Basic Algebra Worksheets - Free Printable

Let's solve each of the algebraic expressions step by step, following the instructions in the worksheet. We'll translate each verbal phrase into an algebraic expression.

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1) a divided by 6

→ $ \frac{a}{6} $ or $ \frac{1}{6}a $

✔ Already given: $ \frac{a}{6} $

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2) halve b and add 5

"halve b" = $ \frac{b}{2} $, then add 5
→ $ \frac{b}{2} + 5 $

✔ $ \frac{b}{2} + 5 $

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3) multiply c by 3 and subtract 7

Multiply c by 3 → $ 3c $, then subtract 7
→ $ 3c - 7 $

✔ $ 3c - 7 $

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4) subtract d from 12

"subtract d from 12" means $ 12 - d $

✔ $ 12 - d $

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5) subtract 12 from e

"subtract 12 from e" means $ e - 12 $

✔ $ e - 12 $

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6) divide f by 4 and add 7

$ \frac{f}{4} + 7 $

✔ $ \frac{f}{4} + 7 $

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7) add 2 to g and then double

Add 2 to g → $ g + 2 $, then double it → $ 2(g + 2) $

✔ $ 2(g + 2) $

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8) add 5 to h and then halve

Add 5 → $ h + 5 $, then halve → $ \frac{h + 5}{2} $

✔ $ \frac{h + 5}{2} $

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9) subtract 4 from i and then multiply by 5

Subtract 4 → $ i - 4 $, then multiply by 5 → $ 5(i - 4) $

✔ $ 5(i - 4) $

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10) add 6 to j and then divide by 3

Add 6 → $ j + 6 $, then divide by 3 → $ \frac{j + 6}{3} $

✔ $ \frac{j + 6}{3} $

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11) multiply k by 2 and then subtract 7

$ 2k - 7 $

✔ $ 2k - 7 $

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12) subtract 7 from l and then divide by 2

$ l - 7 $, then divide by 2 → $ \frac{l - 7}{2} $

✔ $ \frac{l - 7}{2} $

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13) divide m by 3 and then add 10

$ \frac{m}{3} + 10 $

✔ $ \frac{m}{3} + 10 $

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14) add 10 to n and then divide by 4

$ n + 10 $, then divide by 4 → $ \frac{n + 10}{4} $

✔ $ \frac{n + 10}{4} $

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15) add 5 to o and then halve it

$ o + 5 $, then halve → $ \frac{o + 5}{2} $

✔ $ \frac{o + 5}{2} $

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16) multiply p by itself

That means $ p \times p = p^2 $

✔ $ p^2 $

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17) divide q by 5 then add 6

$ \frac{q}{5} + 6 $

✔ $ \frac{q}{5} + 6 $

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18) add 6 to r then divide by 5

$ r + 6 $, then divide by 5 → $ \frac{r + 6}{5} $

✔ $ \frac{r + 6}{5} $

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19) add 1 to s then multiply it by 6

$ s + 1 $, then multiply by 6 → $ 6(s + 1) $

✔ $ 6(s + 1) $

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20) subtract t from 6 then divide it by 4

"subtract t from 6" → $ 6 - t $, then divide by 4 → $ \frac{6 - t}{4} $

✔ $ \frac{6 - t}{4} $

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21) multiply u by itself and subtract 6

$ u \times u = u^2 $, then subtract 6 → $ u^2 - 6 $

✔ $ u^2 - 6 $

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22) add 1 to v and square the answer

Add 1 → $ v + 1 $, then square → $ (v + 1)^2 $

✔ $ (v + 1)^2 $

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23) subtract 2 from w then divide by 7

$ w - 2 $, then divide by 7 → $ \frac{w - 2}{7} $

✔ $ \frac{w - 2}{7} $

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24) add 4 to x and divide 5 by the answer

Add 4 to x → $ x + 4 $, then divide 5 by that → $ \frac{5}{x + 4} $

✔ $ \frac{5}{x + 4} $

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✔ Final Answer Table:

| # | Expression | Algebraic Form |
|---|------------|----------------|
| 1 | a divided by 6 | $ \frac{a}{6} $ |
| 2 | halve b and add 5 | $ \frac{b}{2} + 5 $ |
| 3 | multiply c by 3 and subtract 7 | $ 3c - 7 $ |
| 4 | subtract d from 12 | $ 12 - d $ |
| 5 | subtract 12 from e | $ e - 12 $ |
| 6 | divide f by 4 and add 7 | $ \frac{f}{4} + 7 $ |
| 7 | add 2 to g and then double | $ 2(g + 2) $ |
| 8 | add 5 to h and then halve | $ \frac{h + 5}{2} $ |
| 9 | subtract 4 from i and then multiply by 5 | $ 5(i - 4) $ |
|10 | add 6 to j and then divide by 3 | $ \frac{j + 6}{3} $ |
|11 | multiply k by 2 and then subtract 7 | $ 2k - 7 $ |
|12 | subtract 7 from l and then divide by 2 | $ \frac{l - 7}{2} $ |
|13 | divide m by 3 and then add 10 | $ \frac{m}{3} + 10 $ |
|14 | add 10 to n and then divide by 4 | $ \frac{n + 10}{4} $ |
|15 | add 5 to o and then halve it | $ \frac{o + 5}{2} $ |
|16 | multiply p by itself | $ p^2 $ |
|17 | divide q by 5 then add 6 | $ \frac{q}{5} + 6 $ |
|18 | add 6 to r then divide by 5 | $ \frac{r + 6}{5} $ |
|19 | add 1 to s then multiply it by 6 | $ 6(s + 1) $ |
|20 | subtract t from 6 then divide it by 4 | $ \frac{6 - t}{4} $ |
|21 | multiply u by itself and subtract 6 | $ u^2 - 6 $ |
|22 | add 1 to v and square the answer | $ (v + 1)^2 $ |
|23 | subtract 2 from w then divide by 7 | $ \frac{w - 2}{7} $ |
|24 | add 4 to x and divide 5 by the answer | $ \frac{5}{x + 4} $ |

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🔍 Key Tips:

- Order matters: "subtract d from 12" is $ 12 - d $, not $ d - 12 $
- "Then" indicates sequence: Do one operation first, then the next.
- "Double" or "halve" means multiply/divide by 2.
- "Multiply by itself" means squaring: $ x^2 $
- "Square the answer" means apply exponent after parentheses.

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