Evaluating Expressions and Solving for Variables

Mathematics often involves breaking down complex expressions into simpler components to solve for variables or evaluate the expression. In this article, we will walk you through the process of evaluating the expression 1×3×2×4 and subsequently solving for the variable y in the equation y1324.

Solving the Expression 1×3×2×4

Let's start with the expression 1×3×2×4. The first step is to perform the multiplication operations in sequence.

Step 1: Multiply the first two numbers, 1 and 3.

1×3 3

Step 2: Multiply the result from Step 1 by the next number, 2.

3×2 6

Step 3: Multiply the result from Step 2 by the final number, 4.

6×4 24

The final answer is 24.

Understanding the Role of the Variable y

Let's now consider a more complex expression where a variable y is involved: y 24.

Given Premises

The given condition states that y 1324. This premise might appear confusing, but let's break it down step-by-step.

Breaking Down the Expression

The mathematical phrase in the premises can be written as:

y 1×3^2×4 [Implied multiplication]

First, we solve the exponent:

Step 1: Calculate the exponent 3^2.

32 9

Now, substitute this back into the original expression:

y 1×9×4 [Implied multiplication]

Step 2: Multiply the first two numbers, 1 and 9.

1×9 9

Step 3: Multiply the result from Step 2 by 4.

9×4 36

Therefore, y 36.

Solving for y with Given Information

Now, let's assume we have a different problem where y 1324 is given. We need to break it down further to evaluate it.

Breaking Down the Given Condition

The given condition now is:

y 1×32×4 [Implied multiplication]

We need to consider that the multiplication sign is implied, so we will need to interpret the expression carefully.

Step-by-Step Solution

Step 1: Interpret the implied multiplication in the given condition.

Note that 1×32×4 can be interpreted as (1×32)×4 or 1×(32×4). Let's assume the first interpretation for clarity.

Step 2: Multiply 1 and 32.

1×32 32

Step 3: Multiply the result from Step 2 by 4.

32×4 128

Hence, if we assume the implicit multiplication is meant to be interpreted as 1×32×4, then we get:

y 128.

Concluding Thoughts

Understanding how to evaluate expressions and solve for variables is essential in many areas of mathematics. Whether it's breaking down simple multiplications or more complex expressions, clarity in interpretation and step-by-step calculation are key.

In the given scenarios, we have seen that the interpretation of implied multiplication and step-by-step calculation are vital. Always ensure that you understand the implicit rules of mathematics and follow logical steps in your calculations.