Problem 552 - Prealgebra

Question

Translate and simplify. Ten times two hundred sixty-four

Step-by-Step Solution

Answer

2640

Step 1: Understand the Problem

Identify the numbers involved and the operation required. We have 'ten times' and 'two hundred sixty-four'.

Step 2: Convert Words to Numbers

Convert 'ten' to 10 and 'two hundred sixty-four' to 264.

Step 3: Perform the Multiplication

Multiply 10 by 264. Use the multiplication formula: \( 10 \times 264 = 2640 \)

Step 4: Simplify the Result

Since 2640 is already simplified, no further action is needed.

Key Concepts

Basic Multiplication

Multiplication is a fundamental arithmetic operation. It involves finding the total number when a number is added to itself a certain number of times. For example, if we need to find the total of 'ten times two hundred sixty-four,' we can use the multiplication operation.

In this case, 'ten times' indicates multiplication. We can represent this in simple form by using the multiplication symbol (\times). So, we translate 'ten times two hundred sixty-four' into the equation:
\[10 \times 264\]

This equation tells us to add 264 to itself ten times. Rather than doing repeated addition, multiplication allows us to find the result quickly and accurately.
Using multiplication ensures efficiency and accuracy, which is why it is such a powerful tool in math. Remember that practicing basic multiplication improves your math skills and understanding, making complex problems easier to solve.

Word Problems

Word problems help us understand how to apply math in real-life situations. When dealing with word problems involving multiplication, it’s crucial to first identify the keywords that signify mathematical operations.

• Words like 'times,' 'product,' or 'multiplied by' all indicate multiplication.
• Carefully understand the problem to determine what needs to be multiplied.

For this exercise, the phrase 'ten times' serves as our clue that we need to multiply. Next, we translate the words into numerical values:
'Ten' becomes 10 and 'two hundred sixty-four' becomes 264. So, the problem 'ten times two hundred sixty-four' translates to

\[10 \times 264\]

Once we know what the problem is asking, the next step is to perform the multiplication. Creating a clear mental picture of the problem helps ensure accurate translations and solutions.

Simplifying Results

Simplifying the results means ensuring the answer is presented in its simplest form. In multiplication problems, this often involves making sure the result is neat and comprehensible.

In our example, after computing
\[10 \times 264\]
we get:
\[10 \times 264 = 2640\]

The product 2640 is straightforward and does not need simplifying further. However, not all multiplication results are as direct.

When simplifying multiplication results:

• Ensure there are no unnecessary calculations left.
• Check if the result can be presented in a simpler form like reducing fractions when necessary.
• Confirm the final answer is easy to understand.

Breaking down the steps and checking your calculations help ensure that the final result is correct and simplified. The aim is always to make math easy and accessible, by breaking it down into understandable pieces.