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Chapter 1: Problem 29

Multiply. $$\begin{array}{r} 24 \\ \times 6 \\ \hline \end{array}$$

Short Answer

Expert verified
144

Step by step solution

01

Write down the problem

Write the multiplication problem in the standard vertical format:\[ \begin{array}{r} 24 \ \times 6 \ \hline \end{array} \]
02

Multiply the ones place

Multiply the digit in the ones place of the first number (4) by the second number (6):\( 4 \times 6 = 24 \).Write down 4 in the ones place and carry over the 2 to the tens place.
03

Multiply the tens place and add the carryover

Multiply the digit in the tens place of the first number (2) by the second number (6):\( 2 \times 6 = 12 \).Add the carryover (2) to this result:\( 12 + 2 = 14 \).Write down 14 in front of the 4.
04

Write down the final result

Combine the results from the previous steps to write down the final result of the multiplication:\[ 24 \times 6 = 144 \]

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Key Concepts

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

Multiplication
Multiplication is a fundamental mathematical operation that finds the product of two numbers. It simplifies the process of repeated addition. Instead of adding the number repeatedly, you multiply it by the number of times it is being added. For instance, multiplying 24 by 6 means adding 24 six times. This results in 144. To better understand multiplication in prealgebra, let's break it down with our example.
Carry Over
The carry over technique helps when a digit product exceeds the value of 9. Let's understand this through our example. When we multiply 4 by 6, we get 24. We place the 4 in the ones place and the 2 is the carry over. The carry over is added to the product of the next digits. This is crucial in ensuring accuracy in multiplications that span multiple place values.
Vertical Format
Writing the multiplication problem in a vertical format helps organize the work neatly. Place the larger number on top and the smaller number below it, aligning the digits by their place values. Draw a line under the numbers to separate the problem from the solution. This format aids in systematically solving the problem, reducing errors especially when dealing with larger numbers.
Basic Arithmetic
Basic arithmetic forms the foundation of more complex mathematical concepts. Multiplication is one of the primary operations in arithmetic, alongside addition, subtraction, and division. Mastering these operations opens the door to understanding higher mathematics subjects. In our exercise, understanding basic arithmetic allows us to see how each step in the multiplication process builds on the previous steps, reinforcing fundamental skills.

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