Learn on PengiEureka Math, Grade 4Chapter 27: Repeated Addition of Fractions as Multiplication

Lesson 4: Find the product of a whole number and a mixed number using the distributive property.

In this Grade 4 Eureka Math lesson from Chapter 27, students learn to find the product of a whole number and a mixed number by applying the distributive property to decompose the mixed number into its whole and fractional parts. Students practice expressions such as 4 × 9¾ by breaking them into (4 × 9) + (4 × ¾) and combining the results into a single mixed number or whole number. Tape diagrams and number lines are used throughout to support understanding of the multiplication process.

Section 1

Multiply a Whole Number and a Mixed Number Using the Distributive Property

Property

To multiply a whole number by a mixed number, decompose the mixed number into a sum of its whole and fractional parts. Then, apply the distributive property.

a×(b+cd)=(a×b)+(a×cd)a \times (b + \frac{c}{d}) = (a \times b) + (a \times \frac{c}{d})

Examples

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Multiply a Whole Number and a Mixed Number Using the Distributive Property

Property

To multiply a whole number by a mixed number, decompose the mixed number into a sum of its whole and fractional parts. Then, apply the distributive property.

a×(b+cd)=(a×b)+(a×cd)a \times (b + \frac{c}{d}) = (a \times b) + (a \times \frac{c}{d})

Examples