Problem 78 - Beginning and Intermediate Algebra

Question

Perform each indicated operation. $$ (3-7)+4 $$

Step-by-Step Solution

Answer

0

Step 1: Subtract inside the parentheses

First, perform the operation inside the parentheses. Subtract 7 from 3 to get \( 3 - 7 = -4 \)

Step 2: Add the result to the outside number

Now, take the result from step 1 which is -4 and add the 4 outside the parentheses: \( -4 + 4 = 0 \)

Key Concepts

Parentheses in Arithmetic

Parentheses are used in arithmetic to group numbers and operations that should be performed first. When you see parentheses, always complete the operations inside them before doing anything else.
For example, in the problem \[ (3-7)+4 \], look at the part inside the parentheses \((3-7)\).
Follow the steps below to solve the problem correctly:
1. Perform the subtraction inside the parentheses: \( 3 - 7 = -4 \).
2. After solving inside the parentheses, move to the operations outside: \(-4 + 4 = 0 \).
By using parentheses, you ensure the operations are done in the correct order, which leads to the right answer.

Addition and Subtraction

Addition and subtraction are basic arithmetic operations and are used frequently in everyday math.
It's important to understand how to perform these operations step by step.
Examples:

• To add two numbers, count forward (positively) from the first number.
• To subtract, count backward (negatively).

Let's consider our exercise problem:
1. We start with subtraction inside the parentheses. Subtraction \(3 - 7 = -4 \) results in \(-4 \).
2. Then we take the result and add 4. Adding to a negative number means you move towards zero: \(-4 + 4 = 0 \).
This basic understanding will help you handle more complex arithmetic problems.

Order of Operations

The order of operations is a set of rules that tells you the sequence in which to solve different parts of a math problem.
Often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), it helps you organize multiple operations correctly.
Breaking down the process for our problem \( (3-7)+4 \):

• The parentheses tell us to start with \(3 - 7 \).
• Then we do the addition \(((- 4 + 4) = 0 )\) outside the parentheses.

By following the order of operations, you ensure that each part of the problem is tackled in the correct order to get the right result.