Let’s solve each problem step by step. We’re combining like terms — that means we add or subtract terms that have the same variable (like “n”, “r”, “c”, etc.) or are just numbers (constants).
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1) 8n - n
Think: 8n minus 1n = 7n
→
Answer: 7n
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2) -6 + 8n + 9 - 7n
Group like terms:
- Numbers: -6 + 9 = 3
- n terms: 8n - 7n = 1n → just write as “n”
So: 3 + n
→
Answer: n + 3 (or 3 + n — both are fine)
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3) c + 3c
That’s 1c + 3c = 4c
→
Answer: 4c
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4) 4r - 5r
4r minus 5r = -1r → just write as “-r”
→
Answer: -r
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5) 3p + p
3p + 1p = 4p
→
Answer: 4p
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6) 9r + 3r + 4
Combine r terms: 9r + 3r = 12r
Then add the constant: 12r + 4
→
Answer: 12r + 4
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7) 4z + 9 + 5z - 2
Group z terms: 4z + 5z = 9z
Group numbers: 9 - 2 = 7
→
Answer: 9z + 7
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8) 5 - 4m - 9
Group numbers: 5 - 9 = -4
Keep the m term: -4m
So: -4m - 4
→
Answer: -4m - 4
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9) 7 + 4s + 9
Group numbers: 7 + 9 = 16
Keep s term: 4s
→
Answer: 4s + 16
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10) -7n + 8 + 6 + 2n
Group n terms: -7n + 2n = -5n
Group numbers: 8 + 6 = 14
→
Answer: -5n + 14
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Final Answer:
1) 7n
2) n + 3
3) 4c
4) -r
5) 4p
6) 12r + 4
7) 9z + 7
8) -4m - 4
9) 4s + 16
10) -5n + 14
Parent Tip: Review the logic above to help your child master the concept of simplifying algebraic expressions worksheet.
