Problem 114 - Elementary Algebra

Question

\(2[15 \div 3(5-1)]\)

Step-by-Step Solution

Answer

The answer is 40.

Step 1 - Evaluate Inside the Parentheses

Begin by solving the expression inside the parentheses. Here, subtract 1 from 5 to get: \(5 - 1 = 4\)

Step 2 - Perform the Division inside the Brackets

Next, address the division inside the brackets. Divide 15 by 3: \(15 \div 3 = 5\)

Step 3 - Multiply Inside the Brackets

Now, multiply the result from Step 1 by the result from Step 2. Multiply 5 by 4: \(5 \text{\bf{•}} 4 = 20\)

Step 4 - Multiply Outside the Brackets

Finally, multiply the 2 outside the brackets by the result from Step 3: \(2 \text{\bf{•}} 20 = 40\)

Key Concepts

parentheses

Parentheses are used in mathematics to show which operations should be performed first in an expression. They help to clarify the order of operations. In our example, the expression starts with parentheses: \(2[15 \div 3(5-1)]\).First, we need to solve the operation inside the parentheses. Start by doing the subtraction: \(5 - 1\), which gives us \(4\). Remember: always resolve the innermost parentheses first if there are multiple parentheses in an expression. Practice by identifying and solving parenthesis operations in different exercises to strengthen your understanding.

division

Division means splitting a number into equal parts. In our example, the next step requires division inside the brackets: \(2[15 \div 3(4)]\).After solving inside the parentheses, you get \(4\). Now, divide \(15\) by \(3\): \(15 \div 3 = 5\).Always remember to perform division before moving on to multiplication or addition when following the order of operations. To improve, practice more problems that involve dividing numbers.

multiplication

Multiplication is a math operation that adds a number to itself a specific number of times. The final steps of our example involve multiplication: After performing the division, our expression looks like this: \(2[5 \cdot 4]\).First, solve the multiplication inside the brackets: \(5 \cdot 4 = 20\). After that, multiply the result by the number outside the brackets: \(2 \cdot 20 = 40\).Multiplication often comes after division in the order of operations, unless parentheses dictate otherwise. Practicing multiplication tables and related exercises can help speed up and improve accuracy.