This worksheet helps students practice writing algebraic expressions based on twelve different verbal phrases.

To solve the problem, we need to translate each phrase into an algebraic expression. Let's go through each one step by step:

---

1) Fifty-seven subtracted from \( z \)

- "Fifty-seven subtracted from \( z \)" means we start with \( z \) and subtract 57.
- Algebraic expression: \( z - 57 \)

---

2) The total of sixty and a number \( r \)

- "The total of sixty and a number \( r \)" means we add 60 to \( r \).
- Algebraic expression: \( 60 + r \)

---

3) The product of \( x \) and twenty-two

- "The product of \( x \) and twenty-two" means we multiply \( x \) by 22.
- Algebraic expression: \( 22x \)

---

4) The difference between eight and a smaller number \( x \)

- "The difference between eight and a smaller number \( x \)" means we subtract \( x \) from 8.
- Algebraic expression: \( 8 - x \)

---

5) Twenty-eight more than a number \( j \)

- "Twenty-eight more than a number \( j \)" means we add 28 to \( j \).
- Algebraic expression: \( j + 28 \)

---

6) A number \( y \) raised to the power of 8

- "A number \( y \) raised to the power of 8" means we raise \( y \) to the exponent 8.
- Algebraic expression: \( y^8 \)

---

7) The sum of the ratio of \( y \) to 5 and 4

- "The ratio of \( y \) to 5" is \( \frac{y}{5} \).
- "The sum of the ratio of \( y \) to 5 and 4" means we add 4 to \( \frac{y}{5} \).
- Algebraic expression: \( \frac{y}{5} + 4 \)

---

8) One-fourth of the sum of \( x \) and 4

- "The sum of \( x \) and 4" is \( x + 4 \).
- "One-fourth of the sum of \( x \) and 4" means we take \( \frac{1}{4} \) of \( x + 4 \).
- Algebraic expression: \( \frac{1}{4}(x + 4) \)

---

9) Five times the difference between \( x \) and a smaller number 3

- "The difference between \( x \) and a smaller number 3" is \( x - 3 \).
- "Five times the difference between \( x \) and 3" means we multiply \( x - 3 \) by 5.
- Algebraic expression: \( 5(x - 3) \)

---

10) \( p \) reduced by the quotient of 2 divided by 5

- "The quotient of 2 divided by 5" is \( \frac{2}{5} \).
- "\( p \) reduced by the quotient of 2 divided by 5" means we subtract \( \frac{2}{5} \) from \( p \).
- Algebraic expression: \( p - \frac{2}{5} \)

---

11) Two-sixths of a number decreased by 7

- "Two-sixths of a number" means \( \frac{2}{6} \) of the number. Simplifying \( \frac{2}{6} \) gives \( \frac{1}{3} \).
- "Two-sixths of a number decreased by 7" means we subtract 7 from \( \frac{1}{3} \) of the number.
- Algebraic expression: \( \frac{1}{3}x - 7 \)

---

12) One-fourth of \( z \) subtracted from 19

- "One-fourth of \( z \)" is \( \frac{1}{4}z \).
- "One-fourth of \( z \) subtracted from 19" means we subtract \( \frac{1}{4}z \) from 19.
- Algebraic expression: \( 19 - \frac{1}{4}z \)

---

Final Answer

Here are all the algebraic expressions:

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

\[
\boxed{
\begin{aligned}
1. & \ z - 57 \\
2. & \ 60 + r \\
3. & \ 22x \\
4. & \ 8 - x \\
5. & \ j + 28 \\
6. & \ y^8 \\
7. & \ \frac{y}{5} + 4 \\
8. & \ \frac{1}{4}(x + 4) \\
9. & \ 5(x - 3) \\
10. & \ p - \frac{2}{5} \\
11. & \ \frac{1}{3}x - 7 \\
12. & \ 19 - \frac{1}{4}z
\end{aligned}
}
\]