Problem 59 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. \(-7(3-8)\)

Step-by-Step Solution

Answer

35

Step 1: Simplify Inside the Parentheses

First, calculate the expression inside the parentheses. Subtract 8 from 3 which is -5. So, the expression inside the parentheses becomes \(3 - 8 = -5\).

Step 2: Multiply

Next, multiply \-7\ with \-5\, which is \(-7 \times -5 = 35\).

Key Concepts

Simplifying expressions

In algebra, simplifying expressions means reducing them to their simplest form. This process involves combining like terms, removing parentheses, and performing arithmetic operations. When dealing with complex expressions, always look for opportunities to simplify components of the expression first. This makes the problem easier to solve.
For example, in the original exercise, the expression \( -7(3-8) \) is simplified by first handling the term inside the parentheses, which is \( 3-8 \). After seeing that \( 3-8 = -5 \), we simplify the expression to \(-7 \times -5=35\).
Remember: Simplifying is all about making the math easier for yourself by taking small, manageable steps.

Parentheses

Parentheses are used in algebra to indicate which operations should be performed first. They are crucial for structuring expressions and ensuring calculations are done in the correct order. The order of operations (PEMDAS/BODMAS) dictates that calculations inside parentheses always come before multiplication, division, addition, or subtraction outside the parentheses.
In the sample problem, we have \(3-8\) inside the parentheses. According to the order of operations, we must solve \(3-8\) first before we can move on to any other steps. This helps prevent mistakes and ensures the solution is correct.
Whenever you see parentheses, take them as a cue to deal with the contents inside first before doing anything else.

Multiplication

Multiplication in algebra is a fundamental operation often seen in expressions with parentheses. After simplifying anything inside the parentheses, the next step usually involves multiplying the remaining terms. It's important to know that multiplying negative numbers follows specific rules:

• Negative times a positive = negative
• Negative times a negative = positive
• Positive times a positive = positive

For our exercise, once we simplified inside the parentheses to get \(-5\), we performed the multiplication of \(-7 \times -5\). According to our rules, a negative times a negative equals a positive, hence \( -7 \times -5 = 35 \).
Understanding multiplication rules helps ensure accurate simplifications and solutions in algebra.