Grade 6 Expressions: Distributive Property

Distribute and combine

What You'll Learn

Distribute correctly
Combine after distributing

📖Distribute

Multiply the number outside the parentheses by every term inside: 3(x + 4) = 3x + 12. Then combine any like terms, as in 3(x + 4) + 2x = 5x + 12. Each problem asks for the missing number (?) in the equivalent expression.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
Simplify: 9(y + 2) = 9y + ?
1. Distribute 9: multiply each term inside the parentheses by 9. 9 × y = 9y and 9 × 2 = 18. So 9(y + 2) becomes 9y + 18.
2. Match 9y + 18 to 9y + ?: the missing number is 18.
Answer: 18
Example 2
Simplify: 5(4n + 4) + 3n = ?n + 20
1. Distribute 5: multiply each term inside the parentheses by 5. 5 × 4n = 20n and 5 × 4 = 20. So 5(4n + 4) becomes 20n + 20.
2. Now you have 20n + 20 + 3n.
3. Like terms have the same variable part. Here the n-terms are 20n and 3n; the number term is 20.
4. Combine the n-terms by adding their coefficients: 20 + 3 = 23, so they make 23n.
5. So 5(4n + 4) + 3n = 23n + 20.
6. Match 23n + 20 to ?n + 20: the missing number is 23.
Answer: 23
Example 3
Simplify: 7(k + 8) + 6 = 7k + ?
1. Distribute 7: multiply each term inside the parentheses by 7. 7 × k = 7k and 7 × 8 = 56. So 7(k + 8) becomes 7k + 56.
2. Now you have 7k + 56 + 6.
3. Like terms have the same variable part. Here the k-term is 7k; the number terms are 56 and 6.
4. Combine the number terms: 56 + 6 = 62.
5. So 7(k + 8) + 6 = 7k + 62.
6. Match 7k + 62 to 7k + ?: the missing number is 62.
Answer: 62