Grade 6 Expressions: Simplifying Expressions

Combine like terms

What You'll Learn

Identify like terms
Combine coefficients

📖Simplifying

Like terms have the same variable part. Add their coefficients and keep the variable: 4x + 3x = 7x, and y + y + y = 3y. Numbers combine with numbers. Each problem asks for the missing number (?) in the simplified expression, as in 4x + 5 + 3x = ?x + 5 (answer 7).

Worked examples

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

Example 1
Simplify: 7x + 2y + 3x + 9y = ?x + 11y
1. Like terms have the same variable part. Here the x-terms are 7x and 3x; the y-terms are 2y and 9y.
2. Combine the x-terms by adding their coefficients: 7 + 3 = 10, so they make 10x.
3. Combine the y-terms by adding their coefficients: 2 + 9 = 11, so they make 11y.
4. So 7x + 2y + 3x + 9y = 10x + 11y.
5. Match 10x + 11y to ?x + 11y: the missing number is 10.
Answer: 10
Example 2
Simplify: 7n + 14 + 8n − 7 = 15n + ?
1. Like terms have the same variable part. Here the n-terms are 7n and 8n; the number terms are 14 and −7.
2. Combine the n-terms by adding their coefficients: 7 + 8 = 15, so they make 15n.
3. Combine the number terms: 14 − 7 = 7.
4. So 7n + 14 + 8n − 7 = 15n + 7.
5. Match 15n + 7 to 15n + ?: the missing number is 7.
Answer: 7
Example 3
Simplify: 16k − 7k = ?k
1. Like terms have the same variable part. Here the k-terms are 16k and −7k.
2. Combine the k-terms by adding their coefficients: 16 − 7 = 9, so they make 9k.
3. So 16k − 7k = 9k.
4. Match 9k to ?k: the missing number is 9.
Answer: 9