Problem 323 - Intermediate Algebra

Question

In the following exercises, simplify. $$ 17(0.25)(4) $$

Step-by-Step Solution

Answer

17

Step 1: Simplify the constants inside the parentheses

First, multiply the numbers inside the parentheses: Arrange for 0.25×4: 0.25 × 4 = 1 This gives us the simplified version: 17 × 1

Step 2: Multiply the remaining constants

Lastly, multiply the remaining constants: 17 × 1 = 17

Key Concepts

Multiplication of Constants

When faced with an expression involving constants, the first step is to multiply these constants together. In our example, the constants are 17, 0.25, and 4. Start by arranging the constants to be multiplied together. This helps to keep the problem organized.
For instance, in the given problem 17(0.25)(4), you should first multiply 0.25 and 4. When you multiply 0.25 by 4, you get 1. This simplifies the expression to 17 × 1.
After that, it's usually simpler to handle any remaining multiplication involving constants.

Order of Operations

Order of operations is a fundamental concept in algebra, guiding us on the sequence to solve expressions properly. A common mnemonic is PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition, and Subtraction (from left to right)).
In the provided exercise 17(0.25)(4), multiplication is handled after dealing with any operations inside parentheses. Here,
* You first focus on the multiplication inside the parentheses: Arrange 0.25 × 4 = 1.
Once this is simplified, you are left with: 17 × 1, which is straightforward to solve without additional operations competing for precedence.

Algebraic Simplification

Algebraic simplification means reducing an expression to its simplest form. This involves combining like terms and simplifying constants. It makes equations easier to work with and solutions more apparent.
In the example 17(0.25)(4), you saw how breaking down the multiplication step-by-step allowed a more manageable process. Simplifying the inside of parentheses first, 0.25 × 4 = 1, helps streamline your expression, reducing it to 17 × 1. The resulting operation is much easier to solve, giving us a final simplified answer of 17.
Understanding these steps ensures accuracy and efficiency when dealing with more complex algebraic expressions.