This 5- minute video lesson shows how to divide complex numbers.
- Subject:
- Algebra
- Mathematics
- Numbers and Operations
- Material Type:
- Lecture
- Provider:
- Khan Academy
- Provider Set:
- Khan Academy
- Author:
- Salman Khan
- Date Added:
- 10/11/2012
This 5- minute video lesson shows how to divide complex numbers.
This site presents the numbers in Arabic using the Hindi numeral system. Below each set of Hindi numerals are the corresponding Arabic numerals, and if users scroll over the Hindi numerals, they will see the number written out in the Arabic script. The site contains the numbers 1-19, 20-100 (in intervals of ten), 101, 200, 300, and 400, and then lists powers of ten from one thousand to one billion.
You get the general idea of decimal is and what the digits in different places represent (place value). Now you're ready to do something with the decimals. Adding and subtracting is a good place to start. This will allow you to add your family's expenses to figure out if your little brother is laundering money (perhaps literally). Have fun! Common Core Standard: 5.NBT.B.7
This short video and interactive assessment activity is designed to teach second graders an overview of subtraction (numbers to 100) - word problems.
This short video and interactive assessment activity is designed to teach second graders about comparing values of multiple numbers within a set.
The class reviews the properties of operations. The use of “ask myself” questions to make sense of problems and persevere is modeled. Students review things to do when they feel stuck on a problem. Finally, students use the properties of operations to evaluate expressions.Key ConceptsStudents use the properties of operations to justify whether two expressions are equivalent.Goals and Learning ObjectivesTo start to work on a problem, make sense of the problem by using “ask myself” questions.Persevere in solving a problem even when feeling stuck.Use the properties of operations to evaluate expressions.
This single minute video lesson looks at how to add complex numbers.
Textbook for a Windows Operating System course. Currently focuses on Windows 10 with information about Windows 11 in the last chapter.
The purpose of this task is for students to compare a number and its product with other numbers that are greater than and less than one.
This short video and interactive assessment activity is designed to teach fourth graders about using the four operations with money - word problems.
This short video and interactive assessment activity is designed to teach second graders an overview of subtraction (numbers to 100).
The doctoral seminar 15.764 focuses on theoretical work for studying operations planning and control problems. This term's special topic, "Customer-Driven Operations," considers how a number of companies have succeeded in focusing their operation systems on the customer. The class reviews the quantitative models and theoretical tools underlying some of the customer-driven operational practices of these cutting-edge companies. Students will read and present research papers on topics such as distribution systems, short life-cycle product management, and forecast evolution models.
This MIT OpenCourseWare site is dedicated to the memory of Bhuwan Singh, a member of the class.
Our objective in this course is to introduce you to concepts and techniques related to the design, planning, control, and improvement of manufacturing and service operations. The course begins with a holistic view of operations, where we stress the coordination of product development, process management, and supply chain management. As the course progresses, we will investigate various aspects of each of these three tiers of operations in detail. We will cover topics in the areas of process analysis, materials management, production scheduling, quality improvement, and product design.
To pursue the course objective most effectively, you will have to:
Study the assigned reading materials.
Prepare and discuss cases, readings, and exercises in class.
Prepare written analyses of cases.
A suite of number recognition games for the whiteboard, tablet or computer. Games provide a rich interactive learning setting.
This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.
This short video and interactive assessment activity is designed to teach fourth graders about completion of number patterns.
Students use properties of multiplication to prove that the product of any two negative numbers is positive and the product of a positive number and a negative number is negative.Key ConceptsMultiplication properties can be used to develop the rules for multiplying positive and negative numbers.Students are familiar with the properties from earlier grades:Associative property of multiplication: Changing the grouping of factors does not change the product. For any numbers a, b, and c, (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c).Commutative property of multiplication: Changing the order of factors does not change the product. For any numbers a and b, a ⋅ b = b ⋅ a.Multiplicative identity property of 1: The product of 1 and any number is that number. For any number a, a ⋅ 1 = 1 ⋅ a = a.Property of multiplication by 0: The product of 0 and any number is 0. For any number a, a ⋅ 0 = 0 ⋅ a = 0.Property of multiplication by −1: The product of −1 and a number is the opposite of that number. For any number a, (−1) ⋅ a = −a.Existence of multiplicative inverses: Dividing any number by the same number equals 1. Multiplying any number by its multiplicative inverse equals 1. For every number a ≠ 0, a ÷ a = a ⋅ 1a = 1a ⋅ a = 1.Distributive property: Multiplying a number by a sum is the same as multiplying the number by each term and then adding the products. For any numbers a, b, and c, a ⋅ (b + c) = a ⋅ b + a ⋅ c.In this lesson, students will encounter a proof showing that the product of a positive number and a negative number is negative and two different proofs that the product of two negative numbers is positive. Two alternate proofs are as follows.Proof that the product of two negative numbers is positive:Represent the negative numbers as −a and −b, where a and b are positive.(−a) ⋅ (−b)Original expression= ((−1) ⋅ a) ⋅ ((−1) ⋅ b) Property of multiplication by −1= (−1) ⋅ (a ⋅ (−1)) ⋅ b Associative property of multiplication= (−1) ⋅ ((−1) ⋅ a) ⋅ b Commutative property of multiplication= ((−1) ⋅ (−1)) ⋅ (a ⋅ b) Associative property of multiplication= 1 ⋅ (a ⋅ b) Property of multiplication by −1= a ⋅ b Multiplicative identity property of 1Because a and b are positive, a ⋅ b is positive.Proof that the product of a positive number and a negative number is negative:Let a be the positive number. Let −b be the negative number, where b is positive.a ⋅ (−b)Original expression= a ⋅ ((−1) ⋅ b) Property of multiplication by −1= (a ⋅ (−1)) ⋅ b Associative property of multiplication= ((−1) ⋅ a) ⋅ b Commutative property of multiplication= (−1) ⋅ (a ⋅ b) Associative property of multiplication= −(a ⋅ b) Property of multiplication by −1Because a and b are positive, a ⋅ b is positive, so −(a ⋅ b) must be negative.Goals and Learning ObjectivesReview properties of multiplication.Explain why the product of two negative numbers is positive and the product of a negative number and a positive number is negative.
Students answer questions about low temperatures recorded in Barrow, Alaska, to understand when to use negative numbers and when to use the absolute values of numbers.Key ConceptsThe absolute value of a number is its distance from 0 on a number line.The absolute value of a number n is written |n| and is read as “the absolute value of n.”A number and the opposite of the number always have the same absolute value. As shown in the diagram, |3| = 3 and |−3| = 3.In general, taking the opposite of n changes the sign of n. For example, the opposite of 3 is –3.In general, taking the absolute value of n gives a number, |n|, that is always positive unless n = 0. For example, |3| = 3 and |−3| = 3.The absolute value of 0 is 0, which is neither positive nor negative: |0| = 0.Goals and Learning ObjectivesUnderstand when to talk about a number as negative and when to talk about the absolute value of a number.Locate the absolute value of a and the absolute value of b on a number line that shows the location of a and b in different places in relation to 0.
This 4-minute video lesson looks at the imaginary roots of negative numbers.
Kindergarten students often struggle to remember the names of teen numbers and to count objects in a group where the total number is between 10 and 20. These are practice activities to supplement a mathematics curriculum, and not intended as the sole lesson for counting 11-20. They can be used at center time activities, for an intervention, played in partners, or sent home for extra practice. There are four activities that increase in skill level required. There are pages attached to use as paper spinners and paper domino cards (if actual ones not available) as well as number cards and ten frame activity sheets.