Let's solve each phrase by translating it into an
algebraic expression. We'll use
"x" to represent "a number" since the problem doesn't specify a particular variable.
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1. a number decreased by ninety-two
→ Subtract 92 from the number
✔ x - 92
---
2. the sum of eighty-nine and a number
→ Add 89 and the number
✔ 89 + x or
x + 89
---
3. a number added to thirty-six
→ Add the number to 36
✔ 36 + x or
x + 36
---
4. the sum of a number and twenty-six
→ Add the number and 26
✔ x + 26
---
5. the difference between forty-six and a number
→ Subtract the number from 46 (order matters: "difference between A and B" is A - B)
✔ 46 - x
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6. the sum of a number and forty-three
→ Add the number and 43
✔ x + 43
---
7. the quotient of twenty and a number
→ Divide 20 by the number
✔ 20 ÷ x or
20/x
---
8. a number increased by sixty-five
→ Add 65 to the number
✔ x + 65
---
9. the sum of seventy and a number
→ Add 70 and the number
✔ 70 + x or
x + 70
---
10. a number increased by eighteen
→ Add 18 to the number
✔ x + 18
---
11. fifty-five times a number
→ Multiply 55 by the number
✔ 55x
---
12. fourteen times a number
→ Multiply 14 by the number
✔ 14x
---
13. a number increased by sixty-five
→ Same as #8
✔ x + 65
---
14. the sum of fifty-two and a number
→ Add 52 and the number
✔ 52 + x or
x + 52
---
15. seventy-five more than a number
→ Add 75 to the number
✔ x + 75
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✔ Final Answers:
| Phrase | Algebraic Expression |
|-------|------------------------|
| a number decreased by ninety-two |
x - 92 |
| the sum of eighty-nine and a number |
89 + x |
| a number added to thirty-six |
36 + x |
| the sum of a number and twenty-six |
x + 26 |
| the difference between forty-six and a number |
46 - x |
| the sum of a number and forty-three |
x + 43 |
| the quotient of twenty and a number |
20/x |
| a number increased by sixty-five |
x + 65 |
| the sum of seventy and a number |
70 + x |
| a number increased by eighteen |
x + 18 |
| fifty-five times a number |
55x |
| fourteen times a number |
14x |
| a number increased by sixty-five |
x + 65 |
| the sum of fifty-two and a number |
52 + x |
| seventy-five more than a number |
x + 75 |
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🔍 Key Tips for Translating Phrases:
-
"Sum",
"increased by",
"more than" → Addition (+)
-
"Decreased by",
"difference between" → Subtraction (−)
-
"Times",
"product of" → Multiplication (×)
-
"Quotient of",
"divided by" → Division (÷)
- Always pay attention to
order: "difference between A and B" means
A - B, not B - A.
Let me know if you'd like this turned into a printable worksheet or need help with word problems!
Parent Tip: Review the logic above to help your child master the concept of translating equations worksheet.
