Pre-Algebra Worksheets | Algebraic Expressions Worksheets - Free Printable

Problem: Translate the given verbal descriptions into algebraic expressions.

#### Solution:

1. One-fourth of the sum of \( n \) and 8 minus the product of 6 and \( b \)
- First, find the sum of \( n \) and 8: \( n + 8 \).
- Then, take one-fourth of this sum: \( \frac{1}{4}(n + 8) \).
- Next, find the product of 6 and \( b \): \( 6b \).
- Finally, subtract \( 6b \) from \( \frac{1}{4}(n + 8) \):
\[
\frac{1}{4}(n + 8) - 6b
\]
Answer: \( \frac{1}{4}(n + 8) - 6b \)

2. Add one-fourth to 3 times \( c \)
- First, find 3 times \( c \): \( 3c \).
- Then, add one-fourth (\( \frac{1}{4} \)) to \( 3c \):
\[
3c + \frac{1}{4}
\]
Answer: \( 3c + \frac{1}{4} \)

3. One-sixth of \( y \) is added to 4
- First, find one-sixth of \( y \): \( \frac{1}{6}y \).
- Then, add 4 to \( \frac{1}{6}y \):
\[
4 + \frac{1}{6}y
\]
Answer: \( 4 + \frac{1}{6}y \)

4. \( q \) cubed minus the product of 7 and \( d \) plus 5
- First, find \( q \) cubed: \( q^3 \).
- Next, find the product of 7 and \( d \): \( 7d \).
- Subtract \( 7d \) from \( q^3 \): \( q^3 - 7d \).
- Finally, add 5 to \( q^3 - 7d \):
\[
q^3 - 7d + 5
\]
Answer: \( q^3 - 7d + 5 \)

5. Take away 4 from 8 times \( n \)
- First, find 8 times \( n \): \( 8n \).
- Then, subtract 4 from \( 8n \):
\[
8n - 4
\]
Answer: \( 8n - 4 \)

6. Add 7 to 8 times \( g \)
- First, find 8 times \( g \): \( 8g \).
- Then, add 7 to \( 8g \):
\[
8g + 7
\]
Answer: \( 8g + 7 \)

7. Five-sixths of \( g \) is added to the product of 6 and \( k \)
- First, find five-sixths of \( g \): \( \frac{5}{6}g \).
- Next, find the product of 6 and \( k \): \( 6k \).
- Add \( \frac{5}{6}g \) to \( 6k \):
\[
6k + \frac{5}{6}g
\]
Answer: \( 6k + \frac{5}{6}g \)

8. The sum of one-sixth of \( n \) and one-fifth of \( g \), minus 8
- First, find one-sixth of \( n \): \( \frac{1}{6}n \).
- Next, find one-fifth of \( g \): \( \frac{1}{5}g \).
- Add \( \frac{1}{6}n \) and \( \frac{1}{5}g \): \( \frac{1}{6}n + \frac{1}{5}g \).
- Finally, subtract 8 from this sum:
\[
\frac{1}{6}n + \frac{1}{5}g - 8
\]
Answer: \( \frac{1}{6}n + \frac{1}{5}g - 8 \)

9. One-half of the sum of 5 and \( s \)
- First, find the sum of 5 and \( s \): \( 5 + s \).
- Then, take one-half of this sum:
\[
\frac{1}{2}(5 + s)
\]
Answer: \( \frac{1}{2}(5 + s) \)

10. The sum of one-fifth of \( w \), one-fourth of \( x \), and 7
- First, find one-fifth of \( w \): \( \frac{1}{5}w \).
- Next, find one-fourth of \( x \): \( \frac{1}{4}x \).
- Add \( \frac{1}{5}w \), \( \frac{1}{4}x \), and 7:
\[
\frac{1}{5}w + \frac{1}{4}x + 7
\]
Answer: \( \frac{1}{5}w + \frac{1}{4}x + 7 \)

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \quad \frac{1}{4}(n + 8) - 6b \\
2. & \quad 3c + \frac{1}{4} \\
3. & \quad 4 + \frac{1}{6}y \\
4. & \quad q^3 - 7d + 5 \\
5. & \quad 8n - 4 \\
6. & \quad 8g + 7 \\
7. & \quad 6k + \frac{5}{6}g \\
8. & \quad \frac{1}{6}n + \frac{1}{5}g - 8 \\
9. & \quad \frac{1}{2}(5 + s) \\
10. & \quad \frac{1}{5}w + \frac{1}{4}x + 7
\end{aligned}
}
\]