Division of Large Numbers: Long Division
TLDRThis script outlines a math lesson on long division. It first explains how division is the reverse of multiplication, then demonstrates the step-by-step process of long division using two examples. It divides a 3-digit number by a single-digit number and then a 3-digit number by a 2-digit number, walking through carrying remainders and decimals. The lesson ties long division to other math concepts like repeating decimals and distinguishes rational from irrational numbers. Overall, it aims to reveal the elegance and patterns in the long division algorithm disliked by many from childhood.
Takeaways
- 😀 Long division is an algorithm for dividing large numbers, just like multiplication has an algorithm for multiplying large numbers.
- 😊 It works by dividing the dividend by the divisor one digit at a time, starting from the largest place value.
- 🧐 We put the divisor to the left of the dividend, then determine how many times it goes into the first digit.
- 🤓 That number goes in the quotient above the digit. Multiply it by the divisor, subtract, and bring down the next digit.
- 🤔 If the divisor doesn't go evenly into a digit, put a 0 in the quotient and bring down the next digit to make a new number.
- 😎 Continue this process digit by digit until there is nothing left to divide.
- 🥸 Any leftover number at the end is called the remainder.
- 🤨 Long division can be continued past the decimal point to get decimal places if no remainder is desired.
- 😮 This results in repeating decimals, relating to rational vs irrational numbers.
- 🤩 Mastering long division provides a systematic approach to dividing large numbers.
Q & A
What is long division?
-Long division is an algorithm used to divide large numbers. It works by dividing the dividend by the divisor one digit at a time, going from left to right.
Why do we need to learn long division?
-We need to learn long division because sometimes we need to divide large numbers that are not easy to divide in our heads. Long division gives us an organized method to divide these numbers.
How is long division the reverse of multiplication?
-In multiplication, we multiply the multiplier through the multiplicand starting with the ones place and moving left. In division, we divide the dividend by the divisor starting with the largest place value and moving right.
What do we do when the divisor does not fit into the current digit?
-When the divisor does not fit into the current digit, we put a 0 in the quotient and bring down the next digit to create a new dividend that the divisor may fit into.
What is a remainder?
-The remainder is what is left over when the divisor does not divide the dividend evenly. It is the amount that is left after dividing.
Why do we sometimes get decimals or repeating decimals?
-We get decimals when we continue dividing past the integer portion in order to increase accuracy. Repeating decimals occur when the division continues forever without terminating.
What is done differently when dividing by a two-digit number?
-Nothing conceptually different. The process is the same, we just have to divide by a larger number at each step rather than a single digit.
How can remainders be eliminated?
-Remainders can be eliminated by continuing the long division process to add decimal places. This may result in a repeating decimal.
What is checked for comprehension at the end?
-It is unspecified what exactly is checked for comprehension. Presumably, the instructor would ask questions to ensure students understand the process of long division.
How can long division prepare us for more advanced math concepts?
-Learning long division introduces ideas like remainders and repeating decimals that will be important when learning about rational and irrational numbers. The algorithm itself teaches step-by-step logical thinking.
Outlines
😃 Introducing Long Division
Paragraph 1 introduces the concept of long division as a technique for dividing large numbers, similar to how multiplication has an algorithm for multiplying large numbers. It explains that long division works by dividing the dividend by the divisor one digit at a time from left to right, going through each place value, which is the reverse of the multiplication algorithm.
😊 Walkthrough of Long Division Example
Paragraph 2 provides a step-by-step walkthrough of using long division to divide 624 by 3. It shows how to set up the problem, divide the first digit (6) by 3 to get the first quotient digit (2), multiply and subtract, and repeat with each subsequent digit of the dividend.
🧐 Understanding Remainders
Paragraph 3 explains remainders in long division as what is left over when the divisor does not evenly divide part of the dividend. It shows in the example that 3 divides into 625, 208 times with 1 left over as the remainder.
🤔 Getting Decimal Places
Paragraph 4 demonstrates how to continue the long division process to find decimal place values for the quotient by adding zeros after the decimal point in the dividend. This can yield repeating decimals.
😤 More Long Division Practice
Paragraph 5 provides another long division example working through dividing 397 by 11 to further illustrate the process and technique.
🥳 Checking Comprehension
The final paragraph summarizes that long division works from left to right, unlike multiplication which goes right to left, and introduces students to remainders and repeating decimals as previews of deeper math concepts.
Mindmap
Keywords
💡long division
💡dividend
💡divisor
💡quotient
💡remainder
💡place value
💡repeating decimal
💡rational number
💡irrational number
💡decimal place
Highlights
There is an algorithm for division of large numbers called long division that works by dividing one number by another starting with the largest place value.
To do long division, place the dividend inside the division symbol and the divisor to the left. Then go through the dividend one digit at a time, dividing, multiplying, and subtracting.
If the divisor does not fit into a digit, put a zero in the quotient, multiply to get zero, and subtract to get the original digit back.
After dividing all digits, any remainder is written as a remainder or can be converted to decimal places by adding zeros and continuing.
Dividing by two-digit numbers works the same way by testing how many times the divisor fits into each partial dividend.
Repeating decimals arise from long division when there is an infinitely repeating pattern after the decimal point.
Long division reverses the process of multiplication, working right to left instead of left to right.
Long division reveals elegant patterns in the relationship between divisor and dividend.
Long division is often remembered with disdain from childhood despite its underlying elegance.
Just as there are strategies for multiplying large numbers, long division is the strategy for dividing them.
Long division works digit-by-digit just like the multiplication algorithm, but in reverse order.
Division of small numbers is trivial, but larger numbers require an algorithmic process.
Remainders can be converted to decimals through an infinitely repeating process.
The process of long division reveals patterns in the relationship between numbers.
Mastering division is as important as mastering multiplication when operating on large numbers.
Transcripts
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