Problem 44 - Prealgebra

Question

Add and subtract as indicated. $$8.3-(1.2+3.4)$$

Step-by-Step Solution

Answer

The result is 3.7.

Step 1: Evaluate the Expression in Parentheses

The first step in solving the expression is to handle the operation inside the parentheses. Given is \(1.2 + 3.4\). We add these two numbers together: \(1.2 + 3.4 = 4.6\).

Step 2: Subtract the Result from Outside Number

After calculating the sum inside the parentheses as \(4.6\), the expression now becomes \(8.3 - 4.6\). We need to perform this subtraction to get the final result: \(8.3 - 4.6 = 3.7\).

Key Concepts

Addition

Addition is one of the most basic arithmetic operations where we combine two or more numbers to find their total. It's like putting two piles of objects together to count the total number of objects. In our example, we have the numbers 1.2 and 3.4 inside the parentheses. When adding these, we align the numbers based on their decimal points.

• First, add the decimal parts: 2 + 4 = 6.
• Next, add the whole number parts: 1 + 3 = 4.

Together, it makes 4.6. Remember, each digit in a specific place value must be added to the corresponding digit in the other number. Addition is represented using the plus sign (+), and always results in a larger number than both original numbers unless they are both negative.

Subtraction

Subtraction is a fundamental operation used to find the difference between numbers. When we subtract, we're essentially finding out how much more one number is compared to another. In this exercise, once we calculated the sum as 4.6, it's used in the subtraction step of the equation 8.3 - 4.6.

• Here we line up the numbers, just like in addition.
• Subtract each digit starting from the rightmost decimal part: 3 - 6 requires borrowing, resulting in 7 tenths, leaving us with a total of 3.7.

Subtraction is portrayed by the minus sign (-). The result often gives either a decrease from the original or shows how much more was there. Practicing with different numbers solidifies the understanding of borrowing and lending within subtraction, especially when involving decimal points.

Order of Operations

The order of operations is a set of rules that indicates the sequence in which operations should be performed to accurately solve equations involving more than one operation. The mnemonic 'PEMDAS' helps to remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In our exercise, the expression initially presented is 8.3 - (1.2 + 3.4). According to the order of operations:

• Perform the calculation inside the Parentheses first. This is why we added 1.2 and 3.4 together, resulting in 4.6.
• Then we handle the operation outside the parentheses, the Subtraction of 8.3 minus 4.6, which finally gave us 3.7.

By following these rules, we ensure accuracy in mathematical solving, particularly in more complex calculations involving multiple steps and operations. Understanding and applying the correct order of operations is crucial for ensuring that every calculation is correct.