The process of reducing the common factor of a fraction's numerator and denominator is called canceling.[4]
Approximation isFractional reduction, put a fraction ofmolecule、denominatorAt the same time, divide by the common divisor, and the value of the fraction remains unchanged.The basis of reduction isBasic Properties of Fraction。When reducing minutes, if you can quickly see the numerator and denominatorMaximum common factorIt is easy to remove them directly by their greatest common divisor.
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]
Minimalist fraction
MoleculesdenominatoronlyCommon factorThe fraction of 1 is called the simplest fraction or the numerator and denominator areCoprime numberThe fraction of is called the simplest fraction, also called the reduced fraction.For example: 2/3, 8/9, 3/8, etc.
The simplest fraction is also called bothApproximationNumber, a reduced fraction can be understood as a fraction that has been reduced, that is, a fraction whose numerator and denominator are coprime numbers.
definition
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Convert fractions intoMinimalist fractionThe process is called reducing points.
For example, a/b is a fraction, a can be written as c * d, b can be written as c * e, and a/b can be written as d/e, because there is a common factor, c, which can be both the numerator and denominator.
When dividing, if you can quickly see the greatest common factor of the numerator and denominator, it is easier to remove them directly with their greatest common divisor.
Reduction method
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According to the basic nature of fractions:
"The numerator and denominator of a fraction are divided by the same number (except 0) at the same time, and the size of the fraction remains unchanged - the basic properties of the fraction".
Method 1: can be removed by common factor (except 1) of numerator and denominator
Example:
be
Is the simplest fraction
In this way, a fraction that is equal to it but has a small numerator and denominator is called a reduction (usually reduced to the simplest fraction)
Method 2: Directly remove with the greatest common factor (except 1) of the numerator and denominator of the fraction
Example:
be
Is the simplest fraction
Summary: Generally, the common factor (except 1) of the numerator and denominator is used to remove the numerator and denominator of a fraction until the simplest fraction.
Example
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Writing method:
(The number except for is crossed out, such as 6, 12, 30 and 15 in this example)
You must pay attention to finding the numerator and denominatorCommon factor, cannot just take the denominatorSimplificationOr molecular simplification, the common factor of even numbers must have 2, so you can divide by 2 first, then divide slowly, and then multiply all your divisors to get theirMaximum common factor。
"Approximation, half is half, and the other half is notdenominatorThe number of molecules should be reduced from less to more.It shall be approximately equal. "[2]
Skillfully use difference to reduce points
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When the numerator and denominator of a fraction are relatively large, it is often hard to see how much to use to reduce the fraction. Sometimes, the difference between the numerator and denominator can be used to reduce the fraction.
For example, put
、
、
Reduction is the simplest fraction.
answer:
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The difference between 36 and 30 is 6. Use 6 to remove the numerator and denominator, that is
、
, so 6 is the greatest common factor of the numerator and denominator,
。
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The difference between 95 and 57 is 38. According to the oral calculation, 38 is not a factor of the numerator and denominator. Then decompose 38 into a factor, that is, 38=19 x 2. Using 19 to divide, 19 is a factor of the numerator and denominator
。
about
For example, its numerator and denominator are very different, and the difference is not a factor of the numerator and denominator. It is also troublesome to decompose the difference into factors.At this time, we can use the difference obtained by subtracting a number of decimals from a large number to reduce points, that is, 493-145 x 3=58. When 58 is divided into factors, 58=29 x 2, and 29 is the factor of numerator and denominator, we can get the reduced points
