Division of rational numbers refers to the process of dividing two rational numbers. Rational number is a number that can be expressed as the ratio of two integers, including positive number, negative number and zero. In the division of rational numbers, we need to pay attention to some laws and special cases.
Let's start with a simple example: 8 divided by 4. This can be written as 8/4 or 8÷4, and the result is 2. This result shows that 8 is divisible by 4, and * * * has two 4.
In the division of rational numbers, we need to pay attention to the following rules:
1. Division by 0 is not allowed: the result of dividing any number by 0 is undefined. For example, it is not feasible to divide 5 by 0.
2.0 divided by any number is 0: No matter divided by any number, the result of dividing 0 by this number is 0. For example, 0 divided by 5 equals 0.
3. Symbolic law of division: positive number divided by positive number, negative number divided by negative number, the result is positive number; Positive numbers divided by negative numbers, and negative numbers divided by positive numbers result in negative numbers. For example, -6 divided by -3 equals 2, and 6 divided by -3 equals -2.
4. Reduction: In division, we usually reduce the result, that is, remove the common factor of the numerator and denominator in the result. For example, 8/4 can be roughly divided into 2/ 1.
In actual calculation, we can divide rational numbers according to the following steps:
1. Write the divisor and dividend in fractional form.
2. Convert division into multiplication: Converting division into multiplication can simplify calculation. We can turn the division problem into the problem of finding the inverse of multiplication.
3. Reduction: the result is reduced, and the common factor of the numerator and denominator is removed.
4. Judge the sign of the result: According to the sign rule of division, determine the sign of the result.
It should be noted that there may be some special cases in the calculation, such as the divisor or dividend is a fraction and needs to be simplified or converted into the same denominator. In addition, sometimes you need to pay attention to the operation of decimals and percentages.
Division of rational numbers is a basic operation in mathematics. Knowing the division rules and precautions of rational numbers can better operate rational numbers.