Sure! Let’s go through each problem one by one and translate the verbal phrases into algebraic expressions. I’ll explain each step clearly.
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1) One-fourth of the sum of n and 8 minus the product of 6 and b
- “Sum of n and 8” → `n + 8`
- “One-fourth of” that sum → `(1/4)(n + 8)`
- “Minus the product of 6 and b” → `- (6 × b)` or `-6b`
✔ Final expression:
(1/4)(n + 8) - 6b
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2) Add one-fourth to 3 times c
- “3 times c” → `3c`
- “Add one-fourth to” → `+ 1/4`
✔ Final expression:
3c + 1/4
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3) One-sixth of y is added to 4
- “One-sixth of y” → `(1/6)y` or `y/6`
- “Added to 4” → `+ 4`
✔ Final expression:
4 + (1/6)y or
4 + y/6
*(Note: Order doesn’t matter in addition, so both are correct.)*
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4) q cubed minus the product of 7 and d plus 5
- “q cubed” → `q³`
- “Minus the product of 7 and d” → `- (7 × d)` → `-7d`
- “Plus 5” → `+ 5`
⚠️ Be careful: The phrase says “minus the product... plus 5”, so it’s all one expression:
`q³ - 7d + 5`
✔ Final expression:
q³ - 7d + 5
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5) Take away 4 from 8 times n
- “8 times n” → `8n`
- “Take away 4 from” → subtract 4 → `- 4`
✔ Final expression:
8n - 4
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6) Add 7 to 8 times g
- “8 times g” → `8g`
- “Add 7 to” → `+ 7`
✔ Final expression:
8g + 7
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7) Five-sixths of g is added to the product of 6 and k
- “Five-sixths of g” → `(5/6)g`
- “Product of 6 and k” → `6k`
- “Is added to” → combine with `+`
✔ Final expression:
(5/6)g + 6k
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8) The sum of one-sixth of n and one-fifth of g, minus 8
- “One-sixth of n” → `n/6`
- “One-fifth of g” → `g/5`
- “Sum of” → `(n/6 + g/5)`
- “Minus 8” → `- 8`
✔ Final expression:
(n/6 + g/5) - 8
*(Parentheses help show that the sum is done first before subtracting 8.)*
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9) One-half of the sum of 5 and s
- “Sum of 5 and s” → `5 + s`
- “One-half of” → `(1/2)(5 + s)`
✔ Final expression:
(1/2)(5 + s) or
(5 + s)/2
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10) The sum of one-fifth of w, one-fourth of x, and 7
- “One-fifth of w” → `w/5`
- “One-fourth of x” → `x/4`
- “Sum of” → add them all together → `w/5 + x/4 + 7`
✔ Final expression:
w/5 + x/4 + 7
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✔ Final Answers:
1)
(1/4)(n + 8) - 6b
2)
3c + 1/4
3)
4 + y/6
4)
q³ - 7d + 5
5)
8n - 4
6)
8g + 7
7)
(5/6)g + 6k
8)
(n/6 + g/5) - 8
9)
(5 + s)/2
10)
w/5 + x/4 + 7
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Let me know if you’d like these simplified further or written with different notations (like using fractions vs decimals, etc.)!
Parent Tip: Review the logic above to help your child master the concept of writing math expressions worksheet.
