Problem 78 - Prealgebra

Question

Perform the indicated operations. $$43.5 \times 9$$

Step-by-Step Solution

Answer

The result of multiplying 43.5 by 9 is 391.5.

Step 1: Rewrite the Problem

The problem asks you to multiply two numbers: 43.5 and 9. We start by writing the multiplication operation: \(43.5 \times 9\).

Step 2: Simplify the Multiplication

To make it easier to multiply with decimals, treat 43.5 as \( rac{435}{10} \). So, the multiplication of \(43.5 \times 9\) is equivalent to \((\frac{435}{10}) \times 9\).

Step 3: Multiply Numerators and Denominators

Now, multiply the numerators and denominators: \( \frac{435 \times 9}{10} \). Calculate \( 435 \times 9 \).

Step 4: Calculate the Multiplication

Perform the multiplication: \( 435 \times 9 = 3915 \).

Step 5: Divide by 10

Since \(43.5\) was represented as \( \frac{435}{10} \), divide the product by 10 to account for the decimal place: \( \frac{3915}{10} = 391.5 \).

Step 6: Verify the Result

Verify that dividing 3915 by 10 gives 391.5 by moving the decimal place one position to the left, confirming the result.

Key Concepts

Step-by-step math solution

Understanding a step-by-step math solution is like following a GPS to reach a destination. Each step aims to simplify the process and guide you through complex problems with ease. In our exercise, the goal is to multiply two numbers, specifically 43.5 and 9. This involves several clear stages:

• First, recognize that you are multiplying a decimal by a whole number.
• Begin by rewriting the multiplication statement in a more manageable form.
• Then, follow through a series of calculative steps to arrive at the final product.

By unpacking the problem into smaller, more straightforward steps, tackling each part becomes less daunting. As seen, completing the exercise involves converting, multiplying, and adjusting the result to account for decimals, leading to the solution. It's a systematic approach ensuring even intricate math tasks become less intimidating.

Decimal multiplication simplification

Decimal multiplication simplification transforms complicated operations into easier-to-manage tasks. To multiply decimals effectively, we can temporarily ignore the decimal point. For instance, consider the number 43.5 as \( \frac{435}{10} \). This representation treats the decimal as a fraction, turning a tricky multiplication into a simpler one.Here's how it works:- Write the decimal as a fraction. In the case of 43.5, this turns into \( \frac{435}{10} \).- Multiply normally by the whole number, which in our exercise is 9.- Focus on the numerators first: \( 435 \times 9 = 3915 \).Once the multiplication is complete, reintroduce the decimal by dividing by 10, returning to the original format. This method keeps calculations manageable, especially when involved with decimals.

Mathematical problem-solving steps

Mathematical problem-solving steps involve a logical progression designed to tackle the problem bit by bit. For operations such as decimal multiplication, this method is invaluable. Here's a breakdown of our problem-solving strategy: - **Identify the Problem**: Recognize that you're tasked with multiplying a decimal with a whole number. - **Adjust the Problem**: Convert the decimal into a fraction to make it simpler for multiplication. - **Perform Calculations**: Execute the arithmetic operations on the fraction and the whole number. - **Reintroduce the Decimal**: After calculation, divide by 10, if necessary, to place the decimal correctly. - **Verify**: Always confirm your solution by checking the result, ensuring accuracy. By adhering to a carefully laid out sequence of steps, you not only solve the problem but also gain insight into the arithmetic processes involved. This structured approach equips you with a toolkit versatile for tackling similar mathematical challenges in the future.