Write an equivalent expression by distributing the “-” sign outside the parentheses:
9.8n – (9p + 9.9)
The correct answer and explanation is:
To distribute the negative sign outside the parentheses in the expression 9.8n – (9p + 9.9), follow these steps:
- Understand the rule of distribution: When a negative sign is distributed across terms inside parentheses, each term inside the parentheses is multiplied by -1. So, the negative sign effectively changes the sign of each term inside.
- Apply the distribution: Start by distributing the negative sign to both terms inside the parentheses:
- Multiply 9p by -1, which results in -9p.
- Multiply 9.9 by -1, which results in -9.9.
- Combine the result with the remaining terms: Now, rewrite the expression by combining the distributed terms with the term outside the parentheses:
- The expression becomes 9.8n – 9p – 9.9.
Thus, the equivalent expression is 9.8n – 9p – 9.9.
Explanation:
Distributive property helps simplify expressions involving parentheses. In this case, by distributing the negative sign, you change the signs of the terms inside the parentheses. The negative sign before the parentheses acts like a multiplier, turning the positive terms inside the parentheses into negative ones. This technique is useful in algebra when solving equations or simplifying expressions, as it allows you to eliminate parentheses and make the equation more manageable.