Problem 22 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 18-12 \div(2+1) $$

Step-by-Step Solution

Answer

14

Step 1: Solve Inside the Parentheses

First, solve the expression inside the parentheses \(2+1\). This simplifies to \(3\).

Step 2: Perform the Division

Next, divide \(12\) by the result from Step 1. So, compute \(12 \div 3 = 4\).

Step 3: Subtract the Result from 18

Finally, subtract the result from Step 2 from \(18\). Thus, \(18 - 4 = 14\).

Key Concepts

Parentheses

Parentheses are used in math to prioritize operations within an expression. This means any operations inside parentheses should be performed first before moving on to other calculations. For example, in the expression \((2+1)\), you first add \(2\) and \(1\) to get \(3\).
Always pay attention to parentheses because they can change the outcome of a calculation. Without solving the parentheses first, you might get a completely different answer!
So, remember: if you see parentheses, handle them before anything else.

Division

After dealing with parentheses, the next step is to handle division. Division is a fundamental operation where you determine how many times one number is contained within another. In our exercise, we got \(3\) from the parentheses and then need to divide \(12\) by \(3\).
This means you find out how many \(3\)s fit into \(12\). The answer is \(4\) because \(3 \times 4 = 12\).
Always follow the rule of operations: handle any division or multiplication before moving on to addition or subtraction.

Subtraction

Subtraction comes after division in our order of operations. Subtraction is simply taking one number away from another. In our problem, once we have \(4\) from the division step, we subtract this from \(18\).
So, performing \(18 - 4\) gives us \(14\).
Remember, subtraction follows after you've taken care of any parentheses and division in your expression.
It's important to go step-by-step as shown to arrive at the correct answer.