Understanding the Mathematical Expression 96/3

The mathematical expression 96/3 is a simple arithmetic problem that involves division. In this article, we will break down the process of solving this expression, explain the order of operations, and provide multiple ways to arrive at the correct answer.

The Standard Calculation Method

To solve the expression 96/3, we perform the division directly, which is a straightforward calculation:

96 ÷ 3 32

However, this expression can also be rewritten in a way that makes it clear how the components should be interpreted. Let's explore two alternative methods:

Breaking Down the Expression

The expression 9 × 6 ÷ 3 can be interpreted in different ways due to the lack of parentheses. Let's look at the different ways to solve it:

Method 1: Direct Division

First, multiply 9 by 6: 9 × 6 54 Next, divide 54 by 3: 54 ÷ 3 18

Hence, the expression 9 × 6 ÷ 3 equals 18.

Method 2: Simplifying Fractions

Rewrite the expression as a single division problem: 9 × 6 ÷ 3 can be rewritten as 9 × (6/3). Calculate the fraction first: 6 ÷ 3 2. Then multiply: 9 × 2 18.

Alternatively, we can directly divide the numbers:

96 ÷ 3 32 (if we were solving 96 ÷ 3). However, since we have 9 × 6 ÷ 3, we need to break it down: First, 6 ÷ 3 2. Then, 9 × 2 18.

Understanding the Order of Operations (PEMDAS)

To avoid confusion with such expressions, it's important to understand the order of operations, which is commonly remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). For the expression 9 × 6 ÷ 3, the order of multiplication and division is performed from left to right:

First, perform the multiplication: 9 × 6 54. Next, perform the division: 54 ÷ 3 18.

This confirms that the expression 9 × 6 ÷ 3 indeed equals 18.

Verification and Conclusion

To verify the solution, y 9 × 6 ÷ 3 can be simplified as follows:

y 9 × 6 ÷ 3 y 54 ÷ 3 y 18

Therefore, the solution is y 18, which is confirmed by the original expression.

The final answer is 18.

Conclusion

Multiplication and division are performed from left to right according to the order of operations. Understanding this can significantly help in solving mathematical expressions without ambiguity. If you find the expression 96/3, you can break it down into 9 × 6 ÷ 3 and solve it step by step.

Remember to always keep the rules of PEMDAS in mind to simplify and solve such expressions effectively.