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Notation of a integer

Division is often shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a vinculum or fraction bar, between them. For example, a divided by b is written[1]

\frac ab

This can be read out loud as "a divided by b", "a by b" or "a over b". A way to express division all on one line is to write the dividend (or numerator), then a slash, then the divisor (or denominator), like this:

a/b\,

This is the usual way to specify division in most computer programming languages since it can easily be typed as a simple sequence of ASCII characters. A typographical variation halfway between these two forms uses a solidus (fraction slash) but elevates the dividend, and lowers the divisor:

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Any of these forms can be used to display a fraction. A fraction is a division expression where both dividend and divisor are integers (although typically called the numerator and denominator), and there is no implication that the division must be evaluated further. A second way to show division is to use the obelus (or division sign), common in arithmetic, in this manner:

a \div b

This form is infrequent except in elementary arithmetic. ISO 80000-2-9.6 states it should not be used. The obelus is also used alone to represent the division operation itself, as for instance as a label on a key of a calculator.

In some non-English-speaking cultures, "a divided by b" is written a : b. This notation was introduced in 1631 by William Oughtred in his Clavis Mathematicae and later popularized by Gottfried Wilhelm Leibniz.[2] However, in English usage the colon is restricted to expressing the related concept of ratios (then "a is to b").

In elementary mathematics the notation b)~a or b \overline{)a} is used to denote a divided by b, especially when discussing long division. This notation was first introduced by Michael Stifel in Arithmetica integra, published in 1544.[2][3]

Positive and negative

North Carolina was 34 degrees below zero. This number can be written as -34°F. Numbers that are less than zero are negative numbers. They are written with a negative sign in front of them. On a number line, negative numbers are to the left of zero and positive numbers are to the right of zero.Integers are the set of positive whole numbers (1, 2, 3, . . .), their opposites, and zero. Opposites are numbers that are the same distance from zero in opposite directions on a number line. For example the numbers 2 and −2 are opposites. The numbers −8 and 8 are also opposites.What is the opposite of each number below?Locating Integers on a Number Line.Since the number is four places to the left of zero, the number is -4 When determining what number is shown on a number line, remember that negative integers are to the left of zero and positive integers are to the right of zero.
680582-3282012-110456-AM-1735247767

The integers on a number line.

Absolute value

The absolute value of a number is its distance from zero on a number line. You write the “absolute value of −6” as |-6| Notice that opposite numbers have the same absolute value. Since absolute value represents distance, the absolute value of a number is always positive: -|n| means the opposite of the absolute value of n.

Examples

  • -|2|= -2
  • -|65|= -65

references

  1. [[1]] Division is also used in science
  2. 2.0 2.1 Earliest Uses of Symbols of Operation, Jeff MIller
  3. These are the famous people that are good in math


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