Translate word phrases into algebraic expressions and represent real-life situations with variables.

Problem Analysis:

The task involves translating phrases into variable expressions using the variable `N` (capital N) to represent the number. Additionally, there are situational problems that require expressing real-world scenarios as variable expressions.

Solution:

#### Part 1: Translate Phrases into Variable Expressions

1. Four more than half a number
- Half a number is \( \frac{N}{2} \).
- Four more than half a number is \( \frac{N}{2} + 4 \).
- Expression: `N/2+4`

2. Ten less than one half a number
- One half a number is \( \frac{N}{2} \).
- Ten less than one half a number is \( \frac{N}{2} - 10 \).
- Expression: `N/2-10`

3. Three plus the product of a number and 5
- The product of a number and 5 is \( 5N \).
- Three plus the product is \( 5N + 3 \).
- Expression: `5N+3`

4. Four more than three times a number
- Three times a number is \( 3N \).
- Four more than three times a number is \( 3N + 4 \).
- Expression: `3N+4`

5. Eight times the sum of a number and 2
- The sum of a number and 2 is \( N + 2 \).
- Eight times the sum is \( 8(N + 2) \).
- Expression: `8(N+2)`

6. Two less than 4 times a number
- Four times a number is \( 4N \).
- Two less than 4 times a number is \( 4N - 2 \).
- Expression: `4N-2`

7. The quotient of 3 and a number
- The quotient of 3 and a number is \( \frac{3}{N} \).
- Expression: `3/N`

8. The difference between 3 times a number and 6
- Three times a number is \( 3N \).
- The difference between 3 times a number and 6 is \( 3N - 6 \).
- Expression: `3N-6`

9. Nine increased by twice a number
- Twice a number is \( 2N \).
- Nine increased by twice a number is \( 9 + 2N \).
- Expression: `9+2N`

10. Seven times the difference of a number and 5
- The difference of a number and 5 is \( N - 5 \).
- Seven times the difference is \( 7(N - 5) \).
- Expression: `7(N-5)`

#### Part 2: Represent Situations with Variable Expressions

11. You have 20 pieces of candy that you want to evenly distribute to F of your friends. Write an expression to show the number of pieces of candy each friend would get.
- If you distribute 20 pieces of candy evenly among \( F \) friends, each friend gets \( \frac{20}{F} \) pieces.
- Expression: `20/F`

12. Your friend Amy is A years old but you are 3 years older than her. Write an expression that would represent your age.
- If Amy is \( A \) years old and you are 3 years older, your age is \( A + 3 \).
- Expression: `A+3`

13. The length of a rectangle is 5 less than twice the width (w). Write an expression for the length of the rectangle.
- Twice the width is \( 2w \).
- Five less than twice the width is \( 2w - 5 \).
- Expression: `2w-5`

Final Answer:

\[
\boxed{
\begin{array}{ll}
1. & N/2+4 \\
2. & N/2-10 \\
3. & 5N+3 \\
4. & 3N+4 \\
5. & 8(N+2) \\
6. & 4N-2 \\
7. & 3/N \\
8. & 3N-6 \\
9. & 9+2N \\
10. & 7(N-5) \\
11. & 20/F \\
12. & A+3 \\
13. & 2w-5 \\
\end{array}
}
\]