Learn on PengiBig Ideas Math, Course 1Chapter 2: Fractions and Decimals

Lesson 5: Multiplying Decimals

In this Grade 6 lesson from Big Ideas Math, Course 1 (Chapter 2: Fractions and Decimals), students learn how to multiply decimals by whole numbers and by other decimals by first multiplying as whole numbers and then counting and placing decimal places in the product. The lesson uses base ten blocks, area models, and mental math strategies such as moving the decimal point when multiplying by powers of 10. Students also practice evaluating expressions involving decimal multiplication, supported by estimation to check reasonableness.

Section 1

Multiplying Decimals by Whole Numbers

Property

When multiplying a decimal by a whole number, multiply as if both numbers were whole numbers, then place the decimal point in the product so it has the same number of decimal places as the original decimal factor.

decimal places in product=decimal places in decimal factor\text{decimal places in product} = \text{decimal places in decimal factor}

Section 2

Multiplying a Decimal by a Decimal

Property

To multiply two decimals, first multiply the numbers as if they were whole numbers, ignoring the decimal points. Then, place the decimal point in the product so that the number of decimal places in the product is the sum of the number of decimal places in the factors.

Examples

Section 3

Application: Order of Operations with Decimals

Property

To evaluate expressions with multiple operations, follow the order of operations (PEMDAS/BODMAS):

  1. Parentheses
  2. Exponents
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Multiplying Decimals by Whole Numbers

Property

When multiplying a decimal by a whole number, multiply as if both numbers were whole numbers, then place the decimal point in the product so it has the same number of decimal places as the original decimal factor.

decimal places in product=decimal places in decimal factor\text{decimal places in product} = \text{decimal places in decimal factor}

Section 2

Multiplying a Decimal by a Decimal

Property

To multiply two decimals, first multiply the numbers as if they were whole numbers, ignoring the decimal points. Then, place the decimal point in the product so that the number of decimal places in the product is the sum of the number of decimal places in the factors.

Examples

Section 3

Application: Order of Operations with Decimals

Property

To evaluate expressions with multiple operations, follow the order of operations (PEMDAS/BODMAS):

  1. Parentheses
  2. Exponents
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)

Examples