by 1 does not change its value. Since any non-zero number raised to the power of zero is 1, $10^0 = 1$ . Therefore, dividing by $10^0$ is the same as dividing by 1.

a \div 10^0 = a \div 1 = a

Examples

Book overview

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

Continue this chapter

Chapter 6: Use Models and Strategies to Divide Decimals

Back to enVision, Mathematics, Grade 5

Lesson 1Current
Lesson 1: Patterns for Dividing with Decimals
Learn Practice
Lesson 2
Lesson 2: Estimate Decimal Quotients
Learn Practice
Lesson 3
Lesson 3: Use Models to Divide by a 1-Digit Whole Number
Learn Practice
Lesson 4
Lesson 4: Divide by a 2-Digit Whole Number
Learn Practice
Lesson 5
Lesson 5: Divide by a Decimal
Learn Practice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Dividing by 10 by Unbundling Units

Property

1 \text{ larger unit} = 10 \text{ smaller units to the right}

(\text{Value}) \div 10 = \text{Value shifted one place to the right}

Examples

Section 2

Divide Decimals by 10 Using a Place Value Chart

Property

Examples

To solve $4.5 \div 10$ on a place value chart, the 4 in the ones place moves to the tenths place, and the 5 in the tenths place moves to the hundredths place. The result is $0.45$ .
To solve $3.0 \div 10$ on a place value chart, the 3 in the ones place moves to the tenths place. The result is $0.3$ .
To solve $27.6 \div 10$ on a place value chart, the 2 in the tens place moves to the ones place, the 7 in the ones place moves to the tenths place, and the 6 in the tenths place moves to the hundredths place. The result is $2.76$ .

Explanation

Section 3

Procedure: Dividing by Powers of 10 with Exponents

Property

To divide a decimal by a power of 10, $10^n$ , move the decimal point $n$ places to the left.

Examples

Section 4

Dividing by 10⁰

Property

Dividing a number by 1 does not change its value. Since any non-zero number raised to the power of zero is 1, $10^0 = 1$ . Therefore, dividing by $10^0$ is the same as dividing by 1.

a \div 10^0 = a \div 1 = a

Examples

Book overview

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

Continue this chapter

Chapter 6: Use Models and Strategies to Divide Decimals

Back to enVision, Mathematics, Grade 5

Lesson 1Current
Lesson 1: Patterns for Dividing with Decimals
Learn Practice
Lesson 2
Lesson 2: Estimate Decimal Quotients
Learn Practice
Lesson 3
Lesson 3: Use Models to Divide by a 1-Digit Whole Number
Learn Practice
Lesson 4
Lesson 4: Divide by a 2-Digit Whole Number
Learn Practice
Lesson 5
Lesson 5: Divide by a Decimal
Learn Practice

Overview

Lesson overview

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

Overview

Section 1

Dividing by 10 by Unbundling Units

Property

1 \text{ larger unit} = 10 \text{ smaller units to the right}

(\text{Value}) \div 10 = \text{Value shifted one place to the right}

Examples

Section 2

Divide Decimals by 10 Using a Place Value Chart

Property

Examples

To solve $4.5 \div 10$ on a place value chart, the 4 in the ones place moves to the tenths place, and the 5 in the tenths place moves to the hundredths place. The result is $0.45$ .
To solve $3.0 \div 10$ on a place value chart, the 3 in the ones place moves to the tenths place. The result is $0.3$ .
To solve $27.6 \div 10$ on a place value chart, the 2 in the tens place moves to the ones place, the 7 in the ones place moves to the tenths place, and the 6 in the tenths place moves to the hundredths place. The result is $2.76$ .

Explanation

Section 3

Procedure: Dividing by Powers of 10 with Exponents

Property

To divide a decimal by a power of 10, $10^n$ , move the decimal point $n$ places to the left.

Examples

Section 4

Dividing by 10⁰

Property

Dividing a number by 1 does not change its value. Since any non-zero number raised to the power of zero is 1, $10^0 = 1$ . Therefore, dividing by $10^0$ is the same as dividing by 1.

a \div 10^0 = a \div 1 = a

Examples

Book overview

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

Continue this chapter

Chapter 6: Use Models and Strategies to Divide Decimals

Back to enVision, Mathematics, Grade 5

Lesson 1Current
Lesson 1: Patterns for Dividing with Decimals
Learn Practice
Lesson 2
Lesson 2: Estimate Decimal Quotients
Learn Practice
Lesson 3
Lesson 3: Use Models to Divide by a 1-Digit Whole Number
Learn Practice
Lesson 4
Lesson 4: Divide by a 2-Digit Whole Number
Learn Practice
Lesson 5
Lesson 5: Divide by a Decimal
Learn Practice

Lesson 1: Patterns for Dividing with Decimals

Property

Examples

Property

Examples

Explanation

Property

Examples

Property

Examples

Chapter 6: Use Models and Strategies to Divide Decimals

Lesson 1: Patterns for Dividing with Decimals

Lesson 2: Estimate Decimal Quotients

Lesson 3: Use Models to Divide by a 1-Digit Whole Number

Lesson 4: Divide by a 2-Digit Whole Number

Lesson 5: Divide by a Decimal

Lesson overview

Property

Examples

Property

Examples

Explanation

Property

Examples

Property

Examples

Chapter 6: Use Models and Strategies to Divide Decimals

Lesson 1: Patterns for Dividing with Decimals

Lesson 2: Estimate Decimal Quotients

Lesson 3: Use Models to Divide by a 1-Digit Whole Number

Lesson 4: Divide by a 2-Digit Whole Number

Lesson 5: Divide by a Decimal

Lesson 1: Patterns for Dividing with Decimals

Lesson 2: Estimate Decimal Quotients

Lesson 3: Use Models to Divide by a 1-Digit Whole Number

Lesson 4: Divide by a 2-Digit Whole Number

Lesson 5: Divide by a Decimal