Vedic Math Teachers Manual, Volume 2, Intermediate

India: Motilal Banarsidass. 2005. F First Edition. H Hardcover. New. 2003. Contents:PREFACE LESSON 1 Basic Devices Introduction Digit Sums Left to Right Addition Multiplication Advantages of left to Right Calcn Writing Left to Right Sums Checking Devices Subtraction Subtraction from Left to Right Checking Subtraction Sums LESSON 2 MORE BASIC DEVICES Number Splitting Addition 14 / Subtraction Multiplication 16 / Division All from 9 and the Last from 10 Subtraction from a Base Calculations Involving Money First Extension Second Extension Combining the Extensions Bar Numbers Advantages of Bar Numbers General Subtraction LESSON 3 SPECIAL METHODS Proportionately Doubling and Halving Extending the Multiplication Tables Multiplying by 5, 50, 25 All from 9 and the Last from 10: Multiplication Numbers just below 100 Geometrical Proof Algebraic Proof Other Bases Numbers above the Base One Number ABOVE and one below the Base Proportionately Multiplying Numbers near Different Bases Squaring Numbers near a Base Mental Calculations Special methods LESSON 4 BY ONE MORE THAN THE ONE BEFORE Special Multiplications Squaring Numbers that End in 5 A Variation Multiplication Summary Recurring Decimals Denominator Ending in 9 Proof A Short Cut Proportionately Longer Numerators LESSON 5 AUXILIARY FRACTIONS Auxiliary Fractions: First Type Denominators Ending in 8, 7, 6 Auxiliary Fractions: Second Type Denominators Ending in 1 Alternative Method Denominators Ending in 2, 3, 4 Working 2, 3 etc. Figures at a Time LESSON 6 VERTICALLY AND CROSSWISE Fractions Adding & Subtracting Fractions Proof A Simplification Comparing Fractions Multiplication and Division General Multiplication Revision Multiplying 2-Figure Numbers Explanation Explanation of earlier special method The Digit Sum Check Multiplying 3- Figure Numbers Moving Multiplier Algebraic Multiplications The Digit Sum Check Three-Figure Numbers Four-Figure Numbers Writing Left to Right Sums From Right to Left setting the sums out Using Bar Numbers LESSON 7 SQUARES AND SQUARE ROOTS General Squaring Two-Figure Numbers Number Splitting Algebraic Squaring Squaring Longer Numbers Written Calculations – Left to Right Written Calculations – Right to Left Square Roots of Perfect Squares LESSON 8 SPECIAL MULTIPLICATION METHODS Special Numbers Repeating Numbers Proportionately Disguises Using the Average PROOF Multiplication by Nines Multiplication by 11 Percentages Increasing Reducing LESSON 9 TRIPLES Definitions Triples for 45°, 30° and 60° Triple Addition Double Angle Variations of 3,4,5 Quadrant Angles Rotations LESSON 10 SPECIAL DIVISION Division by Nine Adding Digits A Short Cut Dividing by 8 Algebraic Division Dividing by 11, 12 etc. Larger Divisors Divisor just Below a Base A Simplification Divisor just Above a Base Proportionately LESSON 11 STRAIGHT DIVISION Single Figure on the Flag Short Division Digression Longer Numbers Multiplication Reversed Decimalising the Remainder Negative Flag Digits Larger Divisors ALGEBRAIC DIVISION LESSON 12 EQUATIONS Linear One x Term Two x Terms Quadratic Equations Simultaneous Equations By Addition and By Subtraction A Special Type General Method Another Special Type LESSON 13 APPLICATIONS OF TRIPLES Triple Subtraction Triple Geometry Angle Between Two Lines Half Angle Coordinate Geometry Gradients Circle Problems Length of Perpendicular LESSON 14 SQUARE ROOTS Squaring Square Root of a Perfect square Preamble Two-Figure Answer Reversing Squaring Three-Figure Answer Reversing Squaring General Roots Changing the Divisor Heuristic Proof LESSON 15 DIVISIBILITY Elementary Parts The Ekadhika Osculation Explanation Testing Longer Numbers Other Divisors The Negative Osculator LESSON 16 COMBINED CALCULATIONS Algebraic Arithmetic Pythagoras Theorem SUTRAS AND SUB-SUTRAS 9-POINT CIRCLES REFERENCES INDEX OF THE VEDIC FORMULAE INDEX .