Learn on PengiEureka Math, Grade 5Chapter 13: Partial Quotients and Multi-Digit Decimal Division

Lesson 1: Divide decimal dividends by multiples of 10, reasoning about the placement of the decimal point and making connections to a written method.

In this Grade 5 Eureka Math lesson, students learn to divide decimal dividends by multiples of 10 by reasoning about decimal point placement using place value charts and place value disks. Students explore how dividing by 10 shifts digits one place to the right, connecting unit form thinking to a written method that breaks problems like 1.8 ÷ 60 into two steps. The lesson builds on prior work with whole number division and prepares students for estimating and computing multi-digit decimal quotients.

Section 1

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 2

Divide Decimals by Multiples of 10

Property

To divide a decimal by a multiple of 10, you can use a two-step process. First, divide the decimal by the single-digit factor of the divisor. Then, divide the resulting quotient by 10.

a.b \div (c \times 10) = (a.b \div c) \div 10

Examples

$5.4 \div 60 = (5.4 \div 6) \div 10 = 0.9 \div 10 = 0.09$
$4.8 \div 40 = (4.8 \div 4) \div 10 = 1.2 \div 10 = 0.12$
$0.72 \div 90 = (0.72 \div 9) \div 10 = 0.08 \div 10 = 0.008$

Explanation

This skill extends division by multiples of 10 to decimal dividends. You can simplify the problem by breaking the divisor into its factors (e.g., 60 becomes 6 and 10). First, perform the standard division with the single-digit factor, and then shift the decimal point one place to the left to divide by 10. This method connects basic division facts to the rules of place value for an efficient strategy.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

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 2

Divide Decimals by Multiples of 10

Property

To divide a decimal by a multiple of 10, you can use a two-step process. First, divide the decimal by the single-digit factor of the divisor. Then, divide the resulting quotient by 10.

a.b \div (c \times 10) = (a.b \div c) \div 10

Examples

$5.4 \div 60 = (5.4 \div 6) \div 10 = 0.9 \div 10 = 0.09$
$4.8 \div 40 = (4.8 \div 4) \div 10 = 1.2 \div 10 = 0.12$
$0.72 \div 90 = (0.72 \div 9) \div 10 = 0.08 \div 10 = 0.008$

Explanation

Overview

Lesson overview

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

Overview

Section 1

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 2

Divide Decimals by Multiples of 10

Property

To divide a decimal by a multiple of 10, you can use a two-step process. First, divide the decimal by the single-digit factor of the divisor. Then, divide the resulting quotient by 10.

a.b \div (c \times 10) = (a.b \div c) \div 10

Examples

$5.4 \div 60 = (5.4 \div 6) \div 10 = 0.9 \div 10 = 0.09$
$4.8 \div 40 = (4.8 \div 4) \div 10 = 1.2 \div 10 = 0.12$
$0.72 \div 90 = (0.72 \div 9) \div 10 = 0.08 \div 10 = 0.008$