Sample algebra worksheet featuring eleven problems that ask students to translate written phrases into mathematical expressions and equations.

Let’s go through each problem one by one. We’re turning word phrases into algebraic expressions or equations. Remember:

- “A number” usually means we use a variable like n or x.
- “Minus”, “decreased by”, “difference” → subtraction (–)
- “Plus”, “increased by”, “sum”, “more than” → addition (+)
- “Times”, “product”, “multiplied by” → multiplication (· or just writing numbers/variables next to each other)
- “Divided by”, “quotient” → division (÷ or fraction)
- “Is”, “equals”, “is equal to” → equals sign (=)

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1.) A number minus 18
→ Let the number be n
→ “minus 18” means subtract 18
→ Answer: n – 18

2.) A number decreased by 16
→ “Decreased by” = subtract
→ Answer: n – 16

3.) x plus twelve is twenty one
→ “x plus twelve” = x + 12
→ “is” = equals
→ Answer: x + 12 = 21

4.) x times twelve is forty-six
→ “x times twelve” = x · 12
→ “is” = equals
→ Answer: x · 12 = 46

5.) six increased by twelve
→ “Increased by” = add
→ 6 + 12
→ Answer: 6 + 12

6.) two times eight
→ “Times” = multiply
→ 2 · 8
→ Answer: 2 · 8

7.) six more than twice a number
→ “Twice a number” = 2n
→ “Six more than” = add 6 to that
→ So: 2n + 6
→ Answer: 2n + 6

8.) eight divided by twice a number
→ “Twice a number” = 2n
→ “Eight divided by” that = 8 ÷ (2n) or written as fraction: 8/(2n)
→ But note: sometimes people write it as 8 over 2n, which simplifies to 4/n — but unless told to simplify, we leave it as is.
→ Also, the example shows both forms: 2n + 8 OR 8/(2n) — wait, that doesn’t match! Actually, looking again:
The phrase is “eight divided by twice a number” → so it should be 8 / (2n) or \frac{8}{2n}
But in the image, they wrote “2n + 8 or 8/2n” — that seems wrong for this phrase. Wait — let me double-check.

Actually, re-reading #8: “eight divided by twice a number” → definitely 8 ÷ (2n) → so \frac{8}{2n}

But in the original worksheet answer key shown, it says:
“8.) eight divided by twice a number → 2n + 8 or \frac{8}{2n}”

That first part “2n + 8” is incorrect for this phrase — that would be “twice a number plus eight”. Probably a typo in the worksheet? But since we’re solving correctly, we’ll go with what makes sense.

So correct answer: \frac{8}{2n} or 8/(2n)

But maybe they meant to write only the fraction? Or perhaps it's a mistake. Since the instruction is to solve accurately, I’ll give the correct expression.

Wait — actually, looking at the user’s image again — in row 8, the answer column says:
“2n + 8 or \frac{8}{2n}”

That must be an error in the worksheet. Because “eight divided by twice a number” is NOT “2n + 8”. That’s addition. Division is different.

So for accuracy, we say:
Answer: \frac{8}{2n}

(We can simplify later if needed, but not required here.)

9.) The sum of seven and x
→ “Sum” = addition
→ 7 + x
→ Answer: 7 + x

10.) x times eleven is equal to thirty-three
→ “x times eleven” = x · 11
→ “is equal to” = =
→ Answer: x · 11 = 33

11.) The difference between x and eight is equal to fifteen.
→ “Difference between x and eight” = x – 8 (assuming x is larger; usually we take order as given)
→ “is equal to fifteen” = = 15
→ Answer: x – 8 = 15

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Now, let’s verify all answers match standard translation rules.

All look good except #8 — where the worksheet may have a typo. We’ll provide the mathematically correct version.

Final Answers:

1.) n – 18
2.) n – 16
3.) x + 12 = 21
4.) x · 12 = 46
5.) 6 + 12
6.) 2 · 8
7.) 2n + 6
8.) \frac{8}{2n} *(Note: Worksheet incorrectly includes "2n + 8" — that’s for a different phrase)*
9.) 7 + x
10.) x · 11 = 33
11.) x – 8 = 15

But since the user provided the worksheet with those answers, and we are to solve accurately — we stick to correct math.

However, in many school contexts, they might accept \frac{8}{2n} or even simplified \frac{4}{n}, but unless specified, we leave as \frac{8}{2n}.

Alternatively, if the worksheet intended “eight divided by twice a number” to be written as 8/(2n), then that’s fine.

I think the “2n + 8” in the worksheet is a misprint — probably meant for another problem.

So for our final answer, we list the correct expressions.

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Final Answer:
1.) n - 18
2.) n - 16
3.) x + 12 = 21
4.) x · 12 = 46
5.) 6 + 12
6.) 2 · 8
7.) 2n + 6
8.) \frac{8}{2n}
9.) 7 + x
10.) x · 11 = 33
11.) x - 8 = 15