Grade 5 Pre-Algebra worksheet on simplifying expressions with algebraic equations.
Simplifying expressions worksheet for Grade 5 Pre-Algebra, featuring 20 problems to rewrite algebraic expressions.
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying expressions worksheets | Worsheets library
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Show Answer Key & Explanations
Step-by-step solution for: Simplifying expressions worksheets | Worsheets library
Let's solve each expression by simplifying them using combining like terms. Like terms are terms that have the same variable raised to the same power (e.g., $ 2x $ and $ 3x $, or $ 4y $ and $ -5y $).
We'll go through each problem step-by-step.
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- Combine $ x $-terms: $ 2x + 3x = 5x $
- Combine constants: $ 7 - 2 + 3 = 8 $
- Answer: $ 5x + 8 $
---
- $ x $-terms: $ 3x + 4x = 7x $
- Constants: $ 9 - 5 = 4 $
- Answer: $ 7x + 4 $
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- $ 5x - x = 4x $
- Answer: $ 4x $
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- $ 5y + 7y = 12y $
- Answer: $ 12y $
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- $ y $-terms: $ 2y + 2y - 2y = 2y $
- Constants: $ 7 + 5 = 12 $
- Answer: $ 2y + 12 $
---
- $ x $-terms: $ 6x + x = 7x $
- Constants: $ 2 + 4 = 6 $
- Answer: $ 7x + 6 $
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- $ y $-terms: $ 5y + 9y = 14y $
- Constants: $ 4 + 6 = 10 $
- Answer: $ 14y + 10 $
---
- $ x $-terms: $ 3x + 4x = 7x $
- Constants: $ 9 - 5 = 4 $
- Answer: $ 7x + 4 $
---
- $ y $-terms: $ y + 2y = 3y $
- Constants: $ 5 - 5 = 0 $
- Answer: $ 3y $
---
- $ y $-terms: $ 3y + 3y + 8y = 14y $
- Constants: $ 3 + 1 + 9 = 13 $
- Answer: $ 14y + 13 $
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- $ x $-terms: $ x + 4x = 5x $
- Constants: $ 2 - 1 = 1 $
- Answer: $ 5x + 1 $
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- $ 8y + 4y = 12y $
- Answer: $ 12y $
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- $ y $-terms: $ 5y + 6y + 7y = 18y $
- Constants: $ 5 + 7 + 2 = 14 $
- Answer: $ 18y + 14 $
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- $ x $-terms: $ 2x + 7x = 9x $
- Constants: $ 8 - 7 = 1 $
- Answer: $ 9x + 1 $
---
- $ y $-terms: $ -y + 2y = y $
- Constants: $ 6 + 6 + 6 + 3 = 21 $
- Answer: $ y + 21 $
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- $ y $-terms: $ 3y - y = 2y $
- Constant: $ 1 $
- Answer: $ 2y + 1 $
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- $ y $-terms: $ 7y - 4y = 3y $
- Constants: $ 1 + 6 = 7 $
- Answer: $ 3y + 7 $
---
- $ 4y + y = 5y $
- Answer: $ 5y $
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- $ x $-terms: $ 14x - 8x = 6x $
- Constant: $ 9 $
- Answer: $ 6x + 9 $
---
- $ x $-terms: $ 16x - 4x - 7x = 5x $
- Constants: $ 13 - 11 = 2 $
- Answer: $ 5x + 2 $
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1. $ 5x + 8 $
2. $ 7x + 4 $
3. $ 4x $
4. $ 12y $
5. $ 2y + 12 $
6. $ 7x + 6 $
7. $ 14y + 10 $
8. $ 7x + 4 $
9. $ 3y $
10. $ 14y + 13 $
11. $ 5x + 1 $
12. $ 12y $
13. $ 18y + 14 $
14. $ 9x + 1 $
15. $ y + 21 $
16. $ 2y + 1 $
17. $ 3y + 7 $
18. $ 5y $
19. $ 6x + 9 $
20. $ 5x + 2 $
---
To simplify expressions:
- Group like terms (same variables with same exponents).
- Add or subtract their coefficients.
- Write the simplified expression in standard form (variables first, then constants).
This helps reduce complex expressions into simpler ones while maintaining their value.
Let me know if you'd like this as a printable answer key!
We'll go through each problem step-by-step.
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1. $ 2x + 7 + 3x - 2 + 3 $
- Combine $ x $-terms: $ 2x + 3x = 5x $
- Combine constants: $ 7 - 2 + 3 = 8 $
- Answer: $ 5x + 8 $
---
2. $ 3x + 9 + 4x - 5 $
- $ x $-terms: $ 3x + 4x = 7x $
- Constants: $ 9 - 5 = 4 $
- Answer: $ 7x + 4 $
---
3. $ 5x - x $
- $ 5x - x = 4x $
- Answer: $ 4x $
---
4. $ 5y + 7y $
- $ 5y + 7y = 12y $
- Answer: $ 12y $
---
5. $ 7 + 2y + 2y + 5 - 2y $
- $ y $-terms: $ 2y + 2y - 2y = 2y $
- Constants: $ 7 + 5 = 12 $
- Answer: $ 2y + 12 $
---
6. $ 2 + 6x + 4 + x $
- $ x $-terms: $ 6x + x = 7x $
- Constants: $ 2 + 4 = 6 $
- Answer: $ 7x + 6 $
---
7. $ 4 + 5y + 6 + 9y $
- $ y $-terms: $ 5y + 9y = 14y $
- Constants: $ 4 + 6 = 10 $
- Answer: $ 14y + 10 $
---
8. $ 3x + 9 + 4x - 5 $
- $ x $-terms: $ 3x + 4x = 7x $
- Constants: $ 9 - 5 = 4 $
- Answer: $ 7x + 4 $
---
9. $ 5 + y - 5 + 2y $
- $ y $-terms: $ y + 2y = 3y $
- Constants: $ 5 - 5 = 0 $
- Answer: $ 3y $
---
10. $ 3y + 3 + 3y + 1 + 8y + 9 $
- $ y $-terms: $ 3y + 3y + 8y = 14y $
- Constants: $ 3 + 1 + 9 = 13 $
- Answer: $ 14y + 13 $
---
11. $ 2 + x - 1 + 4x $
- $ x $-terms: $ x + 4x = 5x $
- Constants: $ 2 - 1 = 1 $
- Answer: $ 5x + 1 $
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12. $ 8y + 4y $
- $ 8y + 4y = 12y $
- Answer: $ 12y $
---
13. $ 5y + 5 + 6y + 7 + 7y + 2 $
- $ y $-terms: $ 5y + 6y + 7y = 18y $
- Constants: $ 5 + 7 + 2 = 14 $
- Answer: $ 18y + 14 $
---
14. $ 8 + 2x - 7 + 7x $
- $ x $-terms: $ 2x + 7x = 9x $
- Constants: $ 8 - 7 = 1 $
- Answer: $ 9x + 1 $
---
15. $ 6 + 6 - y + 6 + 2y + 3 $
- $ y $-terms: $ -y + 2y = y $
- Constants: $ 6 + 6 + 6 + 3 = 21 $
- Answer: $ y + 21 $
---
16. $ 1 + 3y - y $
- $ y $-terms: $ 3y - y = 2y $
- Constant: $ 1 $
- Answer: $ 2y + 1 $
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17. $ 7y - 4y + 1 + 6 $
- $ y $-terms: $ 7y - 4y = 3y $
- Constants: $ 1 + 6 = 7 $
- Answer: $ 3y + 7 $
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18. $ 4y + y $
- $ 4y + y = 5y $
- Answer: $ 5y $
---
19. $ 9 + 14x - 8x $
- $ x $-terms: $ 14x - 8x = 6x $
- Constant: $ 9 $
- Answer: $ 6x + 9 $
---
20. $ 16x - 4x - 7x + 13 - 11 $
- $ x $-terms: $ 16x - 4x - 7x = 5x $
- Constants: $ 13 - 11 = 2 $
- Answer: $ 5x + 2 $
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✔ Final Answers:
1. $ 5x + 8 $
2. $ 7x + 4 $
3. $ 4x $
4. $ 12y $
5. $ 2y + 12 $
6. $ 7x + 6 $
7. $ 14y + 10 $
8. $ 7x + 4 $
9. $ 3y $
10. $ 14y + 13 $
11. $ 5x + 1 $
12. $ 12y $
13. $ 18y + 14 $
14. $ 9x + 1 $
15. $ y + 21 $
16. $ 2y + 1 $
17. $ 3y + 7 $
18. $ 5y $
19. $ 6x + 9 $
20. $ 5x + 2 $
---
🔍 Explanation:
To simplify expressions:
- Group like terms (same variables with same exponents).
- Add or subtract their coefficients.
- Write the simplified expression in standard form (variables first, then constants).
This helps reduce complex expressions into simpler ones while maintaining their value.
Let me know if you'd like this as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of simplify expressions worksheet with answers.
