Problem 47 - Algebra 1

Question

Evaluate the expression. $$|6.3|-2$$

Step-by-Step Solution

Answer

The evaluated result of the expression \(|6.3| - 2\) is 4.3

Step 1 Compute Absolute Value

Calculate the absolute value of 6.3, which is \(|6.3|\). Since 6.3 is a positive number, its absolute value will also be 6.3.

Step 2 Perform Subtraction

Now, subtract 2 from the absolute value obtained in step 1. Which is: 6.3 - 2.

Step 3 Final Result

The result of the subtraction in step 2 is the final result. Compute 6.3 - 2 to get 4.3. Hence, \(|6.3| - 2 = 4.3\)

Key Concepts

Evaluate Expressions

When we refer to evaluating expressions, we're talking about finding the actual value of an expression based on the given numbers and operations. Think of it as solving a mini-mystery: each expression is a combination of numbers, variables, and mathematical operations, and your job is to figure out the single numerical value that this combination represents.

For example, when you see an expression like |6.3|-2, you follow a set of steps to unravel the calculation. First, you tackle the absolute value of 6.3, and then you subtract 2 from it to arrive at the final answer. By methodically addressing each part of the expression, you make sure that every 'clue' contributes correctly to the solution.

Absolute Value

The absolute value of a number can be thought of as its distance from zero on the number line, without any concern for direction. It's always a positive number or zero because distance cannot be negative. For instance, the absolute value of both +3 and -3 is 3 because each is three units away from zero on the number line.

When faced with the operation |6.3|, you're being asked, 'How far is 6.3 from zero?' Since 6.3 is already a positive number, its absolute value remains 6.3. This concept is crucial in many areas of math, especially when dealing with real numbers and understanding their magnitudes regardless of their sign.

Arithmetic Operations

Arithmetic operations are the building blocks of all math problems. They consist of addition, subtraction, multiplication, and division. These are the tools you use to manipulate numbers and compute expressions.

In the case of our expression, after calculating the absolute value, we apply subtraction, which is one of these operations, to find our final answer. Knowing how and when to use each operation is key to solving mathematical problems efficiently.

Subtraction

Subtraction, one of the four fundamental arithmetic operations, is essentially a process of taking away or finding the difference between numbers. For example, if you have five apples and you give away two, you're left with three apples. Mathematically, you would express this as 5 - 2 = 3.

With our given expression |6.3|-2, once we've identified that the absolute value of 6.3 is indeed 6.3, we simply subtract 2 to determine what remains. In this case, we're left with 4.3, which completes our evaluation of the expression.