According to the basic properties of the ratio (the two terms before and after the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged), the two terms before and after the ratio are multiplied or divided by the same number that is not 0 at the same time, so that the two terms before and after the ratio become prime numbers.
Simplified proportion: (there are four main situations, as follows)
Simplification of (1) integer ratio (both front and back terms are integers): divide the front and back terms of the ratio by its greatest common factor at the same time (it is not necessary to use the greatest common factor, as long as it is a common factor, but it is troublesome to do it in one step). For example, 240: 720 is an integer ratio, and the greatest common factor of the front and rear terms is (), so the front and rear terms are divided by () at the same time.
(240÷ ) : (720÷ )=( ):( )
(2) Simplification of fractional ratio (both front and back terms are fractions): multiply the latter term of the ratio by the least common multiple of its denominator at the same time, and narrow the denominator to become an integer ratio. If the integer ratio is not the simplest ratio, it should be simplified according to the simplification method of integer ratio.
The ratio of (2/ 15) to (8/27) is a fractional ratio, and the denominator of the preceding and following terms 15 and the least common multiple of 27 is (). The front and back terms are multiplied by () at the same time to form an integer ratio.
((2/ 15)×) ratio ((8/27)× )= () ratio ()
The integer ratio to (): () is not a ratio, and there is the greatest common factor () before and after the item, and then the simplest ratio (): () is obtained by simplifying the integer ratio.
3) Decimal ratio simplification: multiply the front and back terms of the ratio by the same number (generally 10, 100 ... or multiply the decimal part by an integer 10) to form an integer ratio, and then simplify it into the simplest integer ratio by the method of integer ratio simplification.
For example, 2.4: 3.7 is the fraction ratio, the former item can be converted into an integer by multiplying it by 5, and the latter item can be converted into an integer by multiplying it by 10, so the former item and the latter item are always multiplied by ():
2.4 : 3.7=(2.4× ): (3.7× )=( ):( )
The obtained integer ratio (): () is not the simplest ratio, and then the integer ratio is simplified to the simplest ratio (): ().
(4) Simplification of mixing ratio (the front and back terms of the ratio are a mixture of integers, decimals and fractions): The above three methods should be used flexibly.