Learn on PengiEureka Math, Grade 5Chapter 8: The Standard Algorithm for Multi-Digit Whole Number Multiplication

Lesson 2: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.

In this Grade 5 Eureka Math lesson from Chapter 8, students learn to convert numerical expressions into unit form as a mental strategy for multi-digit multiplication. Using the commutative property and decomposition, students practice breaking apart factors — such as rewriting 8 × 31 as 30 eights plus 1 eight — to simplify calculations mentally. The lesson builds fluency with estimating products and applying the distributive property across two- and three-digit multiplication problems.

Section 1

Applying the Distributive Property

Property

The distributive property allows you to multiply a number by a sum or difference by multiplying each part of the sum or difference separately and then adding or subtracting the products.

a×(b+c)=(a×b)+(a×c)a \times (b + c) = (a \times b) + (a \times c)
a×(bc)=(a×b)(a×c)a \times (b - c) = (a \times b) - (a \times c)

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Applying the Distributive Property

Property

The distributive property allows you to multiply a number by a sum or difference by multiplying each part of the sum or difference separately and then adding or subtracting the products.

a×(b+c)=(a×b)+(a×c)a \times (b + c) = (a \times b) + (a \times c)
a×(bc)=(a×b)(a×c)a \times (b - c) = (a \times b) - (a \times c)

Examples