Let's solve each expression by
combining like terms. Like terms are terms that have the same variable raised to the same power (e.g., $2r$ and $-4r$ are like terms).
We'll go through each expression one by one.
---
1. $ 2r + 1 + (-4r) + 7 $
- Combine the $r$ terms: $2r - 4r = -2r$
- Combine the constants: $1 + 7 = 8$
-
Answer: $-2r + 8$
---
2. $ 3z + 2 + (-5z) + 6 $
- Combine the $z$ terms: $3z - 5z = -2z$
- Combine the constants: $2 + 6 = 8$
-
Answer: $-2z + 8$
---
3. $ -3z - z $
- Combine the $z$ terms: $-3z - z = -4z$
-
Answer: $-4z$
---
4. $ -4y - 4 + (-3) $
- The only variable term is $-4y$
- Constants: $-4 + (-3) = -7$
-
Answer: $-4y - 7$
---
5. $ -2k + (-4k) + 5 $
- Combine the $k$ terms: $-2k - 4k = -6k$
- Constant: $+5$
-
Answer: $-6k + 5$
---
6. $ 4t + 2 + (-3t) + 6 $
- Combine $t$ terms: $4t - 3t = t$
- Constants: $2 + 6 = 8$
-
Answer: $t + 8$
---
7. $ 4z - (-3z) $
- Subtracting a negative is adding: $4z + 3z = 7z$
-
Answer: $7z$
---
8. $ -2k - (-5) + 1 $
- $-(-5) = +5$, so: $-2k + 5 + 1$
- Constants: $5 + 1 = 6$
-
Answer: $-2k + 6$
---
9. $ -4q - (-8q) + 10 $
- $-(-8q) = +8q$, so: $-4q + 8q + 10 = 4q + 10$
-
Answer: $4q + 10$
---
10. $ -4h + 3 + (-2h) + 3 $
- Combine $h$ terms: $-4h - 2h = -6h$
- Constants: $3 + 3 = 6$
-
Answer: $-6h + 6$
---
✔ Final Answers:
| Expression | Simplified |
|----------|------------|
| $2r + 1 + (-4r) + 7$ | $-2r + 8$ |
| $3z + 2 + (-5z) + 6$ | $-2z + 8$ |
| $-3z - z$ | $-4z$ |
| $-4y - 4 + (-3)$ | $-4y - 7$ |
| $-2k + (-4k) + 5$ | $-6k + 5$ |
| $4t + 2 + (-3t) + 6$ | $t + 8$ |
| $4z - (-3z)$ | $7z$ |
| $-2k - (-5) + 1$ | $-2k + 6$ |
| $-4q - (-8q) + 10$ | $4q + 10$ |
| $-4h + 3 + (-2h) + 3$ | $-6h + 6$ |
---
💡
Key Tips:
- Always combine variables with the same letter and exponent.
- Remember: subtracting a negative is the same as adding a positive.
- Group like terms before simplifying.
Let me know if you'd like this formatted as a printable worksheet!
Parent Tip: Review the logic above to help your child master the concept of math expressions grade 5 worksheet.
