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Mathematics Chapter 1 Rational Numbers
Chapter 1 of Mathematics organizes the knowledge of rational numbers. Positive numbers, 0, and negative numbers are collectively called rational numbers; positive and negative fractions are collectively called fractions. The chapter focuses on mastering scientific notation, powers of rational numbers, and the operation knowledge of rational numbers.
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Mathematics Chapter 1 Rational Numbers
- bacteria
This is a mind map about bacteria, and its main contents include: overview, morphology, types, structure, reproduction, distribution, application, and expansion. The summary is comprehensive and meticulous, suitable as review materials.
- Plant asexual reproduction
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- Reproductive development of animals
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number study No. one chapter have reason number
The concept of rational numbers
Positive and negative numbers
A number with a negative sign (-) in front of a positive number is called an integer
0 is neither a positive number. Nor is it a negative number
0 can mean "baseline" and "none"
If quantities with opposite meanings appear in a problem, we can use positive numbers and negative numbers to represent them respectively.
Generally speaking, north (east), rise, increase, income, etc. are regarded as positive numbers, and vice versa as negative numbers.
rational numbers
Positive numbers, 0, and negative numbers are collectively called rational numbers; positive fractions and negative fractions are collectively called fractions
Classification
by symbol
have reason number
positive rational numbers
positive score
positive integer
0
negative rational numbers
negative fraction
negative integer
According to the law
have reason number
Fraction
positive score
negative fraction
A positive number
Negative and positive numbers
negative fraction
axis
Three elements
The origin is usually represented by the letter O
direction
Positive direction
It is specified that the positive direction on a straight line is from the origin to the right (or up).
negative direction
Specifies that the negative direction on a straight line is from the origin to the left (or down).
unit length
Select the appropriate length as the unit length
On the straight line from the origin to the right, take a point every other unit length, and thus represent 1, 2, 3, 4...
From the origin to the left on the straight line, take a point every other unit length, and thus represent -1, -2, -3, -4...
0 is the dividing point between positive and negative numbers; the circle point is also the reference point of the number axis
Opposite number
Add the "-" sign in front of a positive number to get the opposite of the positive number.
Add a "-" sign in front of any number, and the new number represents the opposite of the original number.
Like 2 and -2, 5 and -5, two numbers with only different signs are called opposite numbers.
The opposite of 0 is 0
Add 2 opposite numbers and the sum is 0
absolute value
The distance between the point representing the number a and the origin on the general number axis is called the absolute value of a, denoted as |a|
The absolute value of a positive number is itself, the absolute value of a negative number is its opposite, and the absolute value of 0 is 0
Comparison of size
When comparing two numbers with different signs, consider their positive and negative values; when comparing two numbers with the same sign, consider their absolute values.
Positive numbers are greater than 0, 0 is greater than negative numbers, positive numbers are greater than negative numbers
2 negative numbers, the one with a larger absolute value is smaller.
Scientific notation
Express a number greater than 10 in the form of a¹⁰ (where a is greater than or equal to 1 and less than 10, n is a positive number), using scientific notation
Power of rational numbers
The operation of finding the product of n identical factors is called exponentiation, and the result of exponentiation is called power. In aⁿ, a is called the base, and n is called the exponent. When aⁿth power is regarded as the result of a raised to the nth power, it can be read as "a raised to the nth power"
First multiply, then multiply and divide, then add and subtract
Odd, negative, even positive (exponent and base is negative)
2²=4 2³=8 2⁴=16 2⁵=32 ...
Operations with rational numbers
addition
To add two numbers with the same sign, take the same sign and add the absolute values.
To add two places with different signs whose 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.
If you add a number to 0, you still get this number
Subtraction
Subtracting a number is equivalent to adding the opposite of the number, such as a-b=b (-a)
multiplication
When a positive number is multiplied by a positive number, the product is positive; when a positive number is multiplied by a negative number, the product is negative; when a negative number is multiplied by a positive number, the product is also negative; the absolute value of the product is equal to the product of the absolute values of the multipliers.
Multiply the two books, the same sign will be positive, and the different signs will be negative, and multiply the absolute values (negative and negative will be positive)
Any number multiplied by 0 gets 0
Odd, negative, even positive (multiplier is not 0)
division
Dividing by a number that is not equal to 0 is equivalent to multiplying the reciprocal of that number
When dividing two numbers, if they have the same sign, they will get a positive result, if they have different signs, they will get a negative result, and divide the absolute value; 0 divided by any number that is not equal to 0 will get 0