Write in fractionFractional lineThe following number orAlgebraic expressionIt's called denominator.A fraction whose denominator is a known number is calledIntegral form, denominator isunknown numberA fraction of is called a fraction.The denominator cannot be zero.
Fractions (from Latin, "broken") represent parts of a whole, or more generally, any equal number of parts.When speaking in everyday English, scores describe parts of a certain size, such as half, five eighths, and three quarters.Numerators and denominators are also used for uncommon fractions, including compound fractions, complex fractions, and mixed numbers.
In aComplex fractionThe longest fraction line is called the main fraction line of complex fractions. No matter how many numbers or operations there are on or off the main fraction line, they are regarded as complex fractions respectivelymoleculeAnd denominator.
Fractions (from Latin, "broken") represent parts of a whole, or more generally, any equal number of parts.When speaking in everyday English, scores describe parts of a certain size, such as half, five eighths, and three quarters.Numerators and denominators are also used for uncommon fractions, including compound fractions, complex fractions, and mixed numbers.
A fraction represents the fraction of one number to another, or the ratio of one event to all events.Divide the unit "1" into several equal shares, and the number representing such a share or shares is called fraction.The numerator is above and the denominator is below.[1]
The earliest fraction was the reciprocal of an integer: an ancient symbol representing half, a third,quarter, etc.Egyptians use the Egyptian fraction c.1000 bc。About 4000 years ago, Egyptians separated them with slightly different scores.They use least common multiples and unit fractions.Their method gives the same answer as modern methods.Egyptians also have different representations of Akhmim wood chips and second-generation mathematical papyrus.
brief introduction
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Primary school definition:DividenddivideDivisorIt is equal to the dividend of the divisor, that is, the divisor in division is equal to the denominator of the fraction.
The ancient Egyptians considered the following question: How to write a fraction into a sum like 1/n?That is, those fractions whose numerator is 1 and denominator is the sum of positive integers, and the denominators are required to be different from each other, such as
，
Etc.
(Note: In modern mathematics, this kind of fraction is called "unit fraction", which is defined as - the numerator is 1, and the denominator is equal to or greater than 2Natural numberA fraction of is called a unit fraction and is recorded as 1/n.)
1. The denominator represents the value of a population, and the numerator represents the value of the population.
2. In the fraction, the number orAlgebraic expressionIt is called denominator, which means to divide unit 1 into several equal parts.
3. A fraction whose denominator is a known number is calledIntegral formThe fraction whose denominator is unknown is calledfraction。
matters needing attention
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1. The denominator can be all numbers except 0, that is, the denominator is not equal to 0.
In any fraction, if the denominator is equal to 0, the fraction is meaningless.
2. In aComplex fractionThe longestFractional lineIt is called the main fraction line of complex fractions. No matter how many numbers or operations there are, they are regarded as the numerator and denominator of complex fractions.
Rationalizing the denominator
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denominatorRationalize the denominatorQuadratic radicalThe middle denominator was originallyIrrational number, and the process of converting the denominator to a rational number is to remove the root sign from the denominator.
The following introduces two conventional methods of rationalizing the denominator. The basic idea is to multiply the numerator and denominator by the same appropriate algebraic expression, so that the denominator does not contain a root sign.
, and then reduce the score.That is to say, in order to rationalize the denominator of a polynomial, the original denominator is a minus sign. We multiply a formula with the same number but connected by a plus sign, and then use the square difference formula.[2]
This method can be applied to root size comparison.
For the equation: 1) first find the simplest common denominator of all denominators;2) Multiply both sides of the equation by the least common multiple.
aboutInequality: Denominators containing unknowns cannot be deleted at will.
For algebraic expression: the denominator can only be eliminated by reduction.[3]
Example
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3 ÷ 8 is written as a fraction of 3/8, where "8" is called the denominator.
C ÷ (a+b) is written as a fraction of c/(a+b), where "a+b" is called the denominator.
Numbers such as 2/5, a/b, c/(a+b) or "5", "b", "a+b" in the formula are called denominators.
