Learn on PengiEureka Math, Grade 5Chapter 9: Decimal Multi-Digit Multiplication

Lesson 2: Multiply decimal fractions by multi-digit whole numbers through conversion to a whole number problem and reasoning about the placement of the decimal.

In this Grade 5 Eureka Math lesson from Chapter 9, students learn to multiply decimal fractions (including hundredths) by multi-digit whole numbers by converting the problem into a whole number multiplication and then using place value reasoning to position the decimal point in the product. Students practice the standard algorithm alongside estimation and area models to verify their answers. The lesson builds fluency with problems such as 7.38 × 41 and 104.35 × 34, reinforcing the compensation strategy of multiplying by a power of 10 and dividing the result by the same power of 10.

Section 1

Multiplying Decimals Using Unit Form

Property

To multiply a decimal by a whole number, you can express the decimal in unit form (e.g., tenths, hundredths). The product will be in the same unit form. For a decimal to the hundredths place:

a.bc×d=(abc hundredths)×d=(abc×d) hundredthsa.bc \times d = (abc \text{ hundredths}) \times d = (abc \times d) \text{ hundredths}

Examples

Section 2

Multiply Decimals Using Compensation

Property

To multiply a decimal by a whole number, you can multiply the decimal by a power of 10 to make it a whole number, perform the multiplication, and then divide the product by the same power of 10. This compensation strategy keeps the overall value the same.

a×b=(a×10n)×b÷10na \times b = (a \times 10^n) \times b \div 10^n

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Multiplying Decimals Using Unit Form

Property

To multiply a decimal by a whole number, you can express the decimal in unit form (e.g., tenths, hundredths). The product will be in the same unit form. For a decimal to the hundredths place:

a.bc×d=(abc hundredths)×d=(abc×d) hundredthsa.bc \times d = (abc \text{ hundredths}) \times d = (abc \times d) \text{ hundredths}

Examples

Section 2

Multiply Decimals Using Compensation

Property

To multiply a decimal by a whole number, you can multiply the decimal by a power of 10 to make it a whole number, perform the multiplication, and then divide the product by the same power of 10. This compensation strategy keeps the overall value the same.

a×b=(a×10n)×b÷10na \times b = (a \times 10^n) \times b \div 10^n

Examples