Problem 16 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 15(6-1) $$

Step-by-Step Solution

Answer

75

Step 1: Simplify Inside the Parentheses

First, evaluate the expression inside the parentheses. Here, subtract 1 from 6 inside the parentheses: \[ 6 - 1 = 5 \]

Step 2: Perform the Multiplication

Next, multiply the result from Step 1 by 15. So you have: \[ 15 \times 5 = 75 \]

Key Concepts

Order of Operations

To solve arithmetic problems correctly, it's important to follow the order of operations. This sequence, sometimes remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), ensures that everyone evaluates expressions the same way. For example, in the expression given in the exercise, solving the operation inside the parentheses first, before moving on to multiplication, follows the correct order. This avoids confusion and mistakes.

Parentheses

Parentheses play a crucial role in arithmetic expressions. They indicate which operations should be performed first. Consider our example, \(15(6-1)\). The parentheses around \(6-1\) tell us to perform the subtraction inside them before doing any multiplication.

Hence, before multiplying by 15, we subtract 1 from 6: \(6-1 = 5\). Leaving out this step or doing it incorrectly disrupts the entire calculation process. Using parentheses correctly ensures the precise step-by-step approach needed in arithmetic.

Multiplication

After handling the operations within parentheses, the next focus is on multiplication. Multiply the simplified result from the parentheses with the number outside. In our problem, we simplified \(6-1\) to get 5. Next, we multiply: \[15 \times 5 = 75\].

This step shows why multiplication is essential and should be done carefully after solving expressions within parentheses. Multiplication combines quantities or numbers repetitively, reinforcing the importance of following the proper steps in arithmetic operations.