Math - Long Multiplication

The Organic Chemistry Tutor
6 May 201906:25
EducationalLearning
32 Likes 10 Comments

TLDRThe video script provides a comprehensive guide on the long multiplication technique, a fundamental skill in arithmetic. It illustrates the process through a series of examples, starting with simple multiplications like 39 times 8 and 56 times 9, and gradually progressing to more complex calculations such as 46 times 27 and 76 times 52. Each step is explained in detail, from multiplying individual digits to carrying over numbers. The script also challenges viewers with more difficult examples, like multiplying 369 by 43 and 759 by 438, demonstrating the method's applicability to larger numbers. The detailed walkthrough of each example ensures that viewers can follow along and understand the logic behind each step, making it an engaging and informative resource for mastering long multiplication.

Takeaways
  • 📚 Start with basic multiplication: Begin by multiplying the digits in the ones place before moving on to the tens and hundreds.
  • 📝 Carry over: When a product exceeds ten, carry the digit to the next place value.
  • 🔢 Add partial products: Combine the results of each multiplication step, adding them vertically.
  • 📈 Practice with simple examples: Use easy multiplication problems to understand the process before tackling more complex ones.
  • 📉 Understand place value: Recognize the importance of place value in multiplication, especially when carrying over.
  • 🎯 Zero placeholders: Use zeros to maintain the correct digit place when multiplying numbers with different lengths.
  • ✅ Check your work: After completing the multiplication, check your work to ensure accuracy.
  • 🚀 Challenge yourself: Attempt more difficult problems to improve your long multiplication skills.
  • 📈 Gradual progression: Start with simpler examples and gradually increase the complexity to build confidence.
  • 🧮 Long multiplication is a skill: Like any mathematical technique, it requires practice to master.
  • 📈 Use visual aids: Writing down the steps can help visualize the process and avoid mistakes.
Q & A

  • What is the first step in performing long multiplication?

    -The first step in performing long multiplication is to multiply the ones place digits of the two numbers.

  • How do you handle the 'carry over' in long multiplication?

    -In long multiplication, when a product is greater than 10, you carry over the digit in the tens place to the next column of multiplication.

  • What is the result of multiplying 39 by 8 using long multiplication?

    -The result of multiplying 39 by 8 using long multiplication is 312.

  • How is the multiplication of 56 by 9 demonstrated in the script?

    -The multiplication of 56 by 9 is demonstrated by first multiplying 9 by 6 to get 54, writing down the 4 and carrying over the 5, then multiplying 9 by 5 to get 45 and adding the carried over 5 to get 50, resulting in the answer 504.

  • What is the final step in long multiplication?

    -The final step in long multiplication is to add the partial products obtained from each step of the multiplication process.

  • What is the purpose of writing a zero before multiplying in the example of 46 by 27?

    -Writing a zero before multiplying in the example of 46 by 27 is to ensure proper alignment and place value in the final addition step of the long multiplication process.

  • How does the script illustrate the multiplication of 76 by 52?

    -The script illustrates the multiplication of 76 by 52 by first multiplying the ones and tens place digits, carrying over where necessary, and then adding the partial products together to get the final answer, which is 3952.

  • What is the final answer when multiplying 369 by 43 as shown in the video script?

    -The final answer when multiplying 369 by 43 as shown in the video script is 15867.

  • What is the most challenging example provided in the script and what is the final answer?

    -The most challenging example provided in the script is the multiplication of 759 by 438, and the final answer is 332,442.

  • How does the script ensure clarity in the process of long multiplication?

    -The script ensures clarity by breaking down each step of the multiplication process, explaining the carry over process, and providing a step-by-step addition of the partial products to reach the final answer.

  • What is the importance of carrying over in long multiplication?

    -Carrying over in long multiplication is important because it accounts for the value that exceeds the single digit when multiplying larger numbers, ensuring that the final product is accurate.

  • How does the script use zero as a placeholder in the multiplication examples?

    -The script uses zero as a placeholder to maintain the correct column alignment during the multiplication process. For instance, before multiplying 6 by 2 in the example of 46 by 27, a zero is written down to hold the place for the tens column.

Outlines
00:00
📚 Introduction to Long Multiplication

This paragraph introduces the concept of long multiplication, a fundamental arithmetic technique taught in schools. It begins with a simple example of multiplying 39 by 8, demonstrating the process of breaking down the numbers, multiplying each digit, and carrying over where necessary. The explanation continues with another example, 56 times 9, and then progresses to more complex examples, including multiplying 46 by 27 and 76 by 52. Each step is detailed, emphasizing the method's systematic approach to finding the product of two numbers.

05:01
🔢 Advanced Long Multiplication Examples

This paragraph delves into more challenging long multiplication problems, starting with multiplying 369 by 43. It outlines each step of the multiplication process, including carrying over numbers and adding zeros where needed. The explanation is meticulous, showing how to handle larger numbers and more complex multiplication scenarios. The paragraph concludes with the multiplication of 759 by 438, which is presented as the most difficult example in the video. The process is broken down into manageable steps, culminating in the final answer of thirty-two thousand, four hundred and forty-two, thereby reinforcing the viewer's understanding of long multiplication.

Mindmap
Keywords
💡Long multiplication
Long multiplication is a mathematical technique used to multiply two numbers, typically when one or both numbers have more than one digit. It involves breaking down each number into its individual digits, multiplying each pair of digits, and then adding the results together, taking into account their respective positions. In the video, this technique is the central theme, demonstrated through various examples to show how to perform the calculations step by step.
💡Carry over
In the context of long multiplication, 'carry over' refers to the process of adding the value of a digit from one step to the next when the result of a multiplication exceeds the value that can be held in a single digit. For example, when multiplying 9 by 8, which equals 72, the '7' is written down and the '2' is carried over to the next position. This concept is essential for accurately performing long multiplication and is repeatedly used in the video to illustrate the process.
💡Multiplication
Multiplication is one of the four basic arithmetic operations, which involves combining a certain number of groups of equal size. In the video, multiplication is the primary operation being taught and practiced, with the focus on how to multiply numbers using the long multiplication method. It is a fundamental skill in mathematics, and the video aims to reinforce understanding and proficiency in this area.
💡Digit
A digit is a single numerical value, such as 0 through 9, that forms a part of a larger number. In the context of the video, digits are the individual numerical values that are being multiplied in the long multiplication process. For instance, when multiplying 39 by 8, the digits 3 and 9 are considered separately for the multiplication steps.
💡Example
In the video, examples are used to illustrate the process of long multiplication. Each example demonstrates a step-by-step approach to multiplying two numbers, showing the viewer how to handle different scenarios, such as carrying over or adding zeros. Examples are crucial for learners to understand the practical application of the technique and to practice the method themselves.
💡Addition
Addition is another fundamental arithmetic operation that is used in conjunction with multiplication in the long multiplication technique. It is used to sum the results of individual multiplications of digits before adding them together to form the final product. In the video, addition is shown as an integral part of the process, especially when combining the intermediate results to reach the final answer.
💡Position
In the context of long multiplication, 'position' refers to the place value of a digit within a number. The position of a digit determines its value in the overall number. For example, in the number 345, the digit '3' is in the hundreds position, '4' is in the tens position, and '5' is in the ones position. In the video, understanding and correctly aligning the positions of digits is key to performing long multiplication accurately.
💡Zero
In the video, zeros are used as placeholders in the multiplication process when there is no carry over from the previous step. They ensure that the multiplication maintains its correct place value. For instance, when multiplying by a number that ends with a zero, a zero is written down before proceeding with the next multiplication step. This helps in aligning the digits correctly for the final addition.
💡Step-by-step
The phrase 'step-by-step' describes the methodical approach taken in the video to teach long multiplication. Each step in the process is explained in detail, from breaking down the numbers into their digits, performing the multiplications, carrying over, and finally adding the results. This methodical approach is crucial for learners to grasp the technique and apply it to various multiplication problems.
💡Place value
Place value, also known as value place or place, is the position of a digit within a number that determines its value. In the video, understanding place value is essential for correctly performing long multiplication, as it dictates where each partial product should be aligned and how the final addition should be conducted to arrive at the correct answer.
💡Product
In mathematics, the 'product' is the result of a multiplication operation. In the context of the video, the product is the final answer obtained after performing long multiplication. Each step in the process contributes to the calculation of the product, which is the ultimate goal of the long multiplication technique.
Highlights

Long multiplication is a fundamental math technique taught in schools.

Example: 39 times 8 involves multiplying 8 by 9 first, then 8 by 3, and adding the results.

The answer to 39 times 8 is 312.

Example: 56 times 9 involves multiplying 9 by 6 and 9 by 5, then adding the results.

The answer to 56 times 9 is 504.

For more challenging examples, write down the intermediate products and carry over any necessary digits.

Example: Multiplying 46 by 27 involves several steps, resulting in the answer 1,242.

Another example is multiplying 76 by 52, which results in 3,952.

A more complex example is multiplying 369 by 43, which requires carrying over multiple digits.

The answer to 369 times 43 is 15,867.

The most challenging example is multiplying 759 by 438, which involves several steps and carrying over digits.

The answer to 759 times 438 is 330,242.

Long multiplication is a versatile technique that can handle a wide range of numbers.

It involves breaking down the numbers into smaller parts and multiplying them step by step.

Carry over any digits that exceed the value of a single digit place.

Add the intermediate products to get the final result.

Practice is key to mastering long multiplication and improving speed and accuracy.

This technique is useful for solving real-world problems involving multiplication of large numbers.

Long multiplication is a foundational skill that builds a strong base for more advanced math concepts.

Transcripts

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