Sure! Let’s solve each problem step by step and write the
algebraic expression (or equation) for each phrase. We’ll use “n” to represent “a number” unless otherwise specified.
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1. A number squared is equal to one-thousand nine-hundred thirty-six.
- “A number squared” → n²
- “is equal to” → =
- “one-thousand nine-hundred thirty-six” → 1936
✔ Algebraic Expression:
n² = 1936
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2. A number decreased by twenty is equal to zero.
- “A number decreased by twenty” → n – 20
- “is equal to zero” → = 0
✔ Algebraic Expression:
n – 20 = 0
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3. The product of a number and eight squared is equal to eighty-eight.
- “Eight squared” → 8² = 64
- “The product of a number and 64” → n × 64 or 64n
- “is equal to eighty-eight” → = 88
✔ Algebraic Expression:
64n = 88
*(Note: Some might misread this as “(number and eight) squared”, but the phrase says “product of a number and eight squared”, meaning multiply the number by (8²).)*
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4. A number cubed is equal to 64.
- “A number cubed” → n³
- “is equal to 64” → = 64
✔ Algebraic Expression:
n³ = 64
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5. The difference of a number and twelve is thirty-six.
- “Difference of a number and twelve” → n – 12 (assuming “number minus twelve”)
- “is thirty-six” → = 36
✔ Algebraic Expression:
n – 12 = 36
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6. Eight more than a number is 22.
- “Eight more than a number” → n + 8
- “is 22” → = 22
✔ Algebraic Expression:
n + 8 = 22
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7. The product of minus twelve and a number is twenty-two.
- “Product of minus twelve and a number” → -12 × n = -12n
- “is twenty-two” → = 22
✔ Algebraic Expression:
-12n = 22
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8. The sum of minus twelve and a number is equal to twenty-two.
- “Sum of minus twelve and a number” → -12 + n or n – 12
- “is equal to twenty-two” → = 22
✔ Algebraic Expression:
n – 12 = 22
*(Same as #5 — but here it’s phrased as “sum”, which still means addition. So -12 + n = 22, which is equivalent to n – 12 = 22.)*
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9. A number plus four times that number is equal to 44.
- “A number” → n
- “plus four times that number” → + 4n
- “is equal to 44” → = 44
So total: n + 4n = 5n
✔ Algebraic Expression:
5n = 44
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10. A number plus that number squared is equal to fifty-six.
- “A number” → n
- “plus that number squared” → + n²
- “is equal to fifty-six” → = 56
✔ Algebraic Expression:
n + n² = 56
*(You could also write it as n² + n = 56 — same thing.)*
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✔ Final Answers:
1.
n² = 1936
2.
n – 20 = 0
3.
64n = 88
4.
n³ = 64
5.
n – 12 = 36
6.
n + 8 = 22
7.
-12n = 22
8.
n – 12 = 22
9.
5n = 44
10.
n² + n = 56
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Let me know if you’d like to solve any of these for “n” too — these are equations, so we can find the actual value of the number in each case!
Good luck with your algebra! 📘➕➖
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions worksheet with answers.
