Introduction to long division | Multiplication and division | Arithmetic | Khan Academy

Khan Academy
20 Jan 201011:39
EducationalLearning
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TLDRThe video script teaches division by emphasizing the importance of knowing multiplication tables up to 10 times 10. It illustrates how to divide larger numbers by breaking them down and using multiplication facts to find the quotient and remainder, making complex division problems manageable.

Takeaways
  • 📚 Knowing multiplication tables up to 10 times 10 is essential for dividing into larger numbers.
  • 🔢 To divide, visualize grouping objects and counting how many groups of a certain number can be made.
  • 🧩 Quick division involves recalling multiplication tables, such as knowing that 5 times 5 equals 25.
  • 📉 Place the quotient carefully in relation to the place value of the dividend, like writing 5 in the ones place for 25 divided by 5.
  • 🔎 For numbers not directly in the multiplication tables, find the largest multiple and work from there, like dividing 23 by 3.
  • 🔄 Understand that division can result in a remainder, indicating how much is left after the division.
  • 📈 Practice with larger numbers helps in grasping the concept of division, even when numbers exceed known multiplication tables.
  • 📊 When dividing numbers with hundreds, focus on the tens and ones places separately, like dividing 344 by 4.
  • ✂️ Use the process of elimination in multiplication tables to find the correct quotient, such as with 9 times 6 equals 54.
  • 🔢 Division can be approached by breaking down the dividend into manageable parts, like dividing 608 by 8.
Q & A

  • Why is it important to know multiplication tables when dividing into larger numbers?

    -Knowing multiplication tables is crucial because it helps you quickly determine how many times a number can be multiplied to reach another number, which is essential for division. It allows you to mentally calculate or estimate the result of a division problem without having to physically divide objects or use complex calculations.

  • What is the minimum multiplication table knowledge required to start dividing into larger numbers?

    -At least the 1-multiplication tables up to the 10-multiplication tables should be memorized. This means knowing all the products from 1 times 1 up to 10 times 10, which includes the product 100.

  • How can you use multiplication tables to quickly determine the result of dividing 25 by 5?

    -By knowing the 5-multiplication tables, you can quickly recognize that 5 times 5 equals 25. This allows you to conclude that 5 goes into 25 exactly five times, simplifying the division process.

  • What is the significance of place notation in division?

    -Place notation is important in division because it helps maintain the correct value of each digit in the dividend. For example, when dividing 25 by 5, the 5 should be placed in the ones place, indicating that 5 goes into the ones part of 25 five times, not into the tens.

  • How can you handle division problems where the divisor does not completely divide the dividend?

    -In such cases, you find the largest multiple of the divisor that is less than the dividend, divide the dividend by this multiple, and then calculate the remainder. For example, in dividing 23 by 3, you find that 3 times 7 is 21, which is the largest multiple of 3 less than 23. The remainder is then 23 - 21 = 2.

  • What is the process for dividing a number like 344 by 4, which is beyond the basic multiplication tables?

    -You break down the number into parts that can be handled by your known multiplication tables. For 344 divided by 4, you first consider 4 going into 34, which is 8 times, and then multiply this by 10 (since you're actually dealing with hundreds). Then you bring down the remaining digit and continue the division process.

  • How does the script illustrate the division of 344 by 4?

    -The script shows that 4 goes into 34 eight times, resulting in 320. Then, the remainder (4) is brought down, and 4 goes into 24 six times, resulting in no remainder. Thus, 344 divided by 4 equals 86.

  • What is the method for dividing a number like 608 by 8?

    -You start by determining how many times 8 goes into 60, which is seven times. Then, you subtract this product from 60 to find the remainder, and continue the division process with the remaining digits.

  • How does the script demonstrate the division of 91 by 7?

    -The script shows that 7 goes into 91 thirteen times with a remainder of 0. It first finds that 7 goes into 90 ten times, then brings down the 1 and continues the division, finding that 7 goes into 21 three times.

  • Why is it beneficial to practice division with larger numbers?

    -Practicing division with larger numbers helps develop a deeper understanding of the division process, especially when the divisor does not completely divide the dividend. It also reinforces the importance of multiplication tables in solving division problems efficiently.

Outlines
00:00
📚 Mastering Multiplication Tables for Division

This paragraph emphasizes the importance of knowing multiplication tables up to at least 10 times 10 for efficient division. The speaker illustrates how to divide numbers like 25 by 5 and 49 by 7 using multiplication facts. They also discuss how to handle division when the result is not a perfect multiple, using examples like 23 divided by 3 and 344 divided by 4. The key takeaway is that a solid understanding of multiplication tables is essential for quickly solving basic division problems.

05:01
🔢 Tackling Larger Division Problems with Multiplication Tables

The speaker continues to discuss division, focusing on how to approach larger numbers that may not fit neatly into known multiplication tables. They demonstrate how to divide 344 by 4, explaining the process of breaking down the problem into manageable parts and using multiplication tables to find the quotient and remainder. The paragraph also includes examples of dividing 91 by 7 and 608 by 8, reinforcing the method of using multiplication facts to determine how many times a number divides into another and handling remainders.

10:02
📉 Understanding Division with Remainders

In this paragraph, the speaker further elaborates on the division process, particularly when dealing with numbers that result in remainders. They illustrate how to calculate the quotient and remainder when dividing numbers like 60 by 8, emphasizing the importance of knowing multiplication tables up to 10 times 10 or 12 times 12. The explanation includes a step-by-step breakdown of the division process, showing how to determine the largest multiple that fits into the dividend and then handling the remainder to find the exact quotient.

Mindmap
Keywords
💡Multiplication Tables
Multiplication tables are a set of basic arithmetic facts that help in quickly recalling the product of two numbers. In the video, the importance of knowing multiplication tables from 1-multiplication to at least 10-multiplication is emphasized. This knowledge is crucial for performing division, as it allows one to quickly determine how many times a divisor fits into the dividend. For example, knowing that 5 times 5 equals 25 helps in dividing 25 by 5.
💡Division
Division is one of the four basic operations in arithmetic, where a number (dividend) is divided by another number (divisor) to get a quotient. The video script discusses division in the context of breaking down a larger number into groups of a smaller number. It uses examples like dividing 25 by 5 and 49 by 7 to illustrate how knowing multiplication tables simplifies the process.
💡Place Value
Place value refers to the position of a digit within a number, which determines its value. In the context of the video, the speaker emphasizes the importance of correctly placing the quotient in its appropriate place value, such as writing the 5 in the ones place when dividing 25 by 5, to maintain accuracy in the calculation.
💡Remainder
A remainder is the amount left over after division when the dividend is not exactly divisible by the divisor. The script explains how to handle remainders in division problems, such as when dividing 23 by 3, where the remainder is 2. This concept is crucial for understanding that not all divisions result in whole numbers.
💡Multiples
Multiples are the result of multiplying a number by an integer. The video uses multiples to determine how many times a divisor fits into the dividend. For instance, finding the largest multiple of 3 that fits into 23 helps in determining that 3 goes into 23 seven times with a remainder.
💡Quotient
The quotient is the result obtained after dividing one number by another. The script demonstrates how to determine the quotient in various division problems, such as dividing 344 by 4, where the quotient is 86, indicating that 344 can be divided into 86 groups of 4.
💡Decimals and Fractions
Decimals and fractions are used to represent parts of a whole number. Although not the main focus of the video, the script mentions that in the future, learners will learn about decimals and fractions, which are relevant when divisions do not result in whole numbers, providing a more precise representation of the quotient.
💡Hundred's Place
The hundred's place is the third digit from the right in a number, representing hundreds. In the video, the speaker uses the hundred's place to illustrate how to divide numbers like 344 by 4, where the quotient is written in the tens place, indicating hundreds.
💡Tens Place
The tens place is the second digit from the right in a number, representing tens. The script explains how to use the tens place in division, such as when dividing 344 by 4, where the quotient 86 is written with 8 in the tens place, indicating eighty.
💡Borrowing
Borrowing is a technique used in subtraction where a digit is temporarily borrowed from the next higher place value to facilitate the subtraction. The video script briefly mentions borrowing in the context of division, such as when calculating the remainder in 60 minus 56, where one might conceptually borrow to simplify the calculation.
Highlights

Starting point for division is knowing multiplication tables up to 10 times 10.

Division can be visualized by grouping objects into sets.

Quick division involves recalling multiplication tables, e.g., 5 times 5 equals 25.

Place notation is crucial when writing division results, e.g., 5 in the ones place for 25 divided by 5.

Division examples include 7 times 7 equals 49, illustrating the use of multiplication tables.

Multiplication tables can be extended beyond memorized values, e.g., 9 times 6 equals 54.

Division of numbers not directly in multiplication tables involves finding the largest multiple.

Example given for dividing 23 by 3, illustrating the process of finding the largest multiple and remainder.

Division can be approached by breaking down numbers, e.g., dividing 344 by 4 involves focusing on 34.

Multiplication tables help in determining how many times a number divides into another, e.g., 4 times 8 equals 32.

Remainders are handled by subtracting the product of the divisor and quotient from the dividend.

Division of larger numbers can be simplified by focusing on relevant parts of the number, e.g., 344 divided by 4.

Division results can be expressed as a quotient with a remainder, e.g., 344 divided by 4 equals 86 remainder 0.

Practice with larger numbers helps in understanding division, e.g., 91 divided by 7.

Division can be approached by breaking down the number and using multiplication tables, e.g., 608 divided by 8.

Final division results are obtained by combining the quotients from each step of the division process.

Multiplication tables up to 10 times 10 or 12 times 12 are sufficient for tackling basic division problems.

Transcripts

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