Problem 45 - Prealgebra

Question

Add and subtract as indicated. $$(9.7-5.2)-1.4$$

Step-by-Step Solution

Answer

The result is 3.1.

Step 1: Inner Subtraction

First, subtract the inner numbers in the parentheses. Calculate \(9.7 - 5.2\), which equals \(4.5\).

Step 2: Outer Subtraction

Use the result from Step 1 to perform the outer subtraction. Subtract \(1.4\) from \(4.5\), giving you \(3.1\).

Key Concepts

Arithmetic Operations

Arithmetic operations are fundamental mathematical processes that allow us to perform calculations. These include addition, subtraction, multiplication, and division. Understanding how to carry out these operations is crucial for solving both simple and complex math problems.

In the given exercise, we focus on subtraction, which is one of the key arithmetic operations. Subtraction involves taking one number away from another to find the difference between them. For example, if you have a group of 9 apples and you give away 5, you’re left with 4. This simple process of finding what's left is subtraction in action.

Besides subtraction, it's important to recognize that all arithmetic operations have their properties and rules:

• Addition combines numbers to get a sum.
• Multiplication is repeated addition.
• Division is splitting a number into equal parts.

By understanding these operations, you gain the ability to approach problems from various angles, allowing for more effective solutions.

Order of Operations

The order of operations is a fundamental concept that organizes the way in which different arithmetic operations are performed in a mathematical expression. It's crucial to follow these rules accurately to obtain the correct results. The typical order is: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). An easy way to recall this sequence is through the acronym PEMDAS.

For the given problem \[(9.7 - 5.2) - 1.4\] the order of operations dictates that we should first solve the subtraction inside the parentheses. This is an example of how parentheses are prioritized over other operations. By breaking down the problem step-by-step, we can simplify complex expressions into basic arithmetic operations that are easier to solve.

Adhering to the order of operations helps to avoid errors and ensures that everyone calculates expressions the same way, leading to consistent and correct results across different contexts.

Subtraction

Subtraction, one of the basic arithmetic operations, is the process of taking a number away from another number, resulting in a remainder or difference. In the context of prealgebra, subtraction is straightforward but requires attention to detail for accuracy.

In the exercise \((9.7 - 5.2) - 1.4\) we perform subtraction in two steps: the inner and then the outer subtraction.

• The first subtraction is to resolve the expression within the parentheses: \(9.7 - 5.2 = 4.5\)
• Next, we take this result and subtract \(1.4\) from it: \(4.5 - 1.4 = 3.1\)

This layered approach is critical when dealing with more complex expressions involving multiple numbers and operations.

Subtraction is not just about finding differences; it's a tool that can also help in understanding concepts like debt (negative numbers) and giving change (money transactions). Mastery of this operation leads to more advanced mathematical understanding and the ability to solve real-world problems efficiently.