Algebraic Equations Worksheets - The Teachers Cafe - Free Printable

Let's solve the problem step by step.

We are given a table with word phrases, and we need to write an algebraic equation for each phrase. We'll use "x" to represent the unknown number in each case.

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Step-by-step translation of each phrase into algebraic expressions:

1. Sixteen more than a number
→ "More than" means addition.
→ $ x + 16 $

2. Two fewer than a number
→ "Fewer than" means subtraction.
→ $ x - 2 $

3. Six times a number
→ Multiplication.
→ $ 6x $

4. Eighteen more than a number
→ Addition.
→ $ x + 18 $

5. Eighteen times a number
→ Multiplication.
→ $ 18x $

6. A number divided in six equal parts
→ Division by 6.
→ $ \frac{x}{6} $

7. A number shared in three equal groups
→ Divided into 3 parts.
→ $ \frac{x}{3} $

8. Sixty-four times a number
→ Multiplication.
→ $ 64x $

9. Four less than a number
→ Subtraction.
→ $ x - 4 $

10. The quotient of a number and ten
→ "Quotient" means division.
→ $ \frac{x}{10} $

11. A number increased by eleven
→ "Increased by" means addition.
→ $ x + 11 $

12. Seven times a number
→ Multiplication.
→ $ 7x $

13. A number shared in six equal groups
→ Divided into 6 parts.
→ $ \frac{x}{6} $

14. Forty-two times a number
→ Multiplication.
→ $ 42x $

15. One fewer than a number
→ Subtract 1.
→ $ x - 1 $

16. The quotient of a number and nine
→ Division by 9.
→ $ \frac{x}{9} $

17. A number decreased by ninety
→ "Decreased by" means subtraction.
→ $ x - 90 $

18. Two hundred more than a number
→ Addition.
→ $ x + 200 $

19. A number decreased by eighty-nine
→ Subtraction.
→ $ x - 89 $

20. Sixty-five more than a number
→ Addition.
→ $ x + 65 $

21. One hundred fewer than a number
→ "Fewer than" means subtract 100.
→ $ x - 100 $

22. The product of three and a number
→ "Product" means multiplication.
→ $ 3x $

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Final Answer Table (Algebraic Expressions):

| Word Phrase | Algebraic Expression |
|-------------|------------------------|
| Sixteen more than a number | $ x + 16 $ |
| Two fewer than a number | $ x - 2 $ |
| Six times a number | $ 6x $ |
| Eighteen more than a number | $ x + 18 $ |
| Eighteen times a number | $ 18x $ |
| A number divided in six equal parts | $ \frac{x}{6} $ |
| A number shared in three equal groups | $ \frac{x}{3} $ |
| Sixty-four times a number | $ 64x $ |
| Four less than a number | $ x - 4 $ |
| The quotient of a number and ten | $ \frac{x}{10} $ |
| A number increased by eleven | $ x + 11 $ |
| Seven times a number | $ 7x $ |
| A number shared in six equal groups | $ \frac{x}{6} $ |
| Forty-two times a number | $ 42x $ |
| One fewer than a number | $ x - 1 $ |
| The quotient of a number and nine | $ \frac{x}{9} $ |
| A number decreased by ninety | $ x - 90 $ |
| Two hundred more than a number | $ x + 200 $ |
| A number decreased by eighty-nine | $ x - 89 $ |
| Sixty-five more than a number | $ x + 65 $ |
| One hundred fewer than a number | $ x - 100 $ |
| The product of three and a number | $ 3x $ |

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✔ Explanation Summary:
- "More than", "increased by", "sum" → Use addition.
- "Fewer than", "decreased by", "less than" → Use subtraction.
- "Times", "product" → Use multiplication.
- "Divided", "quotient", "shared in equal parts" → Use division.

This is how we translate verbal math expressions into algebraic ones!