Let's solve each problem step by step by translating the verbal phrases into
algebraic expressions using variables.
---
1. Eleven decreased by k
- "Decreased by" means subtraction.
- So, 11 minus k.
-
✔ Answer: $ 11 - k $
---
2. p increased by 9
- "Increased by" means addition.
- So, p plus 9.
-
✔ Answer: $ p + 9 $
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3. Sixteen multiplied by a number h
- "Multiplied by" means multiplication.
- So, 16 times h.
-
✔ Answer: $ 16h $
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4. 1 less than twelve
- "Less than" reverses the order: 12 minus 1.
-
✔ Answer: $ 12 - 1 $ or simply
$ 11 $, but since it says "write an expression", we keep it as $ 12 - 1 $
> Note: If they want variable-based, but here no variable is mentioned — just numbers. So, $ 12 - 1 $ is correct.
✔ Answer: $ 12 - 1 $
---
5. Sixteen less than m
- "Less than" means subtract from m.
- So, m minus 16.
-
✔ Answer: $ m - 16 $
---
6. 8 divided by e
- Division: 8 ÷ e
-
✔ Answer: $ \frac{8}{e} $
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7. The product of 6 and c
- "Product" means multiplication.
- So, 6 × c
-
✔ Answer: $ 6c $
---
8. Eighty-five less than x
- "Less than" means subtract 85 from x.
-
✔ Answer: $ x - 85 $
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9. Two more than m
- "More than" means add 2 to m.
-
✔ Answer: $ m + 2 $
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10. Three-fourths of f
- "Of" means multiplication.
- So, $ \frac{3}{4} \times f $
-
✔ Answer: $ \frac{3}{4}f $
---
11. y diminished by 9
- "Diminished by" means subtracted by.
- So, y minus 9.
-
✔ Answer: $ y - 9 $
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12. The sum of 5 and k
- "Sum" means addition.
- So, 5 + k
-
✔ Answer: $ 5 + k $
---
13. g less than 8
- "Less than" reverses order: 8 minus g.
-
✔ Answer: $ 8 - g $
---
14. The quotient of b and 3
- "Quotient" means division.
- So, b divided by 3.
-
✔ Answer: $ \frac{b}{3} $
---
15. Thrice a number p
- "Thrice" means three times.
- So, 3 × p
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✔ Answer: $ 3p $
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✔ Final Answers:
| # | Expression |
|---|------------|
| 1 | $ 11 - k $ |
| 2 | $ p + 9 $ |
| 3 | $ 16h $ |
| 4 | $ 12 - 1 $ |
| 5 | $ m - 16 $ |
| 6 | $ \frac{8}{e} $ |
| 7 | $ 6c $ |
| 8 | $ x - 85 $ |
| 9 | $ m + 2 $ |
|10 | $ \frac{3}{4}f $ |
|11 | $ y - 9 $ |
|12 | $ 5 + k $ |
|13 | $ 8 - g $ |
|14 | $ \frac{b}{3} $ |
|15 | $ 3p $ |
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🔍 Tips for Translating Words to Algebra:
-
Sum, increased by, more than → Addition (+)
-
Difference, decreased by, less than, diminished by → Subtraction (−)
⚠️ *Note: “less than” reverses order.*
-
Product, times, multiplied by → Multiplication (×)
-
Quotient, divided by → Division (÷)
-
Of → Multiplication
-
Twice, thrice, double, triple → Multiply by 2, 3, etc.
Let me know if you'd like this printed out or formatted for a worksheet!
Parent Tip: Review the logic above to help your child master the concept of fifth grade algebra worksheet.
