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A simple fraction (also known as a common fraction or vulgar fraction) [n 1] is a rational number written as a/b or , where a and b are both integers. [9] As with other fractions, the denominator (b) cannot be zero. Examples include 1 / 2 , − 8 / 5 , −8 / 5 , and 8 / −5 .
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.
In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of b by a (written a \ b) is typically defined as the solution x to the equation a ∗ x = b, if this exists and is unique. Similarly, right division of b by a (written b / a) is the solution y to the equation y ∗ a = b ...
For example, the numerators of fractions with common denominators can simply be added, such that + = and that <, since each fraction has the common denominator 12. Without computing a common denominator, it is not obvious as to what 5 12 + 11 18 {\displaystyle {\frac {5}{12}}+{\frac {11}{18}}} equals, or whether 5 12 {\displaystyle {\frac {5 ...
For algorithms describing how to calculate the remainder, see Division algorithm.) The remainder, as defined above, is called the least positive remainder or simply the remainder . [ 2 ] The integer a is either a multiple of d , or lies in the interval between consecutive multiples of d , namely, q ⋅ d and ( q + 1) d (for positive q ).
a fraction with A as numerator and B as denominator that represents the quotient (i.e., A divided by B, or). This can be expressed as a simple or a decimal fraction, or as a percentage, etc. [7] When a ratio is written in the form A:B, the two-dot character is sometimes the colon punctuation mark. [8]
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
By 1970, a calculator could be made using just a few chips of low power consumption, allowing portable models powered from rechargeable batteries. The first handheld calculator was a 1967 prototype called Cal Tech, whose development was led by Jack Kilby at Texas Instruments in a research project to produce a portable calculator. It could add ...