Knowing that a is any rational number, try to compare the magnitude of a and 2a.

Updated on educate 2024-04-20
10 answers
  1. Anonymous users2024-02-08

    Knowing that a is any rational number, try to compare |a|With the size of -2a: |a|<-2a。

    i.e. compare |a|and the size of -2a.

    When a>0, |a|=a,-2a<0.then |a|>-2aWhen a=0, |a|=0.-2a=0.then |a|>-2aWhen a=0, |a|=-a>0.-2a>0

    a|-(2a)=-a+2a=a<0

    then |a|<-2a

    1. Add two numbers with the same sign, take the same symbol as the additive, and add the absolute value.

    2. If the absolute value is equal, the sum of the two numbers of the opposite number is 0; If the absolute values are not equal, take the sign of the addition with the greater absolute value, and subtract the smaller absolute value from the larger absolute value.

    3. Add two numbers that are opposite to each other to get 0.

    4. Add a number to 0 and still get this number.

    5. Two numbers that are opposite to each other can be added first.

    6. Numbers with the same symbol can be added first.

    7. Numbers with the same denominator can be added first.

    8. If several numbers can be added to get an integer, they can be added first.

  2. Anonymous users2024-02-07

    i.e. compare |a|and the size of -2a.

    This question needs to be discussed in a categorical manner.

    When a>0, |a|=a,-2a<0.then |a|>-2aWhen a=0, |a|=0.-2a=0.then |a|>-2aWhen a=0, |a|=-a>0.-2a>0

    a|-(2a)=-a+2a=a<0

    then |a|<-2a

  3. Anonymous users2024-02-06

    |a|Always a positive number, a can be a positive number, it can also be a negative number, 1, a 0, |a|=a,-2a=-2a,|a|>-2a,2、a<0,|a|=-a, -2a=-2a, is positive, -2a |a|,3、a=0,-2a=|a|。

    Rational numbers are a collective term for integers (positive integers, 0s, negative integers) and fractions, and are a collection of integers and fractions, i.e., the decimal part of a rational number is a finite or infinite cyclic decimal number.

    Rational numbers correspond to irrational numbers (real numbers that are not rational numbers are called irrational numbers), and their decimal parts are infinite non-cyclic numbers. Rational numbers are one of the important contents in the field of "number and algebra", and they are also widely used in real life, which is the basis for continuing to learn real numbers, algebraic formulas, equations, inequalities, Cartesian coordinate systems, functions, statistics and other mathematical content and related subject knowledge.

  4. Anonymous users2024-02-05

    a>0 |a|Must be greater than zero.

    2a must be less than zero so |a|When >-2aa=0, both are of the same size.

    a>0 |a|must be greater than zero, and -2a must also be greater than zero, so the point is to compare the magnitude of the two at a<0.

    It is now known that a<0

    Then the two formulas can be reduced to Compare |a| |2a|The size of the obvious in a rational number |2a| >a|Therefore a<0 -2a>|a|

    To sum up: a>0 |a|When >-2aa=0, both are of the same size.

    a<0 -2a>|a|

  5. Anonymous users2024-02-04

    When a>0, |a|-(2a)=-a+2a=a<0, so |a|<-2a;

    When a>0, |a|-(2a)=0, so |a|=-2a;

    When a>0, |a|-(2a)=a+2a=3a 0, so |a|>-2a;

  6. Anonymous users2024-02-03

    a|It is always a positive number, a may be a positive number, or the nucleus will be negative.

    1、a>0,|a|=a,-2a=-2a

    a|>-2a

    2, a hall brother 0, |a|=-a, -2a=-2a, are positive numbers.

    2a>|a|

    3. False excavation a=0

    2a=|a|

  7. Anonymous users2024-02-02

    i.e. compare |a|and -2a size scale.

    This topic needs to be discussed by category.

    When the car is hidden a>0, |a|=a,-2a-2a

    When a>0, |a|=0.-2a=0.then |a|=-2a when a0-2a>0

    a|-(2a)=-a+2a=a

  8. Anonymous users2024-02-01

    Rational numbers include positive and negative numbers, as well as 0

    So it is discussed in three situations.

    a 0 a a

    a 0 a a

    a 0 a a

  9. Anonymous users2024-01-31

    When a is a positive number, a > a

    When it is 0, a = a

    When negative, a< a

  10. Anonymous users2024-01-30

    i.e. compare |a|and the size of -2a.

    This question needs to be discussed in a categorical manner.

    When a>0, |a|=a,-2a<0.then |a|>-2aWhen a=0, |a|=0.-2a=0.

    then |a|=-2aWhen a<0, the bridge trace, |a|=-a>0.-2a>0a|-(2a)=-a+2a=a<0

    then |a|"Dissipation-2a

Related questions
11 answers2024-04-20

1. Rational numbers can be divided into integers and fractions can also be divided into three types: one; positive, two; 0,three; Negative number. Real numbers other than infinite non-cyclic decimals are collectively referred to as rational numbers. >>>More

9 answers2024-04-20

1. When m is greater than 0, (n+3) 2+|m|=m becomes (n+3) 2-m=m, i.e., n+3) 2=0 >>>More

10 answers2024-04-20

In the range of real numbers, can it be expressed as a fraction to distinguish between rational and irrational numbers? For example, the integer 3 can be expressed as 3 1, the fraction 3 4 (can also be expressed as a finite decimal), and the fraction 1 3 (can also be expressed as an infinite cyclic decimal number, in short, they can all be expressed as fractions, called rational numbers. However, the root number 2, pi, and the natural constant e, none of these numbers can be expressed as fractions (they are all infinite non-cyclic decimals), and they are called irrational numbers. >>>More

13 answers2024-04-20

Number of fieldsTo put it simply, a set of 0s and 1s is closed to the four operations (the result of the computation still belongs to this set). >>>More

10 answers2024-04-20

This question may seem complicated, but it is not difficult to solve it step by step. >>>More