Pre-Algebra Worksheets | Algebraic Expressions Worksheets - Free Printable

Let's solve each of these algebraic expression translation problems step by step. We'll convert each verbal phrase into a correct algebraic expression.

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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 → $ \frac{1}{4}(n + 8) $
- "Product of 6 and b" → $ 6b $
- "Minus" means subtract:
→ $ \frac{1}{4}(n + 8) - 6b $

✔ Answer: $ \frac{1}{4}(n + 8) - 6b $

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2) Add one-fourth to 3 times c

- "3 times c" → $ 3c $
- "Add one-fourth" → $ 3c + \frac{1}{4} $

✔ Answer: $ 3c + \frac{1}{4} $

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3) One-sixth of y is added to 4

- "One-sixth of y" → $ \frac{1}{6}y $
- "Added to 4" → $ 4 + \frac{1}{6}y $

✔ Answer: $ 4 + \frac{1}{6}y $

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4) q cubed minus the product of 7 and d plus 5

- "q cubed" → $ q^3 $
- "Product of 7 and d" → $ 7d $
- "Minus" → $ q^3 - 7d $
- "Plus 5" → $ q^3 - 7d + 5 $

✔ Answer: $ q^3 - 7d + 5 $

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5) Take away 4 from 8 times n

- "8 times n" → $ 8n $
- "Take away 4" → $ 8n - 4 $

✔ Answer: $ 8n - 4 $

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6) Add 7 to 8 times g

- "8 times g" → $ 8g $
- "Add 7" → $ 8g + 7 $

✔ Answer: $ 8g + 7 $

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7) Five-sixths of g is added to the product of 6 and k

- "Five-sixths of g" → $ \frac{5}{6}g $
- "Product of 6 and k" → $ 6k $
- "Added to" → $ \frac{5}{6}g + 6k $

✔ Answer: $ \frac{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" → $ \frac{1}{6}n $
- "One-fifth of g" → $ \frac{1}{5}g $
- "Sum of" → $ \frac{1}{6}n + \frac{1}{5}g $
- "Minus 8" → $ \frac{1}{6}n + \frac{1}{5}g - 8 $

✔ Answer: $ \frac{1}{6}n + \frac{1}{5}g - 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" → $ \frac{1}{2}(5 + s) $

✔ Answer: $ \frac{1}{2}(5 + s) $

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10) The sum of one-fifth of w, one-fourth of x, and 7

- "One-fifth of w" → $ \frac{1}{5}w $
- "One-fourth of x" → $ \frac{1}{4}x $
- "Sum of" all three → $ \frac{1}{5}w + \frac{1}{4}x + 7 $

✔ Answer: $ \frac{1}{5}w + \frac{1}{4}x + 7 $

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✔ Final Answers:

1) $ \frac{1}{4}(n + 8) - 6b $
2) $ 3c + \frac{1}{4} $
3) $ 4 + \frac{1}{6}y $
4) $ q^3 - 7d + 5 $
5) $ 8n - 4 $
6) $ 8g + 7 $
7) $ \frac{5}{6}g + 6k $
8) $ \frac{1}{6}n + \frac{1}{5}g - 8 $
9) $ \frac{1}{2}(5 + s) $
10) $ \frac{1}{5}w + \frac{1}{4}x + 7 $

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