Learn on PengiEureka Math, Grade 5Chapter 7: Mental Strategies for Multi-Digit Whole Number Multiplication

Lesson 1: Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive and associative properties.

In this Grade 5 Eureka Math lesson from Chapter 7, students learn to multiply multi-digit whole numbers and multiples of 10 by applying place value patterns along with the distributive and associative properties. Fluency activities build skills in multiplying by 10, 100, and 1,000, composing and decomposing place value units, and rounding to prepare students for mental multiplication strategies. Concept development guides students through problems such as 4 × 30, 40 × 30, and 4,000 × 30 to reveal how place value relationships simplify larger products.

Section 1

Multiply by Powers of 10

Property

Multiplying a whole number by a power of 10 (10,100,1000,…10, 100, 1000, \dots) involves annexing (adding) zeros to the end of the number. The number of zeros added is equal to the number of zeros in the power of 10.

  • n×10=n0n \times 10 = n0
  • n×100=n00n \times 100 = n00
  • n×1000=n000n \times 1000 = n000

Examples

  • 5×10=505 \times 10 = 50
  • 82×100=820082 \times 100 = 8200
  • 45×1000=4500045 \times 1000 = 45000

Explanation

When you multiply a whole number by 10, 100, or 1000, you are making the number that many times larger. This has the effect of shifting each digit to a larger place value. A simple way to find the product is to count the number of zeros in the power of 10 and add that many zeros to the end of the original number.

Section 2

Multiply Multiples of 10 Using Place Value Units

Property

To multiply multiples of 10, express each factor as a digit times a place value unit. The final product is found by multiplying the digits and multiplying the place value units separately, then combining the results.

(a×unit1)×(b×unit2)=(a×b)×(unit1×unit2)(a \times \text{unit}_1) \times (b \times \text{unit}_2) = (a \times b) \times (\text{unit}_1 \times \text{unit}_2)

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Multiply by Powers of 10

Property

Multiplying a whole number by a power of 10 (10,100,1000,…10, 100, 1000, \dots) involves annexing (adding) zeros to the end of the number. The number of zeros added is equal to the number of zeros in the power of 10.

  • n×10=n0n \times 10 = n0
  • n×100=n00n \times 100 = n00
  • n×1000=n000n \times 1000 = n000

Examples

  • 5×10=505 \times 10 = 50
  • 82×100=820082 \times 100 = 8200
  • 45×1000=4500045 \times 1000 = 45000

Explanation

When you multiply a whole number by 10, 100, or 1000, you are making the number that many times larger. This has the effect of shifting each digit to a larger place value. A simple way to find the product is to count the number of zeros in the power of 10 and add that many zeros to the end of the original number.

Section 2

Multiply Multiples of 10 Using Place Value Units

Property

To multiply multiples of 10, express each factor as a digit times a place value unit. The final product is found by multiplying the digits and multiplying the place value units separately, then combining the results.

(a×unit1)×(b×unit2)=(a×b)×(unit1×unit2)(a \times \text{unit}_1) \times (b \times \text{unit}_2) = (a \times b) \times (\text{unit}_1 \times \text{unit}_2)

Examples