Let's go through each problem step by step and write the correct algebraic expression for each phrase. I'll explain the reasoning behind each one.
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Part 1: Write the phrase as an expression
1.
12 more than x
→ "More than" means addition. So, we add 12 to x.
✔ x + 12
2.
x less than 36
→ "Less than" means subtraction, but be careful: it's *x less than 36*, so we subtract x from 36.
✔ 36 - x
3.
One-third of a
→ "Of" means multiplication. One-third times a.
✔ (1/3)a or
a/3
4.
17 times s
→ "Times" means multiplication.
✔ 17s
5.
b multiplied by 5
→ Multiplication: b × 5
✔ 5b (or 5 × b)
6.
y to the fourth power
→ Exponentiation: y raised to the 4th power
✔ y⁴
7.
64 plus k
→ Addition: 64 + k
✔ 64 + k
8.
u tripled
→ Tripled means multiplied by 3
✔ 3u
9.
p cubed
→ Cubed means raised to the 3rd power
✔ p³
10.
18 minus x
→ Subtraction: 18 - x
✔ 18 - x
11.
4 less than k
→ "Less than" reverses order: k - 4
✔ k - 4
12.
z increased by 12
→ "Increased by" means addition
✔ z + 12
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Part 2: Write an expression to answer each question
13.
What is the product of 82 and g?
→ Product means multiplication
✔ 82g
14.
What is the difference between n and 7?
→ Difference means subtraction. Order matters: n - 7
✔ n - 7
15.
What is the quotient of 32 and x?
→ Quotient means division: 32 ÷ x
✔ 32/x
16.
What is the sum of h and 7?
→ Sum means addition
✔ h + 7
17.
What is 31 less than c?
→ "Less than" reverses order: c - 31
✔ c - 31
18.
What is the fifth power of t?
→ Raised to the 5th power
✔ t⁵
19.
What is one-eighth of r?
→ "Of" means multiplication: (1/8) × r
✔ (1/8)r or
r/8
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✔ Final Answers:
1. x + 12
2. 36 - x
3. (1/3)a or a/3
4. 17s
5. 5b
6. y⁴
7. 64 + k
8. 3u
9. p³
10. 18 - x
11. k - 4
12. z + 12
13. 82g
14. n - 7
15. 32/x
16. h + 7
17. c - 31
18. t⁵
19. (1/8)r or r/8
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📝 Tips:
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"More than", "plus", "increased by" → Addition
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"Less than", "minus", "decreased by" → Subtraction (watch order!)
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"Times", "product", "multiplied by" → Multiplication
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"Quotient", "divided by" → Division
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"To the power of", "squared", "cubed" → Exponents
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"Of" often means multiplication (especially with fractions)
Let me know if you'd like this in a printable format!
Parent Tip: Review the logic above to help your child master the concept of writing math expressions worksheet.
