Fractional division is a basic operation in mathematics. Its concept is to divide one fraction by another to get a new fraction. In fractional division, the numerator and denominator of dividend and divisor will change accordingly, and a new fraction will be obtained as quotient.
A fractional division operation "/",for two fractions A and B, a/b is A divided by B. In mathematical expressions, we can write a÷b or a/b, and the two expressions are equivalent. When a fraction is divided by another fraction, the numerator and denominator of the dividend are divided by the numerator and denominator of the divisor, respectively, to get a new fraction. In digital division.
For any non-zero real numbers A and B, there is (a÷b)÷c=a÷(b×c), which reflects the associative law of division. For any real number A, B and C, there is A \u( B×C)=(A \u B)\u C = A \u B \u C, which reflects the distribution law of division.
Some applications of fractional division
1, average problem: Given that the average of a group of numbers is b, find the number of this group of numbers. Solution: multiply the average value b by the number of groups n to get the sum of these groups, and then divide the sum by the average value of each number to get the number of groups n.
2. Solving the problem: the concentration of the solution is known as A, and the weight of distilled water needed to dilute the solution into B. Solution: multiply the weight of the solution by the concentration A to get the weight of solute in the solution, then divide the weight of solute by the dilution concentration B to get the weight of solution, and finally subtract the weight of the original solution to get the weight of distilled water to be added.
3. Distance problem: It is known that the speed of car A is one kilometer, and the speed of car B is b kilometers. Find the relative speed of two cars. Solution: Add the speed of car A and car B to get the relative speed of the two cars.