Let’s solve each expression step by step. We’ll plug in the given value for the variable and then simplify using order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division left to right, Addition/Subtraction left to right).
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1. c · c ÷ 4 (c = 5)
→ 5 · 5 ÷ 4
→ 25 ÷ 4
→
6.25
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2. u + 4u (u = 6)
→ 6 + 4·6
→ 6 + 24
→
30
*(Note: You could also combine like terms first: u + 4u = 5u → 5·6 = 30)*
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3. 2b – b (b = 9)
→ 2·9 – 9
→ 18 – 9
→
9
*(Or: 2b – b = b → so answer is just 9)*
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4. u ÷ u² (u = 2)
→ 2 ÷ (2²)
→ 2 ÷ 4
→
0.5
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5. 5 + 3 – c (c = 8)
→ 5 + 3 – 8
→ 8 – 8
→
0
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6. z⁴ ÷ z (z = 1)
→ 1⁴ ÷ 1
→ 1 ÷ 1
→
1
*(Also: z⁴ ÷ z = z³ → 1³ = 1)*
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7. 7b ÷ b (b = 2)
→ 7·2 ÷ 2
→ 14 ÷ 2
→
7
*(Or: 7b ÷ b = 7 → always 7 as long as b ≠ 0)*
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8. (10 – 9) · c (c = 10)
→ (1) · 10
→
10
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9. u + 4 + 8 (u = 2)
→ 2 + 4 + 8
→ 6 + 8
→
14
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10. 10 + 2 – x (x = 6)
→ 10 + 2 – 6
→ 12 – 6
→
6
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11. z ÷ (8 – z) (z = 1)
→ 1 ÷ (8 – 1)
→ 1 ÷ 7
→
1/7 or ≈ 0.1429
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12. 6 – x ÷ 6 (x = 7)
→ 6 – (7 ÷ 6)
→ 6 – 1.166...
→
4.833... or 4⅚
*(Remember: division before subtraction!)*
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13. (10 + y) ÷ y (y = 9)
→ (10 + 9) ÷ 9
→ 19 ÷ 9
→
19/9 or ≈ 2.111...
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14. z · z ÷ z (z = 2)
→ 2 · 2 ÷ 2
→ 4 ÷ 2
→
2
*(Or: z·z÷z = z → so answer is 2)*
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15. c(6 – 2) (c = 4)
→ 4 · (4)
→
16
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Final Answer:
1. 6.25
2. 30
3. 9
4. 0.5
5. 0
6. 1
7. 7
8. 10
9. 14
10. 6
11. 1/7
12. 4⅚ (or 29/6)
13. 19/9
14. 2
15. 16
Parent Tip: Review the logic above to help your child master the concept of solving algebraic expressions worksheet.
