To solve the problem, we need to translate each phrase into an algebraic expression. Let's go through each phrase step by step:
1. A number decreased by ninety-two
- Phrase: "decreased by" means subtraction.
- Algebraic expression: \( x - 92 \)
2. The sum of eighty-nine and a number
- Phrase: "sum of" means addition.
- Algebraic expression: \( 89 + x \)
3. A number added to thirty-six
- Phrase: "added to" means addition.
- Algebraic expression: \( x + 36 \)
4. The sum of a number and twenty-six
- Phrase: "sum of" means addition.
- Algebraic expression: \( x + 26 \)
5. The difference between forty-six and a number
- Phrase: "difference between" means subtraction (order matters).
- Algebraic expression: \( 46 - x \)
6. The sum of a number and forty-three
- Phrase: "sum of" means addition.
- Algebraic expression: \( x + 43 \)
7. The quotient of twenty and a number
- Phrase: "quotient of" means division.
- Algebraic expression: \( \frac{20}{x} \)
8. A number increased by sixty-five
- Phrase: "increased by" means addition.
- Algebraic expression: \( x + 65 \)
9. The sum of seventy and a number
- Phrase: "sum of" means addition.
- Algebraic expression: \( 70 + x \)
10. A number increased by eighteen
- Phrase: "increased by" means addition.
- Algebraic expression: \( x + 18 \)
11. Fifty-five times a number
- Phrase: "times" means multiplication.
- Algebraic expression: \( 55x \)
12. Fourteen times a number
- Phrase: "times" means multiplication.
- Algebraic expression: \( 14x \)
13. A number increased by sixty-five
- Phrase: "increased by" means addition.
- Algebraic expression: \( x + 65 \)
14. The sum of fifty-two and a number
- Phrase: "sum of" means addition.
- Algebraic expression: \( 52 + x \)
15. Seventy-five more than a number
- Phrase: "more than" means addition.
- Algebraic expression: \( x + 75 \)
Final Answer:
\[
\boxed{
\begin{aligned}
1. & \quad x - 92 \\
2. & \quad 89 + x \\
3. & \quad x + 36 \\
4. & \quad x + 26 \\
5. & \quad 46 - x \\
6. & \quad x + 43 \\
7. & \quad \frac{20}{x} \\
8. & \quad x + 65 \\
9. & \quad 70 + x \\
10. & \quad x + 18 \\
11. & \quad 55x \\
12. & \quad 14x \\
13. & \quad x + 65 \\
14. & \quad 52 + x \\
15. & \quad x + 75 \\
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of translating phrases into algebraic expressions worksheet.
