Simplifying expressions worksheet for Grade 5 students, offering 20 algebraic problems to practice combining like terms.

You've uploaded a Grade 5 Pre-Algebra Worksheet titled “Simplifying Expressions.” The task is to rewrite each expression by combining like terms.

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🔍 What does “simplify expressions” mean?

It means to combine like terms — terms that have the same variable and exponent. For example:
- `2x + 3x = 5x` (like terms)
- `4y - y = 3y`
- Constants (numbers without variables) can also be combined: `7 + 3 = 10`

We do not combine different variables (e.g., `x` and `y`) or numbers with variables.

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Let’s solve each problem step-by-step:

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✏️ Problems 1–10

1. `2x + 7 + 3x - 2 + 3`
→ Combine `x` terms: `2x + 3x = 5x`
→ Combine constants: `7 - 2 + 3 = 8`
✔ Answer: `5x + 8`

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2. `3x + 9 - 4x - 5`
→ `3x - 4x = -x`
→ `9 - 5 = 4`
✔ Answer: `-x + 4`

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3. `5x - x`
→ `5x - 1x = 4x`
✔ Answer: `4x`

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4. `5y + 7y`
→ `5y + 7y = 12y`
✔ Answer: `12y`

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5. `7 + 2 + 6y - 2y + 5 - 2y`
→ Constants: `7 + 2 + 5 = 14`
→ `y` terms: `6y - 2y - 2y = 2y`
✔ Answer: `2y + 14`

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6. `2 + 6x + 4 + x`
→ Constants: `2 + 4 = 6`
→ `x` terms: `6x + x = 7x`
✔ Answer: `7x + 6`

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7. `4 + 5y + 6 + 9y`
→ Constants: `4 + 6 = 10`
→ `y` terms: `5y + 9y = 14y`
✔ Answer: `14y + 10`

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8. `3x + 9 - 4x - 5`
→ `3x - 4x = -x`
→ `9 - 5 = 4`
✔ Answer: `-x + 4` *(Same as #2)*

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9. `5 + y - 5 + 2y`
→ Constants: `5 - 5 = 0`
→ `y` terms: `y + 2y = 3y`
✔ Answer: `3y`

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10. `3y + 3 + 3y + 1 + 8y + 9`
→ `y` terms: `3y + 3y + 8y = 14y`
→ Constants: `3 + 1 + 9 = 13`
✔ Answer: `14y + 13`

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✏️ Problems 11–20

11. `2 + x - 1 + 4x`
→ `x + 4x = 5x`
→ `2 - 1 = 1`
✔ Answer: `5x + 1`

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12. `8y + 4y`
→ `8y + 4y = 12y`
✔ Answer: `12y`

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13. `5y + 6 + 6y + 7 + 7y + 2`
→ `y` terms: `5y + 6y + 7y = 18y`
→ Constants: `6 + 7 + 2 = 15`
✔ Answer: `18y + 15`

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14. `8 + 2x - 7 + 7x`
→ `2x + 7x = 9x`
→ `8 - 7 = 1`
✔ Answer: `9x + 1`

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15. `8y + 6 - y + 6 + 2y + 3`
→ `y` terms: `8y - y + 2y = 9y`
→ Constants: `6 + 6 + 3 = 15`
✔ Answer: `9y + 15`

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16. `1 + 3y - y`
→ `3y - y = 2y`
→ Constant: `1`
✔ Answer: `2y + 1`

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17. `7y - 4y + 1 + 6`
→ `7y - 4y = 3y`
→ `1 + 6 = 7`
✔ Answer: `3y + 7`

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18. `4y + y`
→ `4y + y = 5y`
✔ Answer: `5y`

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19. `9 + 14x - 8x`
→ `14x - 8x = 6x`
→ Constant: `9`
✔ Answer: `6x + 9`

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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 Summary:

| Problem | Answer |
|---------|---------------|
| 1 | 5x + 8 |
| 2 | -x + 4 |
| 3 | 4x |
| 4 | 12y |
| 5 | 2y + 14 |
| 6 | 7x + 6 |
| 7 | 14y + 10 |
| 8 | -x + 4 |
| 9 | 3y |
| 10 | 14y + 13 |
| 11 | 5x + 1 |
| 12 | 12y |
| 13 | 18y + 15 |
| 14 | 9x + 1 |
| 15 | 9y + 15 |
| 16 | 2y + 1 |
| 17 | 3y + 7 |
| 18 | 5y |
| 19 | 6x + 9 |
| 20 | 5x + 2 |

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✔ Key Tip for Students: Always group like terms — same variables together, constants together — then simplify each group. Double-check signs!

Let me know if you’d like a printable answer key or explanation for any specific problem!