Chapter 22: Combining Like Terms and Distributive Property
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Combining Like Terms and Distributive Property with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Factor (a number that divides another number exactly)
- Variable (a letter or symbol representing a number)
- Coefficient (the number multiplying a variable)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
22.1 Like terms
A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Like terms .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Like terms .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Like terms .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Like terms .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Like terms .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Like terms .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Like terms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.2 Unlike terms
A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Unlike terms .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Unlike terms .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Unlike terms .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Unlike terms .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Unlike terms .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Unlike terms .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Unlike terms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.3 Combining positive terms
A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining positive terms .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining positive terms .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining positive terms .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining positive terms .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining positive terms .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining positive terms .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Combining positive terms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.4 Combining negative terms
A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining negative terms .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining negative terms .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining negative terms .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining negative terms .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining negative terms .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining negative terms .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Combining negative terms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.5 Constant terms
A constant is a fixed number that does not change. This topic focuses on Constant terms .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A constant is a fixed number that does not change. This topic focuses on Constant terms .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A constant is a fixed number that does not change. This topic focuses on Constant terms .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A constant is a fixed number that does not change. This topic focuses on Constant terms .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A constant is a fixed number that does not change. This topic focuses on Constant terms .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A constant is a fixed number that does not change. This topic focuses on Constant terms .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Constant terms. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.6 Expressions with two variables
A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Expressions with two variables .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Expressions with two variables .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Expressions with two variables .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Expressions with two variables .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Expressions with two variables .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Expressions with two variables .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Expressions with two variables. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.7 Distributive property
Distributive property is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: Distributive property is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: Distributive property is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: Distributive property is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: Distributive property is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: Distributive property is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Distributive property. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.8 Positive coefficients
A coefficient is the number multiplying a variable. This topic focuses on Positive coefficients .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Positive coefficients .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Positive coefficients .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Positive coefficients .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Positive coefficients .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Positive coefficients .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Positive coefficients. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.9 Negative coefficients
A coefficient is the number multiplying a variable. This topic focuses on Negative coefficients .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Negative coefficients .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Negative coefficients .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Negative coefficients .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Negative coefficients .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A coefficient is the number multiplying a variable. This topic focuses on Negative coefficients .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Negative coefficients. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.10 Combining after distribution
Combining after distribution is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Combining after distribution: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Combining after distribution is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Combining after distribution: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Combining after distribution is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Combining after distribution: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Combining after distribution is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Combining after distribution: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Combining after distribution is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Combining after distribution: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Combining after distribution is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Combining after distribution in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Combining after distribution becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Combining after distribution and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Combining after distribution becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Combining after distribution using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Combining after distribution becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Combining after distribution problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Combining after distribution becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Combining after distribution could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Combining after distribution becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Combining after distribution. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.11 Factoring as reverse distribution introduction
A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factoring as reverse distribution introduction .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factoring as reverse distribution introduction .
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factoring as reverse distribution introduction .
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factoring as reverse distribution introduction .
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factoring as reverse distribution introduction .
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factoring as reverse distribution introduction .
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: List all positive factors of 18.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 9, 18
Worked Example 7
Problem: List all positive factors of 24.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 8
Problem: List all positive factors of 30.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 5, 6, 10, 15, 30
Worked Example 9
Problem: List all positive factors of 42.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 6, 7, 14, 21, 42
Worked Example 10
Problem: List all positive factors of 60.
- Test whole numbers that divide with no remainder.
Very beginner explanation: A factor divides a number exactly.
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Practice Exercise
Create one new question about Factoring as reverse distribution introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.12 Simplifying multi-term expressions
A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Simplifying multi-term expressions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Simplifying multi-term expressions .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Simplifying multi-term expressions .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Simplifying multi-term expressions .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Simplifying multi-term expressions .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Simplifying multi-term expressions .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Simplifying multi-term expressions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
22.13 Checking equivalent expressions
An algebraic expression combines numbers, variables, and operations without an equals sign. This topic focuses on Checking equivalent expressions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: An algebraic expression combines numbers, variables, and operations without an equals sign. This topic focuses on Checking equivalent expressions .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: An algebraic expression combines numbers, variables, and operations without an equals sign. This topic focuses on Checking equivalent expressions .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: An algebraic expression combines numbers, variables, and operations without an equals sign. This topic focuses on Checking equivalent expressions .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: An algebraic expression combines numbers, variables, and operations without an equals sign. This topic focuses on Checking equivalent expressions .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: An algebraic expression combines numbers, variables, and operations without an equals sign. This topic focuses on Checking equivalent expressions .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Checking equivalent expressions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Like terms . Show your reasoning and check your answer.
- Create and solve a new question about Unlike terms . Show your reasoning and check your answer.
- Create and solve a new question about Combining positive terms . Show your reasoning and check your answer.
- Create and solve a new question about Combining negative terms . Show your reasoning and check your answer.
- Create and solve a new question about Constant terms . Show your reasoning and check your answer.
- Create and solve a new question about Expressions with two variables . Show your reasoning and check your answer.
- Create and solve a new question about Distributive property . Show your reasoning and check your answer.
- Create and solve a new question about Positive coefficients . Show your reasoning and check your answer.
- Create and solve a new question about Negative coefficients . Show your reasoning and check your answer.
- Create and solve a new question about Combining after distribution . Show your reasoning and check your answer.
- Create and solve a new question about Factoring as reverse distribution introduction . Show your reasoning and check your answer.
- Create and solve a new question about Simplifying multi-term expressions . Show your reasoning and check your answer.
Common Mistakes
- Combining unlike terms.
- Changing only one side of an equation.
- Forgetting to distribute to every term.
- Using a pattern rule that works only for the first few terms.
- Writing code without tracing variable values.
- Using a mathematical model without stating assumptions.
30 Review Questions and Answers
Q1. What is important to remember about Like terms?
Answer: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Like terms.
Q2. What is important to remember about Unlike terms?
Answer: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Unlike terms.
Q3. What is important to remember about Combining positive terms?
Answer: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining positive terms.
Q4. What is important to remember about Combining negative terms?
Answer: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Combining negative terms.
Q5. What is important to remember about Constant terms?
Answer: A constant is a fixed number that does not change. This topic focuses on Constant terms.
Q6. What is important to remember about Expressions with two variables?
Answer: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Expressions with two variables.
Q7. What is important to remember about Distributive property?
Answer: Distributive property is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Positive coefficients?
Answer: A coefficient is the number multiplying a variable. This topic focuses on Positive coefficients.
Q9. What is important to remember about Negative coefficients?
Answer: A coefficient is the number multiplying a variable. This topic focuses on Negative coefficients.
Q10. What is important to remember about Combining after distribution?
Answer: Combining after distribution is an important Grade 7 idea in Combining Like Terms and Distributive Property. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q11. What is important to remember about Factoring as reverse distribution introduction?
Answer: A factor (a number that divides another number exactly) helps with simplifying, grouping, and fraction work. This topic focuses on Factoring as reverse distribution introduction.
Q12. What is important to remember about Simplifying multi-term expressions?
Answer: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Simplifying multi-term expressions.
Q13. What is important to remember about Checking equivalent expressions?
Answer: An algebraic expression combines numbers, variables, and operations without an equals sign. This topic focuses on Checking equivalent expressions.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q26. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q27. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q28. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q29. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q30. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.