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Here are the translations for each phrase into mathematical expressions or sentences using variables:

1. **The sum of a number and 10**  
   Expression: \( x + 10 \)

2. **The product of two numbers**  
   Expression: \( x \times y \) or \( xy \)

3. **The product of -1 and a number**  
   Expression: \( -1 \times x \) or \( -x \)

4. **One-half times the sum of two numbers**  
   Expression: \( \frac{1}{2} \times (x + y) \) or \( \frac{1}{2}(x + y) \)

5. **Twice a number**  
   Expression: \( 2x \)

6. **Five less than a number**  
   Expression: \( x - 5 \)

7. **A number, less 8**  
   Expression: \( x - 8 \)

8. **Six more than a number**  
   Expression: \( x + 6 \)

9. **A number, plus 6**  
   Expression: \( x + 6 \)

10. **The square of a number**  
    Expression: \( x^2 \)

11. **Four times the square of a number**  
    Expression: \( 4x^2 \)

12. **One-half of a number is 5**  
    Expression: \( \frac{1}{2}x = 5 \)

13. **Three less than twice a number**  
    Expression: \( 2x - 3 \)

14. **Five more than three times a number**  
    Expression: \( 3x + 5 \)

15. **The square of the sum of 5 and a number**  
    Expression: \( (5 + x)^2 \)

16. **The sum of the squares of two numbers is 25**  
    Expression: \( x^2 + y^2 = 25 \)

17. **There are twice as many boys (b) as there are girls (g)**  
    Expression: \( b = 2g \)

18. **There are 10 more cars (c) than jeeps (j)**  
    Expression: \( c = j + 10 \)

19. **A man’s age (a) 10 years ago is 43**  
    Expression: \( a - 10 = 43 \)

20. **The length (l) of a rectangle is 7 more than its width (w)**  
    Expression: \( l = w + 7 \)

Would you like more detailed explanations or clarifications on any of these? 

Here are 5 related questions to expand your understanding:

1. How would you express "5 less than twice a number"?
2. What is the mathematical expression for "the product of a number and its square"?
3. How can you translate "three times the difference between a number and 4"?
4. How do you form an equation if "a number decreased by 12 equals 20"?
5. How would you represent "the sum of a number and its reciprocal"?

**Tip**: When translating word problems into algebraic expressions, identify keywords like "sum," "product," "less than," and "more than" to determine the appropriate operation.

Translate the following phrases into mathematical expressions/sentences. Use as few variables as possible.

This exercise translates word phrases into algebraic expressions and sentences, covering basic algebraic operations like addition, subtraction, multiplication, and squaring numbers. Suitable for middle school students in grades 6-8.

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