Divide and Conquer

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Visualizing Decimals
Expand into the realm of decimals by probing the connection between decimals and fractions, focusing on decimals that repeat. Can they all be expressed as fractions? If so, is there a straightforward way to convert repeating decimals to fractions using the dots-and-boxes method? Of course there is!
The 8 videos in this collection focus on all aspects of Arithmetic, from fractions to percentages and ratios.
Percentages: That Make Sense
Part of the Series: Math Series 1
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,…
Mental Addition and Subtraction
Episode 2 of Secrets of Mental Math
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
Episode 8 of Secrets of Mental Math
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.
Pushing the Picture of Fractions
Delve into irrational numbers--those that can't be expressed as the ratio of two whole numbers (i.e., as fractions) and therefore don't repeat. But how can we be sure they don't repeat? Prove that a famous irrational number, the square root of two, can't possibly be a fraction.
Surprise! The Fractions Take Up No Space
Drawing on the bizarre conclusions from the previous lecture, reach even more peculiar results by mapping all of the fractions (i.e., rational numbers) onto the number line, discovering that they take up no space at all! And this is just the start of the weirdness.
Advanced Multiplication
Episode 11 of Secrets of Mental Math
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
Episode 34 of Geometry
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
Episode 9 of Secrets of Mental Math
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!
Episode 1 of Secrets of Mental Math
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
Episode 7 of Secrets of Mental Math
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…