Episode 4 of Secrets of Mental Math

Turn now to the last fundamental operation of arithmetic: division. Explore a variety of shortcuts for dividing by one- and two-digit numbers; learn how to convert fractions such as 1/7 and 3/16 into decimals; and discover methods for determining when a large number is divisible by numbers such as 3, 7, and 11.

Running Time

34 mins

Year

2011

Kanopy ID

1148000

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Mental Addition and Subtraction

Professor Benjamin demonstrates how easily you can mentally add and subtract one-, two-, and three-digit numbers. He also shows you shortcuts using the complement of a number (its distance from 100 or 1000) and demonstrates the uses of mental addition and subtraction for quickly counting calories and making change.

The Speed of Vedic Division

Vedic mathematics, which has been around for centuries, is extremely helpful for solving division problems: much more efficiently than the methods you learned in school. Learn how Vedic division works for dividing numbers of any length by any two-digit numbers.

Arithmetic

The 8 videos in this collection focus on all aspects of Arithmetic, from fractions to percentages and ratios.

Percentages: That Make Sense

Key concepts explained: converting percentages into decimals and fractions, and converting decimals and fractions into percentages.
Taking examples from the widespread use of percentages in everyday life from the percentage of cappuchinos to regular coffee a coffee shop sells, to the percentage of sharks to other fish in an aquarium,…

Advanced Multiplication

Professor Benjamin shows you how to do enormous multiplication problems in your head, such as squaring three-digit and four-digit numbers; cubing two-digit numbers, and multiplying two-digit and three-digit numbers. While you may not frequently encounter these large problems, knowing how to mentally solve them cements your knowledge of basic mental…

The Geometry of Figurate Numbers

Ponder another surprising appearance of geometry--the mathematics of numbers and number theory. Look into the properties of square and triangular numbers, and use geometry to do some fancy arithmetic without a calculator.

Memorizing Numbers

Think that memorizing long numbers sounds impossible? Think again. Investigate a fun: and effective: way to memorize numbers using a phonetic code in which every digit is given a consonant sound. Then practice your knowledge by trying to memorize the first 24 digits of pi, all of your credit card…

Math in Your Head!

Dive right into the joys of mental math. First, learn the fundamental strategies of mental arithmetic (including the value of adding from left to right, unlike what you do on paper). Then, discover how a variety of shortcuts hold the keys to rapidly solving basic multiplication problems and finding squares.

Intermediate Multiplication

Take mental multiplication to an even higher level. Professor Benjamin shows you five methods for accurately multiplying any two-digit numbers. Among these: the squaring method (when both numbers are equal), the close together method (when both numbers are near each other), and the subtraction method (when one number ends in…

The Joy of Numbers

How do you add all the numbers from 1 to 100--instantly? What makes a square number square and a triangular number triangular? Why do the rules of arithmetic really work, and how do you calculate in bases other than 10?

The Joy of Infinite Series

Starting with the analysis of the proposition 0.999999999 ... = 1, this lecture explores what it means to add up an infinite series of numbers. Some infinite series converge on a definite value, while others grow arbitrarily large.

Complex Numbers in Geometry

In lecture 6, you saw how 17th-century mathematician Rene Descartes united geometry and algebra with the invention of the coordinate plane. Now go a step further and explore the power and surprises that come from using the complex number plane. Examine how using complex numbers can help solve several tricky…

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