Four Operations on Rational Numbers C Hurry!!!

Four arithmetic. In elementary mathematics, when the first-level operation (addition and subtraction) and the second-level operation (multiplication and division) appear in a formula at the same time, their order of operation is first multiplication and division, then addition and subtraction, if there are parentheses, first count the parentheses in the brackets and then count the parentheses, the same level of operation order is from left to right Such operations are called four operations,

The four rules refer to the calculation rules of addition, subtraction, multiplication, and division.

The formula for a four-rule operation does not necessarily need to have four operator symbols, and generally refers to an operation in which two or more operator symbols and parentheses are combined into a single number.

Addition: The operation of merging two numbers into one number The operation of combining two decimals into one decimal.

Subtraction: The operation of knowing the sum of two additions and one of the additions, and finding the other addition.

Multiplication: A simple operation to find the sum of several identical additions, multiplying a decimal by an integer has the same meaning as integer multiplication.

Multiplying a number by a pure decimal is to find the tenths of the number, the hundredths of the ......Multiplying fractions by integers has the same meaning as integer multiplication.

Division: Knowing the product of two factors and one of the factors, finding the other factor has the same meaning as integer division Example:

1. Multiplication: Find how many are the numbers; Find out how many multiples of a number are; Find the area and volume of the object; Find out what fractions or hundredths of a number are.

2. Division: Divide a number into several parts evenly and find several of them; Find how many other numbers there are in one number; Knowing what fractions or hundredths of a number are, find this number.

3. Addition: sum; Inverse subtraction.

4. Subtraction: find the remainder; Compare; Inverse of addition.

Addition and subtraction are inverses of each other; Multiplication and division are inverse operations; Multiplication is a simple operation of addition.

1. Addition of rational numbers.

1) Predetermined symbols;

2) The absolute value of the same sign is added; Example of subtraction (big-small) with different signs1+

2. Subtraction of rational numbers.

1) Enough to reduce quietly and correctly;

2) not enough to reduce the burden;

3) add the absolute value of the loss to the loss;

4) Negative and negative to positive or subtract and subtract to add, and convert subtraction into addition.

Example: a b = a + ( b).

3. Multiplication of rational numbers.

1) Multiplication: the same number has to be started and taken; Variant gets minus.

4. Division of rational numbers.

1) Division: Dividing by a number is equal to multiplying it by its reciprocal number, which is converted into multiplication operation. Note: 0 cannot be used as a divisor.

How important are the four operations of rational numbers.

The ability to operate rational numbers is the basis for learning algebra (which has a great impact on the learning of integers, equations, and fractions) and affects the overall performance of junior high school mathematics.

A rational number refers to the ratio of two integers. Rational numbers are a collective term for integers (positive integers, 0s, negative integers) and fractions. Positive integers and positive fractions are collectively called positive rational numbers, and negative integers and negative fractions are collectively referred to as negative rational numbers.

Definition of rational numbers

A rational number refers to the ratio of two integers. A rational number is a collection of integers and fractions. An integer can also be thought of as a fraction with a denominator of one.

The decimal part of a rational number is a finite or infinitely looping number. Positive integers and positive fractions are collectively called positive rational numbers, and negative integers and negative fractions are collectively referred to as negative rational numbers. Therefore, the number of rational numbers in the set of rational numbers can be divided into positive rational numbers, negative rational numbers, and zeros.

The addition of rational numbers

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

2.If the absolute values are equal, the sum of the two numbers of opposite numbers 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.Two numbers that are opposite to each other are added to give 0.

4.A number is added to 0 and still gives this number.

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

6.Numbers with the same sign 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.

Subtraction of rational numbers

Subtracting a number is equivalent to adding the opposite of the number, that is, the subtraction of rational numbers uses the opposite number of numbers to add for operation.

Multiplication of rational numbers

1.The same sign is positive, the different sign is negative, and the absolute values are multiplied.

2.Any number multiplied by zero gives zero.

3.Several numbers that are not equal to zero are multiplied, and the sign of the product is determined by the number of negative factors, when there are odd numbers of negative factors, the product is negative, and when there are even numbers of negative factors, the product is positive.

4.Multiply several numbers, and if there is a factor that is zero, the product is zero.

5.To multiply several numbers that are not equal to zero, first determine the sign of the product, and then multiply the absolute values.

The rules of division for rational numbers

1.Dividing by a number that is not equal to zero is equal to multiplying by the reciprocal of this number.

2.Divide the two numbers, the same sign is positive, the different sign is negative, and divide the absolute value. Zero divided by any number that is not equal to zero gives zero.

Note: Zero cannot be a divisor and denominator.

Multiplication of rational numbers

1.The odd power of a negative number is a negative number, and the even power of a negative number is a positive number. For example: (-2) (2 to the 3rd power) = -8, (-2) (2 to the 2nd power) = 4.

2.Any power of a positive number is a positive number, and any power of any positive number of zeros is zero. For example: 2 (2 to the 2nd power) = 4, 2 (2 to the 3rd power) = 8, 0 (0 to the 3rd power) = 0.

3.The power of zero is meaningless.

4.Since the power is a special case of multiplication, the power operation of rational numbers can be done with the multiplication operation of rational numbers.

Any power is 1, the even power of -1 is 1, and the odd power is -1.

commutative property of multiplication ab=ba;

Associative law of multiplication a(bc)=(ab)c;

Distributive property a(b+c)=ab+ac;

The same sign is positive, the different sign is negative, any number multiplied by 0 gives 0, and the multiplication law for integers also applies to all rational numbers.

Hey, classmates, don't bring this, so much!