Grade 7 Expressions: Combining Like Terms

Worked examples

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

1. Example 1

   Simplify: −8m + 11n − 8m − 15n = −16m + ?n

   1. Like terms have the same variable part. Here the m-terms are −8m and −8m; the n-terms are 11n and −15n.
   2. Combine the m-terms by adding their coefficients: −8 − 8 = −16, so they make −16m.
   3. Combine the n-terms by adding their coefficients: 11 − 15 = −4, so they make −4n.
   4. So −8m + 11n − 8m − 15n = −16m − 4n.
   5. Match −16m − 4n to −16m + ?n: the missing number is −4.

   Answer: −4

2. Example 2

   Simplify: −n + 5n − 10 = ?n − 10

   1. Like terms have the same variable part. Here the n-terms are −n and 5n; the number term is −10.
   2. Combine the n-terms by adding their coefficients: −1 + 5 = 4, so they make 4n.
   3. So −n + 5n − 10 = 4n − 10.
   4. Match 4n − 10 to ?n − 10: the missing number is 4.

   Answer: 4

3. Example 3

   Simplify: 10x + 4y − 3x − 13y = ?x − 9y

   1. Like terms have the same variable part. Here the x-terms are 10x and −3x; the y-terms are 4y and −13y.
   2. Combine the x-terms by adding their coefficients: 10 − 3 = 7, so they make 7x.
   3. Combine the y-terms by adding their coefficients: 4 − 13 = −9, so they make −9y.
   4. So 10x + 4y − 3x − 13y = 7x − 9y.
   5. Match 7x − 9y to ?x − 9y: the missing number is 7.

   Answer: 7