Problem 86

Question

For exercises 85-88, use a calculator to evaluate. If the calculator has parentheses, use them. $$ 18-12 \div(2+1) $$

Step-by-Step Solution

Verified
Answer
14
1Step 1 - Evaluate inside the parentheses
First, evaluate the expression inside the parentheses. Here, you have \((2+1)\). Calculate this sum first: \(2+1 = 3\).
2Step 2 - Division
Next, perform the division part of the expression. Now you have \(12 \div 3\). Calculate this division: \(12 \div 3 = 4\).
3Step 3 - Subtraction
Finally, perform the subtraction part of the expression. Now the expression is \(18 - 4\). Calculate this subtraction: \(18 - 4 = 14\).

Key Concepts

parentheses in arithmeticdivisionsubtraction in arithmetic
parentheses in arithmetic
Parentheses, also known as brackets, are used in arithmetic to change the normal order of operations. Normally, calculations follow the order of PEMDAS/BODMAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
When we use parentheses, we ensure that certain parts of an equation are computed first.
This means that whatever is inside the parentheses will be calculated before any other operations outside of them.
In the example provided, we have the expression \(18 - 12 \div (2 + 1)\).
According to PEMDAS, we first calculate inside the parentheses:
  • Start with \(2+1=3\)...
This is how parentheses help in setting the right priorities in arithmetic calculations.
division
Division is a fundamental arithmetic operation that involves splitting a number into equal parts.
In our given example, after dealing with the parentheses, we're left with our intermediate result: \(18-12 \div 3\).
This means we now need to divide 12 by 3.
  • Calculate \(12 \div 3 = 4\)...
It’s important to follow the order of operations strictly. This ensures that we get the correct result.
When division comes after parentheses in an equation, it must be done before subtraction or addition.
subtraction in arithmetic
Subtraction is another basic arithmetic operation that involves taking one quantity away from another.
After handling the parentheses and division in our initial equation, we are left with the expression: \(18 - 4\).
  • Subtract 4 from 18 to get 14:
\(18 - 4 = 14\)
In subtraction, especially when combined with other operations like division, it's crucial to perform it in the correct order as dictated by PEMDAS.
This rule ensures that you achieve the correct and final result.