Secrets of mental math - Arthur Benjamin

  1. Easy (and impressive) calculations
  1. A little give and take: Mental addition and subtraction
  1. Products of a misspent youth: Basic multiplication
  1. New and improved products: intermediate multiplication
  1. Divide and conquer: Mental division
  1. Good enough: The art of "Guesstimation"
  1. Math for the board: Pencil-and-paper math
  1. A memorable chapter: memorizing numbers
  1. The tough stuff made easy: advanced multiplication
  1. Presto-digitation: the art of mathematical magic
  1. Epilogue: how math helps us think about weird things

Short-cut math - Gerard w. Kelly

  1. Fundamentals of short-cut methods
  1. Addition
  1. Subtraction
  1. Multiplication
  1. Division
  1. Fractions, mixed numbers, and percentages

How to calculate quickly, full course in speed arithmetic - Henry Sticker

  1. Addition
  1. Subtraction
  1. Multiplication
  1. Division
  1. Fractions
  1. Decimals
  1. Short cuts
  1. Addition in general
  1. Adding single columns by pairs, starts on
  1. Adding single columns by trios, start on
  1. Mental addition of large numbers, start on
  1. Two-column addition, starts on
  1. Subtraction in general
  1. Left-to-right subtraction, starts on
  1. Multiplication in general
  1. Factoring, starts on
  1. Direct multiplication by numbers greater than 12, start on
  1. Multiplying three figures by one, start on
  1. Multiplying two figures by two, starts on
  1. Multiplying three figures by two, start on
  1. Multiplying three figures by three, start on
  1. Division in general
  1. Direct division by numbers greater than 12, starts on
  1. Mental division of large numbers, starts on
  1. Division by three figures, starts on
  1. Division by two figures, starts on
  1. Fractions in general
  1. Addition and subtraction of fractions, starts on
  1. Decimals in general
  1. Decimal equivalents of fractions, starts on
  1. Horizontal addition
  1. Combined addition and subtraction
  1. Multiplying by a near number

Aliquot parts in multiplication

  1. Simplifying the multiplier
  1. Multiplication by factoring
  1. Factors between 11 and 19
  1. Multiplying by 11
  1. Multiplying by 21, 31, 41, etc
  1. Squares of numbers, starts on
  1. Multiplying when corresponding orders are alike
  1. Multiplying a sum by a difference
  1. Multiplications involving fractions, starts on
  1. Aliquot parts in division
  1. Cubes of numbers
  1. Algebraic multiplication
  1. Instant multiplication
  1. Squaring and more
  1. More practical tips
  1. Improve your memory
  1. Left-to-right addition

Two-digit addition

Three digit addition

  1. Left-to-right subtraction

two-digit subtraction

Three-digit subtraction

Using complements (you're welcome!)

  1. 2-by-1 multiplication problems

Rounding up

  1. 3-by-1 multiplication problems
  1. Be there of b2: squaring two-digit numbers
  1. Why these tricks work
  1. 2-by-2 multiplication problems

The addition method

The subtraction method

The factoring method

Numbers with friendly products

  1. Approaching multiplication creatively
  1. Three-digit squares
  1. Cubing

One-digit division

  1. The rule of "Thumb"
  1. Two-digit division

Simplifying division problems

  1. Matching wits with a calculator: learning decimalization
  1. Testing for divisibility
  1. Fractions

Multiplying fractions

Dividing fractions

Simplifying fractions

Adding fractions

Subtracting fractions

  1. Addition guesstimation

Guesstimating at the supermarket

  1. Subtracting guesstimation
  1. Division guesstimation
  1. Multiplication guesstimation
  1. Square root estimation: divide and average
  1. More tips on tips
  1. Not-too-taxing calculations
  1. Some "interesting" calculations
  1. Guesstimation exercises
  1. Columns of numbers
  1. Mod sums
  1. Subtracting on paper
  1. Pencil-and-paper square roots
  1. Pencil-and-paper multiplication
  1. Casting out elevens
  1. Pencil-and-paper mathematics exercises
  1. Using mnemonics
  1. The phonetic code

The number-word list

  1. How mnemonics makes mental calculation easier
  1. Memory magic
  1. Four-digit squares
  1. 3-by-2 multiplication

Factoring methods

The addition method

The subtraction method

  1. Five-digit squares
  1. 3-by-3 multiplication

Factoring method

Close-together method

Addition method

Subtraction method

When-all-else-fails method

  1. 5-by-5 multiplication
  1. Psychic math
  1. The magic 1089!

Why this trick works

Why this trick works

  1. Missing-digit tricks
  1. Leapfrog addition

Why this trick works

  1. Magic squares
  1. How to construct a magic square

Why this trick works

  1. Quick cube roots
  1. Simplified square roots
  1. An "Amazing" sum

Why this trick works

  1. A day for any date
  1. Basic ways of simplifying calculations
  1. Results are what you want
  1. Combining mental and written math for best results
  1. Approximating and rounding off
  1. Achieving accuracy with speed
  1. Testing answers by casting out 9's
  1. Basic principles
  1. Adding by 10-groups
  1. Reaching 10-levels
  1. Adding by other combinations of numbers
  1. Adding by multiplying
  1. Adding two or more columns
  1. Adding long columns
  1. No-carry additions
  1. Rounding off numbers for addition
  1. Rounding off dollars and cents for addition
  1. Adding a regular series of numbers
  1. Add-and-subtract method of simplifying numbers
  1. Splitting numbers into easy parts
  1. Thinking of numbers as "Dollars" and "Cents"
  1. Checking your answer by adding again in reverse
  1. Checking addition by the no-carry method
  1. Checking addition by casting out 9's
  1. Introduction
  1. Add-or-subtract method of simplifying numbers
  1. Subtraction without borrowing
  1. Splitting numbers into easy parts
  1. Counting change after purchase
  1. Checking your answer in subtraction
  1. Basic principles
  1. Multiplication when one number has all digits alike
  1. To multiply by a number made up of multiples
  1. No-carry multiplication
  1. To multiply a number by 10, 100, 1000, etc.
  1. General method for multiplying by aliquot parts
  1. To multiply by .5, 5, 50, or 500
  1. To multiply by .25, 2.5, 25, or 250
  1. To multiply by .125, 1.25, 12.5, or 125
  1. To multiply by .75, 7.5, 75, or 750
  1. To square a number ending in 1
  1. To square a number ending in 4
  1. To square a number ending in 5
  1. To square a number ending in 6
  1. To square a number ending in 9
  1. To multiply two numbers with a difference of 1
  1. To multiply two numbers with a difference of 2
  1. To multiply two numbers with a difference of 3
  1. To multiply two numbers with a difference of 4
  1. To multiply two numbers with a difference of 6
  1. General method for multiplying by numbers ending in 1
  1. To multiply a number by 11
  1. To multiply a number by 21
  1. To multiply a number by 31, 41, 51, etc.
  1. To multiply by 15, 25, 35, 45, etc. halve-and double method
  1. Alternate method for multiplying a number by 15
  1. Alternate method for multiplying a number by 45
  1. Alternate method for multiplying a number by 55
  1. To multiply one number by another when they both end in 5 and the sum of their other digits is even
  1. To multiply one number by another when they both end in 5 and the sum of their other digits is odd
  1. To multiply a number by 9
  1. To multiply a number by 19, 29, 39, etc.
  1. To multiply by a multiple of 9 from 18 to 81
  1. To multiply a number by 99
  1. To multiply by a multiple of 99
  1. To multiply a number by 98
  1. To multiply a number by 101
  1. To multiply a number by 102
  1. To multiply one "teen" number by another
  1. To multiply two numbers when their end digits add to 10 and their other digits are the same
  1. To multiply two two-digit numbers when their first digit add to 10 and their end digits are the same
  1. Estimate the answer before you multiply
  1. Checking multiplication by multiplying in reverse
  1. Checking multiplication by using short-cut
  1. Checking multiplication by dividing the product by one of the factors used
  1. Checking multiplication by casting out 9's
  1. Basic principles
  1. Doing short division
  1. Doing long division
  1. To divide by 10, 100, 1000, etc.
  1. General method for dividing by aliquot parts
  1. To divide by .5, 5, 50, or 500
  1. To divide by .25, 2.5, 25, or 250
  1. To divide by .125, 1.25, 12.5, or 125
  1. To divide by .75, 7.5, 75, or 750
  1. Test for divisibility by odd and even numbers
  1. Test for divisibility by 2
  1. Test for divisibility by 3
  1. Test for divisibility by 4
  1. Test for divisibility by 5
  1. Test for divisibility by 6
  1. Test for divisibility by 7
  1. Test for divisibility by 8
  1. Test for divisibility by 9
  1. Test for divisibility by 10
  1. Test for divisibility by 11
  1. Test for divisibility by 12
  1. Test for divisibility by 15
  1. Test for divisibility by 18
  1. Extending the test to divisibility by larger divisors
  1. Simplifying the dividend by adding or subtracting
  1. Simplifying the dividend by breaking it into parts
  1. Simplifying the divisor by factoring it
  1. Simplifying the dividend and divisor by multiplying or dividing both by the same number
  1. Problems involving both multiplication and divisors
  1. Estimate the answer before you divide
  1. Check the subtractions in long division as you go
  1. Checking division by multiplying your answer by the divisor
  1. Checking division by dividing your answer into the dividend
  1. Checking division by using a short-cut
  1. Checking division by casting out 9's
  1. Definitions and basic principles

Common fractions

  1. Finding a common denominator
  1. Converting fractions to decimals for easier adding or subtracting
  1. Faster way to add any pair of fractions
  1. Fastest way to subtract any pair of fractions
  1. To add two fractions with numerators of 1
  1. To subtract two fractions with numerators of 1
  1. To multiply by a fraction
  1. To divide by a fraction
  1. To multiply a number by 3/4
  1. Simplifying a mixed number before multiplying
  1. To square a mixed number ending in 1/2
  1. To multiply a number by a mixed number ending in 1/2: Halve-and-double method
  1. To divide a number by a mixed number ending in 1/2
  1. To multiply two mixed numbers when they both end in 1/2 and the sum of their whole numbers is even
  1. To multiply two mixed numbers when they both end in 1/2 and the sum of their whole number is odd
  1. To multiply two mixed numbers having the same whole numbers, and fractions that add to 1
  1. To multiply or divide by 2*1/2
  1. To multiply or divide by 12*1/2
  1. To multiply or divide by 16*2/3
  1. To multiply or divide by 33*2/3
  1. To multiply or divide by 66*2/3
  1. To find 16*2/3% of a number
  1. To find 20% of a number
  1. To find 33*1/3% of a number
  1. To find 50% of a number
  1. To find 66*2/3% of a number