Question

Compute \(-7(-5)-4(-8-6) \div(-2)\) A. -217 B. 63 C. 31 D. 7

Short answer

7

Step-by-step solution

Identify the Expression Inside the Parentheses

First, simplify the expression inside the parentheses. Start with (-8 - 6) which equals -14.

Simplify Multiplications and Divisions

Next, simplify the multiplications and divisions in the expression. Compute (-4)(-14) divided by -2. (-4)(-14) equals to 56. Now divide 56 by -2, which gives -28.

Evaluate the Remaining Expression

Now address the remaining terms. (-7)(-5) equals 35. Finally, add 35 and -28 together to get 7.

Key concepts

Order of Operations

When solving math problems, the order of operations is crucial. This set of rules guides us on how to simplify expressions correctly. The common acronym used is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's break it down:

• **Parentheses**: Solve anything inside parentheses first.
• **Exponents**: Then, handle the exponents or powers.
• **Multiplication/Division**: Next, perform all multiplications and divisions as they appear from left to right.
• **Addition/Subtraction**: Finally, solve all additions and subtractions from left to right.

For the given problem \(-7(-5)-4(-8-6) \div(-2)\), we follow these steps to solve it accurately and avoid mistakes.

Negative Numbers Multiplication

Multiplying negative numbers can sometimes be confusing. Here’s how it works:

• **Negative times Negative**: When you multiply two negative numbers, the result is positive. For instance, \(-4\times-14=56\).
• **Negative times Positive**: When you multiply a negative number by a positive number, the result is negative. For example, \(-7\times 5 = -35 \).

Knowing these rules helps us simplify complex expressions involving multiplications, especially in the given problem.

Parentheses in Math

Parentheses play a pivotal role in math, indicating which operations to execute first. In expressions like \(-7(-5)-4(-8-6) \div(-2)\), parentheses become essential to follow the correct order of operations. By simplifying inside the parentheses first, we ensure all calculations are accurate.

Parentheses help us by:

• **Grouping Numbers and Operations**: This helps in breaking down complex expressions into simpler parts.
• **Clarifying the Order**: It makes clear which operations to perform first, reducing the risk of errors.
< /ul>Remember to always simplify the innermost parentheses first and work your way outwards while following the established order of operations.