Let's solve
Activity #2: Translating Algebraic Expressions step by step. We will match each phrase in
Column A with the correct mathematical expression in
Column B.
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🔍 Step-by-Step Matching:
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1. the number x doubled
→ "Doubled" means multiplied by 2.
So, $ 2x $
✔ Match:
n. 2x
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2. The difference of a number x and eight
→ "Difference" means subtraction.
"Of x and 8" → $ x - 8 $
✔ Match:
i. x – 8
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3. The average of two numbers x and y
→ Average = sum divided by 2 → $ \frac{x + y}{2} $
✔ Match:
l. (x+y)/2
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4. the sum of x and three
→ Sum means addition → $ x + 3 $
✔ Match:
c. x + 3
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5. x squared
→ Squared means $ x^2 $
✔ Match:
h. x²
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6. Thrice the sum of x and y
→ "Thrice" = 3 times; "sum of x and y" = $ x + y $ → $ 3(x + y) $
✔ Match:
g. 3(x + y)
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7. one-half the difference of x and y
→ Difference = $ x - y $; half of that = $ \frac{1}{2}(x - y) $ or $ \frac{x - y}{2} $
✔ Match:
o. (x−y)/2
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8. Four more than twice a number x
→ Twice x = $ 2x $; four more = $ 2x + 4 $
✔ Match:
e. 2x + 4
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9. seven more than a number x
→ More than = addition → $ x + 7 $
✔ Match:
b. x + 7
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10. five less than twice a number x
→ Twice x = $ 2x $; five less = $ 2x - 5 $
✔ Match:
a. 2x − 5
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11. multiply 3 by the sum of four and x
→ Sum of 4 and x = $ 4 + x $; multiply by 3 → $ 3(4 + x) $
✔ Match:
k. 3(4 + x)
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12. nine subtracted from x
→ Subtracting 9 from x → $ x - 9 $
✔ Match:
d. x − 9
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13. the product of x and y divided by z
→ Product = $ xy $; divided by z → $ \frac{xy}{z} $
✔ Match:
m. (xy)/z
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14. five times x increased by three times y
→ Five times x = $ 5x $; three times y = $ 3y $; increased by → $ 5x + 3y $
✔ Match:
j. 5x + 3y
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15. the quotient of a number x and 5
→ Quotient = division → $ \frac{x}{5} $
✔ Match:
f. x/5
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✔ Final Answer Key:
| Column A | Match |
|---------|-------|
| 1. the number x doubled |
n |
| 2. The difference of a number x and eight |
i |
| 3. The average of two numbers x and y |
l |
| 4. the sum of x and three |
c |
| 5. x squared |
h |
| 6. Thrice the sum of x and y |
g |
| 7. one-half the difference of x and y |
o |
| 8. Four more than twice a number x |
e |
| 9. seven more than a number x |
b |
| 10. five less than twice a number x |
a |
| 11. multiply 3 by the sum of four and x |
k |
| 12. nine subtracted from x |
d |
| 13. the product of x and y divided by z |
m |
| 14. five times x increased by three times y |
j |
| 15. the quotient of a number x and 5 |
f |
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📝 Summary:
The key to solving these is understanding
mathematical keywords:
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Sum → +
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Difference → −
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Product → ×
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Quotient → ÷
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More than / Increased by → +
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Less than / Subtracted from → −
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Twice / Doubled → ×2
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Thrice → ×3
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Squared → $ x^2 $
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Average → sum ÷ 2
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One-half → $ \frac{1}{2} $
Let me know if you'd like this printed as a completed worksheet!
Parent Tip: Review the logic above to help your child master the concept of translating sentences into equations worksheet.
