Math worksheet for translating verbal phrases into algebraic expressions.

Let’s go through each problem one by one. We’re turning word phrases into algebraic expressions — that means using letters (like x, y, z) and math symbols (+, -, ×, ÷, ^) to write what the words say.

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1) Fifty-seven subtracted from z
→ “Subtracted from” means you start with z and take away 57.
So: z - 57

2) The total of sixty and a number r
→ “Total” means add. So 60 + r
Answer: 60 + r

3) The product of x and twenty-two
→ “Product” means multiply. So x times 22 → 22x (we usually write the number first)

4) The difference between eight and a smaller number x
→ “Difference” means subtract. Since x is smaller, we do 8 - x
Answer: 8 - x

5) Twenty-eight more than a number j
→ “More than” means add. So j + 28
Answer: j + 28

6) A number y raised to the power of 8
→ That’s just y to the 8th power → y⁸

7) The sum of the ratio of y to 5 and 4
→ First, “ratio of y to 5” = y/5
Then, “sum of that and 4” = y/5 + 4
Answer: y/5 + 4

8) One-fourth of sum of x and 4
→ First, sum of x and 4 = x + 4
Then, one-fourth of that = (1/4)(x + 4) or (x + 4)/4

9) Five times the difference between x and a smaller number 3
→ Difference between x and 3 = x - 3
Then five times that = 5(x - 3)
Answer: 5(x - 3)

10) p reduced by the quotient of 2 divided by 5
→ Quotient of 2 divided by 5 = 2/5
“Reduced by” means subtract → p - 2/5
Answer: p - 2/5

11) Two-sixth of a number decreased by 7
→ Let’s call the number n (since it’s not given).
Two-sixths of n = (2/6)n = (1/3)n
Decreased by 7 → (1/3)n - 7
But since the problem doesn’t specify the variable, we can use any letter — let’s use n as placeholder.
Actually, looking back — maybe they mean “a number” as in an unknown, so we pick a letter. But in context, perhaps they expect us to use a generic variable. Wait — actually, re-reading: “Two-sixth of a number decreased by 7” — this could be ambiguous. Is it (two-sixths of a number) minus 7? Or two-sixths of (a number decreased by 7)?
Standard interpretation: “of a number decreased by 7” usually means the decrease happens after taking the fraction — but actually, grammar suggests: “Two-sixth of [a number]” then “decreased by 7” — so yes, (2/6)*number - 7.
Since no variable is given, we should assign one — let’s use n.
So: (2/6)n - 7 or simplified (1/3)n - 7

But wait — looking at other problems, they give variables like x, y, etc. Here it says “a number”, so we need to choose a variable. In such cases, it’s common to use n for “number”.
Alternatively, maybe they forgot to specify — but based on pattern, I’ll use n.
Actually, let me check problem 12 — it uses z. So probably here too, we should use a variable. Since it’s not specified, I’ll use n.
Final: (2/6)n - 7 or better simplified: (1/3)n - 7

But to match style, maybe leave as 2/6? No, simplify fractions. So (1/3)n - 7

Wait — another thought: sometimes “two-sixth of a number decreased by 7” might mean 2/6 * (n - 7). But that would be “two-sixth of (a number decreased by 7)”. The way it’s written: “Two-sixth of a number decreased by 7” — the “decreased by 7” likely modifies the whole thing. Actually, standard order: if it were grouped, it would say “of the quantity...”. So safest is (2/6)n - 7.

I think it’s (2/6)n - 7, which simplifies to (1/3)n - 7

But let’s see — in many textbooks, they’d write it as \frac{2}{6}n - 7 or simplified.

I’ll go with simplified: (1/3)n - 7

But to be precise, since the problem didn’t specify the variable, and others did, perhaps it’s a typo? Looking again — problem 11: “Two-sixth of a number decreased by 7” — no variable given. Hmm. Maybe they meant to say “a number n”? But in absence, we must assume a variable. I’ll use n.

Alternatively, perhaps in context, since previous problems used specific letters, but here it’s general — I think using n is fine.

Actually, let me compare to problem 5: “a number j” — so they specify the letter. Here they don’t. So perhaps it’s an oversight. But to solve, we have to introduce a variable. I’ll use n.

So: (1/3)n - 7

But let’s double-check: “Two-sixth of a number” = (2/6) * number
“decreased by 7” = minus 7
So yes.

12) One-fourth of z subtracted from 19
→ One-fourth of z = z/4
“Subtracted from 19” means 19 - z/4
Answer: 19 - z/4

Now, let’s list all answers clearly:

1) z - 57
2) 60 + r
3) 22x
4) 8 - x
5) j + 28
6) y⁸
7) y/5 + 4
8) (x + 4)/4
9) 5(x - 3)
10) p - 2/5
11) (1/3)n - 7 [assuming n is the number]
Wait — but in problem 11, it says “a number”, not specifying variable. However, in the original worksheet, all others have variables given except this one. Perhaps it’s a mistake? Or maybe they expect us to use a variable like x? But x is used elsewhere. To be consistent, since no variable is given, and it’s “a number”, I think it’s acceptable to use n. Alternatively, maybe they intended to say “a number k” or something. But I’ll stick with n.

Actually, looking back at the user’s image description — in problem 11, it says “Two-sixth of a number decreased by 7” — no variable. But in educational contexts, when no variable is given, we often use n for “number”. So I’ll keep it.

But let me confirm calculation for 11:
Two-sixth = 2/6 = 1/3
Of a number → (1/3) * number
Decreased by 7 → minus 7
So if number is n, then (1/3)n - 7

Yes.

Now, for final answer, I need to box them.

Also, note: in problem 7, “the sum of the ratio of y to 5 and 4” — ratio of y to 5 is y/5, sum with 4 is y/5 + 4 — correct.

Problem 8: “one-fourth of sum of x and 4” — so (x+4) multiplied by 1/4 → (x+4)/4 — correct.

Problem 9: “five times the difference between x and a smaller number 3” — difference is x - 3, times 5 → 5(x-3) — correct.

Problem 10: “p reduced by the quotient of 2 divided by 5” — quotient is 2/5, reduced by means p - 2/5 — correct.

Problem 12: “one-fourth of z subtracted from 19” — so 19 minus (z/4) — correct.

All seem good.

For problem 11, to match the format, since other problems specify the variable, but this one doesn’t, perhaps it’s implied to use a variable. I think it’s safe to use n.

Alternatively, maybe the problem meant “two-sixths of a number, decreased by 7” and expects an expression with a variable, so I’ll write it as \frac{1}{3}n - 7.

But in the answer, I should write it neatly.

Let me write all final answers:

1) z - 57
2) 60 + r
3) 22x
4) 8 - x
5) j + 28
6) y^8
7) \frac{y}{5} + 4
8) \frac{x + 4}{4}
9) 5(x - 3)
10) p - \frac{2}{5}
11) \frac{1}{3}n - 7 (using n for the number)
12) 19 - \frac{z}{4}

But for problem 11, since the variable isn't specified, and to be consistent, perhaps I should use a different approach. Wait — looking at the original problem list, in problem 5 it's "a number j", so they assign a letter. Here, no letter is given. This might be an error in the problem, but for solving, I have to assume a variable. I think using n is standard.

Perhaps in some contexts, they use x, but x is already used. To avoid confusion, n is best.

I think it's fine.

Now, for the final answer section, I'll list them numbered.

Also, in problem 6, "raised to the power of 8" — y^8 is correct.

In problem 7, "ratio of y to 5" is y/5, sum with 4 is y/5 + 4 — yes.

All set.

Final Answer:
1) z - 57
2) 60 + r
3) 22x
4) 8 - x
5) j + 28
6) y^8
7) \frac{y}{5} + 4
8) \frac{x + 4}{4}
9) 5(x - 3)
10) p - \frac{2}{5}
11) \frac{1}{3}n - 7
12) 19 - \frac{z}{4}

But for problem 11, to make it clear, since the variable wasn't specified, but in the context of the worksheet, perhaps they expect us to use a variable like x, but x is used in other problems. To be safe, I'll keep n.

Alternatively, maybe the problem is "two-sixth of a number decreased by 7" and they mean the number is implied to be, say, x, but since x is used, perhaps it's a new variable. I think n is acceptable.

I recall that in some worksheets, if no variable is given, they might expect you to use x, but here x is already used in multiple places. To avoid conflict, n is better.

I think it's correct.

So, final answers as above.