Sure! Let’s go through each phrase one by one and translate it into an algebraic expression. We’ll use the variable
x to represent “a number” in each case.
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1. a number decreased by ninety-two
→ "Decreased by" means subtraction.
✔ x – 92
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2. the sum of eighty-nine and a number
→ "Sum" means addition.
✔ 89 + x (or
x + 89 — same thing)
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3. a number added to thirty-six
→ "Added to" means 36 + x.
✔ 36 + x
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4. the sum of a number and twenty-six
→ Again, sum = addition.
✔ x + 26
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5. the difference between forty-six and a number
→ "Difference between A and B" usually means A – B. So:
✔ 46 – x
*(Note: Sometimes people interpret this as |46 – x|, but in basic algebra, unless specified, we take the order given: first minus second.)*
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6. the sum of a number and forty-three
→ Addition.
✔ x + 43
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7. the quotient of twenty and a number
→ "Quotient" means division.
✔ 20 ÷ x or
20/x
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8. a number increased by sixty-five
→ "Increased by" means addition.
✔ x + 65
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9. the sum of seventy and a number
→ Addition.
✔ 70 + x
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10. a number increased by eighteen
→ Addition.
✔ x + 18
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11. fifty-five times a number
→ "Times" means multiplication.
✔ 55x
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12. fourteen times a number
→ Multiplication.
✔ 14x
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13. a number increased by sixty-five
→ Same as #8.
✔ x + 65
*(This is repeated — probably a typo in the worksheet.)*
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14. the sum of fifty-two and a number
→ Addition.
✔ 52 + x
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15. seventy-five more than a number
→ "More than" means add to the number.
✔ x + 75
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##
✔ Final Answer Key:
1.
x – 92
2.
89 + x
3.
36 + x
4.
x + 26
5.
46 – x
6.
x + 43
7.
20/x
8.
x + 65
9.
70 + x
10.
x + 18
11.
55x
12.
14x
13.
x + 65 *(duplicate of #8)*
14.
52 + x
15.
x + 75
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## 💡 Tips for Translating Phrases:
-
“Sum” → Add
-
“Difference” → Subtract (watch order!)
-
“Product” or “times” → Multiply
-
“Quotient” → Divide
-
“Increased by” / “more than” → Add
-
“Decreased by” → Subtract
Let me know if you want to practice writing the reverse (from expression to words) or solving equations based on these!
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Parent Tip: Review the logic above to help your child master the concept of translating verbal expressions into algebraic expressions worksheet.
