Learn on PengiReveal Math, Course 1Module 5: Numerical and Algebraic Expressions

5-6 Use the Distributive Property

In this Grade 6 lesson from Reveal Math, Course 1, students learn to apply the Distributive Property to expand algebraic expressions such as 2(x + 3) into 2x + 6, evaluate numerical expressions with mixed numbers, and factor expressions using the greatest common factor. The lesson covers both expanding and factoring numerical and algebraic expressions, giving students a complete understanding of how multiplication distributes over addition and subtraction.

Section 1

distributive property

Property

To expand an expression, multiply the term outside the parentheses by each term inside: $a(b+c) = a \cdot b + a \cdot c$ .

Examples

$3(w+m) = 3w+3m$
$5(x-3) = 5x-15$
$2(x+7) = 2x+14$

Explanation

Think of it as sharing snacks! The number outside the parentheses, 'a', has to be distributed to every single friend, 'b' and 'c', inside. No one gets left out of the multiplication party, ensuring everyone gets their share of the mathematical treat!

Section 2

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

Examples

Section 3

Factoring Numerical Expressions using GCF

Property

To factor a numerical expression, find the greatest common factor (GCF) of the terms. Then use the distributive property in reverse to write the expression as the GCF multiplied by a sum of the remaining factors. The general form is $ab + ac = a(b+c)$ , where $a$ is the GCF.

Examples

To factor $12 + 18$ , the GCF of $12$ and $18$ is $6$ . So, $12 + 18 = 6(2) + 6(3) = 6(2+3)$ .
To factor $35 + 50$ , the GCF of $35$ and $50$ is $5$ . So, $35 + 50 = 5(7) + 5(10) = 5(7+10)$ .
To factor $24 + 36$ , the GCF of $24$ and $36$ is $12$ . So, $24 + 36 = 12(2) + 12(3) = 12(2+3)$ .

Explanation

Factoring a numerical expression is the opposite of expanding it. First, identify the greatest common factor (GCF) of the numbers in the sum. Then, you "pull out" the GCF and write the remaining factors inside parentheses. This process rewrites a sum as a product, which is a key application of the distributive property.

Book overview

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Module 5: Numerical and Algebraic Expressions

Back to Reveal Math, Course 1

Lesson 1
5-1 Powers and Exponents
Learn Practice
Lesson 2
5-2 Numerical Expressions
Learn Practice
Lesson 3
5-3 Write Algebraic Expressions
Learn Practice
Lesson 4
5-4 Evaluate Algebraic Expressions
Learn Practice
Lesson 5
5-5 Factors and Multiples
Learn Practice
Lesson 6Current
5-6 Use the Distributive Property
Learn Practice
Lesson 7
5-7 Equivalent Algebraic Expressions
Learn Practice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

distributive property

Property

To expand an expression, multiply the term outside the parentheses by each term inside: $a(b+c) = a \cdot b + a \cdot c$ .

Examples

$3(w+m) = 3w+3m$
$5(x-3) = 5x-15$
$2(x+7) = 2x+14$

Explanation

Section 2

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

Examples

Section 3

Factoring Numerical Expressions using GCF

Property

Examples

To factor $12 + 18$ , the GCF of $12$ and $18$ is $6$ . So, $12 + 18 = 6(2) + 6(3) = 6(2+3)$ .
To factor $35 + 50$ , the GCF of $35$ and $50$ is $5$ . So, $35 + 50 = 5(7) + 5(10) = 5(7+10)$ .
To factor $24 + 36$ , the GCF of $24$ and $36$ is $12$ . So, $24 + 36 = 12(2) + 12(3) = 12(2+3)$ .

Explanation

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Module 5: Numerical and Algebraic Expressions

Back to Reveal Math, Course 1

Lesson 1
5-1 Powers and Exponents
Learn Practice
Lesson 2
5-2 Numerical Expressions
Learn Practice
Lesson 3
5-3 Write Algebraic Expressions
Learn Practice
Lesson 4
5-4 Evaluate Algebraic Expressions
Learn Practice
Lesson 5
5-5 Factors and Multiples
Learn Practice
Lesson 6Current
5-6 Use the Distributive Property
Learn Practice
Lesson 7
5-7 Equivalent Algebraic Expressions
Learn Practice

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

distributive property

Property

To expand an expression, multiply the term outside the parentheses by each term inside: $a(b+c) = a \cdot b + a \cdot c$ .

Examples

$3(w+m) = 3w+3m$
$5(x-3) = 5x-15$
$2(x+7) = 2x+14$

Explanation

Section 2

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

Examples

Section 3

Factoring Numerical Expressions using GCF

Property

Examples

To factor $12 + 18$ , the GCF of $12$ and $18$ is $6$ . So, $12 + 18 = 6(2) + 6(3) = 6(2+3)$ .
To factor $35 + 50$ , the GCF of $35$ and $50$ is $5$ . So, $35 + 50 = 5(7) + 5(10) = 5(7+10)$ .
To factor $24 + 36$ , the GCF of $24$ and $36$ is $12$ . So, $24 + 36 = 12(2) + 12(3) = 12(2+3)$ .

Explanation

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Module 5: Numerical and Algebraic Expressions

Back to Reveal Math, Course 1

Lesson 1
5-1 Powers and Exponents
Learn Practice
Lesson 2
5-2 Numerical Expressions
Learn Practice
Lesson 3
5-3 Write Algebraic Expressions
Learn Practice
Lesson 4
5-4 Evaluate Algebraic Expressions
Learn Practice
Lesson 5
5-5 Factors and Multiples
Learn Practice
Lesson 6Current
5-6 Use the Distributive Property
Learn Practice
Lesson 7
5-7 Equivalent Algebraic Expressions
Learn Practice

5-6 Use the Distributive Property

Property

Examples

Explanation

Property

Examples

Property

Examples

Explanation

Module 5: Numerical and Algebraic Expressions

5-1 Powers and Exponents

5-2 Numerical Expressions

5-3 Write Algebraic Expressions

5-4 Evaluate Algebraic Expressions

5-5 Factors and Multiples

5-6 Use the Distributive Property

5-7 Equivalent Algebraic Expressions

Lesson overview

Property

Examples

Explanation

Property

Examples

Property

Examples

Explanation

Module 5: Numerical and Algebraic Expressions

5-1 Powers and Exponents

5-2 Numerical Expressions

5-3 Write Algebraic Expressions

5-4 Evaluate Algebraic Expressions

5-5 Factors and Multiples

5-6 Use the Distributive Property

5-7 Equivalent Algebraic Expressions

5-1 Powers and Exponents

5-2 Numerical Expressions

5-3 Write Algebraic Expressions

5-4 Evaluate Algebraic Expressions

5-5 Factors and Multiples

5-6 Use the Distributive Property

5-7 Equivalent Algebraic Expressions