Problem 27 - Fundamentals of Mathematics

Question

Find each value. Check each result with a calculator. \(1-5 \cdot(8-8)\)

Step-by-Step Solution

Answer

The value of the expression is 1.

Step 1: Simplify Inside the Parentheses

Start by solving the expression inside the parentheses. Here, we have \(8 - 8\). \[8 - 8 = 0\]

Step 2: Multiply by the Result

Now, replace the expression inside the parentheses with the result and simplify:\[5 imes 0\]

Step 3: Perform the Multiplication

Perform the multiplication of 5 and 0: \[5 imes 0 = 0\]

Step 4: Subtract the Result

Subtract the result of the multiplication from 1: \[1 - 0 = 1\]

Step 5: Verify the Calculation

Finally, check the result with a calculator to ensure accuracy. Calculating \(1 - 5 imes (8 - 8)\) should also give a result of 1, confirming our manual calculation.

Key Concepts

Parentheses

When you see parentheses in a math problem, it means that you need to tackle the content inside them first. This is the first step in following the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). By solving the expression inside the parentheses first, you simplify your problem right down to the basics. For example, in the given exercise, we start with solving:

• \(8 - 8\)

This simplifies to 0. After removing parentheses by solving their contents, the equation becomes easier to work with. Parentheses help us to keep track of operations that need to be prioritized in a complicated equation.

Multiplication

Multiplication often follows right after you have simplified parentheses. The order of operations dictates that multiplication must be performed before addition and subtraction unless grouped by parentheses. In our exercise, after solving the parentheses, we arrived at the expression:

• \(5 \times 0\)

When you multiply any number by zero, the result is always zero. It's a fundamental rule in mathematics that helps simplify calculations and predict outcomes when dealing with zero. The multiplication step is crucial as it shows how different numbers interact with each other.

Subtraction

After completing multiplication, the next step in the order of operations is subtraction. In this exercise, we subtract the product from the earlier step from 1:

• \(1 - 0\)

When you subtract zero from any number, the number remains unchanged. Subtraction, like addition, is a basic operation in mathematics that adjusts quantities. By understanding subtraction, you can balance accounts, track quantities, and translate real-world problems into mathematical solutions. Here, the subtraction is straightforward and confirms the simplified outcome of our expression.

Verify calculations

It's essential to verify your calculations to ensure that no errors were made during the process. Whether learning math or working through a complex problem, double-checking your final answer helps confirm its accuracy. In this exercise, using a calculator to verify:

• \(1 - 5 \times (8 - 8)\)

This should return a value of 1. By verifying with a calculator, we make sure that each step followed the correct order of operations, and we achieved the right result. Accurate verification builds confidence in handling various mathematical problems with precision.