Simplify: \(5x+3y-2x+4y\)
- A \(3x+7y\)
- B \(7x+7y\)
- C \(3x-y\)
- D \(10xy\)
Check answer and explanation
Answer A: \(3x+7y\)
Group like terms by variable: \((5x-2x)+(3y+4y)=(5-2)x+(3+4)y=3x+7y\).
CH04-02 lesson
Simplifying Expressions by Combining Like Terms Learning Activity
A focused Grade 7 learning session for Simplifying Expressions by Combining Like Terms using visual models, worked examples, strategy guidance, and a short mastery check.
- 15
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 7 mastery of simplifying expressions by combining like terms using models, equations, and test-style reasoning.
Student goal: I can solve problems involving simplifying expressions by combining like terms.
Helpful first:
Writing and Evaluating Expressions
Learn the Idea
Simplifying Expressions by Combining Like Terms is part of Grade 7 Expressions. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of simplifying expressions by combining like terms using models, equations, and test-style reasoning.
See the Math
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Follow a Worked Example
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Simplifying Expressions by Combining Like Terms, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Connect It to a Real Situation
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
Avoid Mistakes and Choose a Strategy
- Underline the exact question before solving.
- Label units, variables, or graph axes when they appear.
- Estimate first so unreasonable answers are easier to catch.
- Review missed questions and write the reason for each mistake.
Remember the Key Idea
I can solve problems involving simplifying expressions by combining like terms.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsSimplify: \(8a+5b-3a-2b\)
- A \(5a+3b\)
- B \(11a+3b\)
- C \(5a+7b\)
- D \(16ab\)
Check answer and explanation
Answer A: \(5a+3b\)
Combine like terms: \((8a-3a)+(5b-2b)=5a+3b\).
guided
1 questionWhich terms are like terms?
- A \(4x\) and \(4y\)
- B \(3x^2\) and \(3x\)
- C \(7m\) and \(2m\)
- D \(5xy\) and \(5x\)
Check answer and explanation
Answer C: \(7m\) and \(2m\)
Like terms have the same variable and exponent. Both \(7m\) and \(2m\) contain the variable \(m\) with exponent 1.
practice
5 questionsSimplify: \(12x-7x+3x\)
- A \(8x\)
- B \(22x\)
- C \(2x\)
- D \(12x\)
Check answer and explanation
Answer A: \(8x\)
Combine coefficients: \((12-7+3)x=8x\).
Identify which pair are NOT like terms.
- A \(6a^2\) and \(9a^2\)
- B \(5x\) and \(5x^2\)
- C \(-3y\) and \(4y\)
- D \(2mn\) and \(mn\)
Check answer and explanation
Answer B: \(5x\) and \(5x^2\)
These have different exponents (\(x^1\) vs. \(x^2\)), so they are not like terms.
Simplify: \(4p+6q+2p-q\)
- A \(6p+5q\)
- B \(6p+7q\)
- C \(4p+6q\)
- D \(12pq\)
Check answer and explanation
Answer A: \(6p+5q\)
Combine like terms: \((4p+2p)+(6q-q)=6p+5q\).
Which expression is simplified?
- A \(3x+2x-y\)
- B \(5x+2x-y+y\)
- C \(5x-y\)
- D \(2x+3x+4y\)
Check answer and explanation
Answer C: \(5x-y\)
A simplified expression has all like terms combined. Option C has no like terms remaining.
Simplify: \(-2m-5m+3n+n\)
- A \(-7m+4n\)
- B \(-3m+4n\)
- C \(-7m+3n\)
- D \(7m+4n\)
Check answer and explanation
Answer A: \(-7m+4n\)
Combine like terms: \((-2m-5m)+(3n+n)=-7m+4n\).
exit
3 questionsWhat is the coefficient of \(x\) in the simplified form of \(9x-4x+2y\)?
- A \(9\)
- B \(5\)
- C \(4\)
- D \(13\)
Check answer and explanation
Answer B: \(5\)
Simplify: \((9-4)x+2y=5x+2y\). The coefficient of \(x\) is \(5\).
Simplify: \(\frac{1}{2}a+\frac{1}{4}a\)
- A \(\frac{1}{8}a\)
- B \(\frac{1}{6}a\)
- C \(\frac{3}{4}a\)
- D \(\frac{2}{6}a\)
Check answer and explanation
Answer C: \(\frac{3}{4}a\)
Combine: \(\frac{1}{2}a+\frac{1}{4}a=\frac{2}{4}a+\frac{1}{4}a=\frac{3}{4}a\).
Simplify: \(6x^2+2x^2-3x\)
- A \(8x^2-3x\)
- B \(5x^2\)
- C \(8x^2-3x^2\)
- D \(5x^3\)
Check answer and explanation
Answer A: \(8x^2-3x\)
Combine \(x^2\) terms: \((6+2)x^2-3x=8x^2-3x\). The \(x\) term is not like the \(x^2\) terms.
