Problem 61 - Elementary Algebra

Question

\(16 \div(8 \cdot 2)\)

Step-by-Step Solution

Answer

1

Step 1 - Understand the Expression

First, understand the expression given: \(16 \div (8 \cdot 2)\). This expression involves division and multiplication.

Step 2 - Solve Inside the Parentheses

According to the order of operations (PEMDAS/BODMAS), solve the expression inside the parentheses first. Calculate \(8 \cdot 2\). \(8 \cdot 2 = 16\).

Step 3 - Perform the Division

Now replace the parentheses in the original expression with the calculated value: \(16 \div 16\). Perform the division: \(16 \div 16 = 1\).

Key Concepts

Division

Division is one of the four basic arithmetic operations where we split a number into equal parts.
In our exercise, we have the expression \(16 \div (8 \cdot 2)\).
The division \(16 \div 16\) means we are splitting 16 into 16 equal parts, which equals 1.
When dividing numbers:

• Ensure the dividend (the number being divided) and the divisor (number you are dividing by) are clear.
• Use the division symbol \( \div \) or a slash \( / \).
• Example: \(20 \div 4 = 5\).

Multiplication

Multiplication is another fundamental arithmetic operation. It is essentially repeated addition.
In our exercise, the expression inside the parentheses \(8 \cdot 2\) means adding 8 twice (which equals 16).
Key points about multiplication:

• Use the times symbol \( \cdot \) or an asterisk \( * \).
• Multiplying two numbers results in a product.
• Example: \(3 \cdot 4 = 12\).

PEMDAS

PEMDAS is an acronym to remember the order of operations in math. It stands for: Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right).
In our expression \(16 \div (8 \cdot 2)\), PEMDAS dictates that we first solve the expression within the parentheses:

• First, solve inside Parentheses: \( 8 \cdot 2 = 16 \).
• Then, perform the Division: \( 16 \div 16 = 1 \).

Understanding PEMDAS ensures we solve expressions correctly and in the right order.