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Multiply. See Examples 1 through \(5 .\) $$ \begin{array}{r} 526 \\ \times \quad 23 \\ \hline \end{array} $$

Short Answer

Expert verified
The product is 12,098.

Step by step solution

01

Set Up the Problem

Begin by writing the numbers one under the other, aligning them by their rightmost digits: \[\begin{array}{c} 526 \\times 23 \\hline\end{array}\]
02

Multiply the Bottom Number's Units Digit by the Top Number

Take the units digit of the bottom number, which is 3, and multiply it by 526. Calculate it as follows:\[526 \times 3 = 1578\]Write this result below the line, ensuring that the last digit (8) is aligned with the units place.
03

Multiply the Bottom Number's Tens Digit by the Top Number

Now, take the tens digit of the bottom number, which is 2. Multiply it by 526, but since it's in the tens place, remember to add a zero at the end:\[526 \times 2 = 1052\]Write this result shifted one position to the left, so it aligns with the tens place:\[\begin{array}{c}1578 \+10520 \\hline\end{array}\]
04

Add the Results

Add the two results from the previous steps together:\[\begin{array}{c}1578 \+10520 \\hline12098\end{array}\]This addition will give you the final product.
05

Write the Final Answer

The final answer after adding the two products together is:\[12098\]This is the product of multiplying 526 by 23.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Step by Step Solution
In mathematics, solving problems using a structured approach helps ensure accuracy and understanding. The step-by-step solution involves breaking down a problem into manageable parts to find the final answer.
Begin by clearly setting up the problem, aligning the numbers correctly. This helps to avoid mistakes and makes calculations easier to follow.
For the exercise of multiplying 526 by 23, the problem is initially set up by aligning the digits vertically. Next, each digit of the bottom number (23) is used to multiply with the top number (526), treating them as separate smaller problems.
Each step builds upon the previous one, ensuring no detail is overlooked. After solving each part, the results are added together to find the overall product.
This method not only leads to the correct solution but also enhances understanding of how larger multiplication problems can be simplified into basic operations of multiplication and addition.
Multi-digit Multiplication
Multi-digit multiplication is the process of multiplying numbers that have more than one digit. This exercise demonstrates a classic case of multi-digit multiplication with the numbers 526 and 23.
Breaking it down, we first multiply 526 by the 3 in 23. This is done just like a single-digit multiplication problem.
Then, 526 is multiplied by the 2, but since this 2 represents a value in the tens place, the result is shifted to the left by one digit (adding a zero).
  • Start with single digit multiplication.
  • Use place value to align each multiplied result.
  • Add results to achieve the final product.
By understanding this process, students can more easily handle bigger numbers without getting overwhelmed, seeing how basic multiplication rules apply no matter the number of digits.
Arithmetic Operations
Arithmetic operations, which include addition, subtraction, multiplication, and division, are fundamental building blocks of mathematics.
In the exercise of multi-digit multiplication, the primary focus is on multiplication and addition, as seen in the solution steps.
Each operation is crucial: multiplication is used to generate intermediate results, while addition combines these results into a final answer.
Multiplication involves multiplying each digit individually and aligning each partial product correctly before adding them together.
This exercise emphasizes understanding the arithmetic processes, reinforcing how these basic operations work together in solving more complex problems.
Math Problem Solving
Math problem-solving is an essential skill that involves not just calculation but also understanding the underlying principles and methods. Solving problems step by step aids in developing this skill.
In the case of multiplying 526 and 23, problem-solving entails using methodical steps to reach an accurate final result.
  • Identify each necessary operation.
  • Apply the correct mathematical rules.
  • Verify each step before proceeding.
Developing strong problem-solving skills involves practicing with various exercises, improving in areas like multi-digit calculations and arithmetic operations.
This structured approach builds confidence, making mathematics less intimidating and more manageable.

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