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Learn how to perform arithmetical calculations using only the human brain, with no help from any supplies or devices. Explore various methods and techniques for multiplying, subtracting, and adding numbers, such as casting out nines, factors, and FOIL.
Learn how to express a rational fraction as a sum of a polynomial and fractions with simpler denominators. See the basic principles, examples, methods and applications of partial fraction decomposition in algebra and calculus.
Long division is a standard algorithm for dividing multi-digit numbers by hand. It involves finding the largest multiple of the divisor that does not exceed each digit of the dividend, and subtracting it from the dividend.
The first step is to determine a common denominator D of these fractions – preferably the least common denominator, which is the least common multiple of the Q i. This means that each Q i is a factor of D , so D = R i Q i for some expression R i that is not a fraction.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Learn about the invention and evolution of electronic calculators, from the first solid-state device in the 1960s to the modern smartphones and PDAs. Compare different models of calculators, such as basic, scientific, graphing, and memory calculators, and their functions and features.
Learn about the history, notation and calculation methods of Egyptian fractions, a finite sum of distinct unit fractions. Find out how they were used by ancient and medieval mathematicians and how they differ from vulgar fractions and decimal notation.
On a 30-year term, you’d normally pay $1,146 per month, but with the 10/15 rule that amount would be $1,643 across 16 years and nine months, saving you $83,000 in the process.