The methods for comparing the sizes of two rational numbers are:
1, which is directly compared according to the positions of points corresponding to rational numbers on the number axis;
2. Comparison according to regulations: two positive numbers; Positive numbers and zeros; Negative numbers and zeros; Positive and negative numbers; Two negative numbers reflect the mathematical idea of classified discussion; ?
3. Difference method: A-B >; 0 ? a & gtb；
4. Commercial Law: A/B > 1，b & gt0 ? a & gtb；
5. Compare sizes with absolute values.
Comparison of two positive numbers: the one with the largest absolute value is the largest;
Comparison of two negative numbers: first calculate their absolute values, the larger the absolute value, the smaller.
Extended data
Basic operations of rational numbers
First, rational number addition.
Add two numbers with the same sign, use the same sign as the addend, and then add the absolute values.
When two numbers with different signs are added, if the absolute values are equal or the sum of the opposite numbers is 0; If the absolute values are not equal, take the sign of the addend with the larger absolute value and subtract the smaller absolute value from the larger absolute value.
0 plus two opposite numbers. Adding a number to 0 still gets this number. You can add two opposite numbers first. Numbers with the same sign can be added first. Numbers with the same denominator can be added first. If several numbers can be added to get an integer, they can be added first.
Second, the rational number subtraction operation
Subtracting a number is equivalent to adding the reciprocal of this number, that is, the subtraction of rational numbers is converted into addition.
Third, rational number multiplication operation
The same sign is positive, the different sign is negative, and the absolute value is multiplied. Any number multiplied by zero equals zero.
Multiply several numbers that are not equal to zero. The sign of the product is determined by the number of negative factors. When there are odd negative factors, the product is negative, and when there are even negative factors, the product is positive.
Multiply several numbers, one factor is zero and the product is zero. Multiply several numbers that are not equal to zero, first confirm the sign of the product, and then multiply by the absolute value.
Fourth, rational number division operation.
Dividing by a number that is not equal to zero is equal to multiplying the reciprocal of this number. Divide two numbers, the same sign is positive, the different sign is negative, and divide by the absolute value. Divide zero by any number that is not equal to zero to get zero.
Zero can't be a divisor and denominator. Division and multiplication of rational numbers are reciprocal operations.
In the division operation, according to the law that the same sign is positive and the different sign is negative, the sign is determined first and then divided by the absolute value. If there is a fraction in the formula, it is usually calculated by turning it into a false fraction first. If it is not divisible, all division operations are converted into multiplication operations.
Five, rational number power operation
1, the odd power of a negative number is negative, and the even power of a negative number is positive. For example, the third power of (-2) = -8.
2. Any degree of a positive number is a positive number, and any degree of a positive number is zero. For example: the second power of 2 =4.
The zeroth power of zero is meaningless.
4. Because power is a special case of multiplication, the multiplication of rational numbers can be completed by the multiplication of rational numbers.
5. The arbitrary power of 1 is 1, the even power of-1 is1and the odd power is-1.
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