Addition, subtraction, multiplication and division.

Addition: add two numbers with the same sign to take the same symbol; and add up the absolute values; Add the two numbers with different signs, take the sign of the addition with the greater absolute value, and subtract the smaller absolute value from the larger absolute value.

Subtracting a number is equal to adding the opposite of the number.

Multiply (divide) two rational numbers, get positive with the same sign, get negative with different signs, and multiply (divide) the absolute values

Multiplying 0 by any number gives 0, and dividing 0 by any non-0 number gives 0Dividing by a number is equal to multiplying by the reciprocal of that number

Addition and subtraction of integer numbers:

1) To align the same digits, add or subtract the numbers on the same counting unit;

2) Whoever reaches the age of ten will advance to the previous one.

2. Calculation rules of decimal addition and subtraction:

1) Calculate the addition and subtraction of decimals, first align the decimal points of each number (that is, align the numbers on the same digit), 2) then calculate according to the rules of addition and subtraction of integer numbers, and finally align the decimal point on the horizontal line in the obtained number.

There is a 0 at the end of the decimal part of the number, and the 0 should be removed in general. ）

3. Calculation rules for addition and subtraction of fractions:

1) When the denominator is the same, only the numerator is added and subtracted, and the denominator remains unchanged;

2) When the denominator is not the same, it is necessary to divide the fraction with the same denominator first, and then add and subtract.

4. Integer multiplication rule:

1) From the right, multiply the first factor by the number on each of the second factor, and the end of the number will be aligned with which digit of the second factor is the same as which digit of the second factor;

2) Then add up the numbers that you have multiplied several times.

Multiply with 0 at the end of an integer: you can first multiply the numbers before 0, and then see how many zeros there are at the end of each factor, and add a few zeros to the end of the multiplied number. ）

5. Decimal multiplication rule:

1) Calculate the product according to the rule of integer multiplication;

2) If you look at how many decimal places there are in the factor, count the number from the right side of the number, and point to the decimal point.

3) There is 0 at the end of the decimal part of the number, and the 0 should be removed in general.

6. The law of fraction multiplication: multiply the numerator of each fraction as the numerator, and multiply the denominator of each fraction as the denominator, (that is, multiply the reciprocal of the fraction), and then reduce the fraction.

7. The division rule of integers.

1) Start from the quotient of the dividend, first see how many digits there are in the divisor, and then use the divisor to try to divide the first few digits of the dividend, if it is smaller than the divisor, try to divide by one more digit;

2) Divide to the digit of the dividend, write the quotient on that digit;

3) The remaining number after each division must be smaller than the divisor.

8. The divisor is the decimal division rule of an integer:

1) Remove according to the law of integer division, and the decimal point of the quotient should be aligned with the decimal point of the dividend;

2) If there is still a remainder at the end of the dividend, add zero after the remainder and continue dividing.

9. The divisor is the decimal division rule for decimals:

1) First look at how many decimal places there are in the divisor, move the decimal point of the dividend to the right by a few places, and make up with zero if the number is not enough;

2) Then divide by decimal division where the divisor is an integer.

10. The division rule of fractions:

1) Multiply the numerator of the dividend by the denominator of the divisor as the numerator;

2) Multiply the denominator of the dividend by the numerator of the divisor as the denominator.

The relationship between the parts of addition, subtraction, multiplication and division:

1. Add the number of additions and. and one plus and the other plus.

2. The subtracted number is subtracted and the difference is subtracted. Subtracted Difference Subtracted. The difference subtracted by the subtracted number.

3. Factor Factor product. The product of one factor is another factor.

4. The dividend quotient of the divisor. The dividend quotient is the divisor. The quotient divisor is the dividend.

Addition, subtraction, multiplication, and division are explained as follows:

1. Addition is one of the four basic operations, which refers to the calculation of combining two or more numbers and quantities into one number or quantity. The symbol for addition is the plus sign "+", and when adding, the items are connected with a plus sign.

2. Subtraction is one of the four operations, and the operation of subtracting another number from one number is called subtraction; The sum of two additions is known to be the sum of one of the additions, and the operation of finding the other addition is called subtraction. The symbol for subtraction is "-" read as a minus sign.

3. Multiplication refers to a shortcut to add up the same numbers. The result is called the product, and "x" is the multiplier sign. From a philosophical point of view, multiplication is the result of a qualitative change caused by the quantitative change of addition.

The multiplication of integers (including negative numbers), rational numbers (fractions), and real numbers is defined by the systematic generalization of this basic definition.

4. The division of two numbers is also called the ratio of two numbers. If ab=c(b≠0), the operation of finding another factor a using the product c and the factor b is division, written as c b, which is read as c divided by b (or b divided by c). where c is called the dividend, b is called the divisor, and the result a is called the quotient.

Addition, subtraction, multiplication and division are the basic four operations, in the absence of parentheses, the order of operations is multiplication and division first, then addition and subtraction.

Addition and subtraction: 1) Commutative property: a+b=b+a, a-b=-b+a(2) Associative property: a+b+c=a+(b+c), a+b-c=a+(b-c) Multiplication: (1) Commutative property, ab=ba

2) Associative law, a(bc) = (ab)c

3) Distributive property, a(b+c)=ab+ac

Division: 100 (dividend) 2 (divisor) = 50 (quotient).

Addition: Rational numbers are added, and positive ones are calculated according to formal addition and subtraction, such as: 10+2=12Negative, can be calculated by subtraction, and add a negative sign after the number, such as: 2-10=-(10-2)=-8

Subtraction: Positive is calculated according to the formal addition and subtraction, such as: 12-10=2The negative ones are as follows:1One positive and one negative, e.g. -10-2=-(10+2)=-12

2.Two negatives, e.g. -10-(-2)=-10+2=-8

The rule of changing parentheses: the parentheses are preceded by a positive sign, and the parentheses are removed, and the invariant number in the parentheses is as follows: 10+(8-3)=10+8-3

The parentheses are preceded by a negative sign, remove the parentheses, and change the number within the parentheses. For example, 10-(8-3) = 10-8+3

Multiplication: positive multiplication positive = positive, such as; 2 times 2 = 4Negative times negative = positive; e.g. -2 times -2 = 4positive multiplied by negative = negative; 2 times 2 = 4

Division: Same as the law of multiplication!

1. Explore, understand and master the arithmetic and calculation methods of dividing a number by a fraction in combination with specific problem situations, and be able to calculate correctly. 2. In the process of exploring the calculation method of dividing a number by a fraction, the basic mathematical ideas of transformation and combination of numbers and shapes are further infiltrated, so that students can feel the wonder and charm of mathematical ideas.

Commutative law of addition: a+b=b+a

Additive associative law: a+b+c=a+(b+c).

Commutative law of multiplication: a*b=b*a

Multiplicative associativity: a*b*c=a*(b*c).

Multiplicative distributive property: (a+b)*c=a*c+b*c property of subtraction: a-b-c=a-(b+c).

The property of division: a b c=a (b*c).

Sibling operations from left to right (from left to right) Heterogeneous operations are counted from two to one (second level operations are counted first, then first level 1 operations, for level 2, + is level 1) with parentheses first inside and then outside (first count the ones in parentheses, then count outside the brackets).

Addition and subtraction, multiplication and division Addition + addition = sum.

Addition = sum - another addition sum = addition + addition subtraction - subtraction = difference subtraction = subtraction - subtraction difference = subtraction - subtraction subtraction = difference + subtraction factor factor = product.

Factor = Product Another Factor Product = Factor Factor Dividend Divisor = Quotient Divisor = Dividend Quotient Quotient = Dividend Divisor = Quotient Quotient Quotient = Dividend Quotient = Quotient Divisor.

There are parentheses that are counted as brackets first, and small brackets take precedence, and then middle brackets and then large braces.

Multiply and divide first, then add and subtract.

Only multiplication and division are preceded by the equation.

Only the addition and subtraction are calculated first.

Calculation method: The main thing to master is to remember to calculate multiplication and division first, and then addition and subtraction. In the case of multiplication and division, the calculation is performed in order from left to right.

When you encounter parentheses, you want to first calculate the inside of the parentheses. In the process of detachment, it is necessary to draw the line of the operation order according to the order of operation, and also to achieve "three checks", one is to check whether the numbers and symbols copied from the book to the homework book are correct. Second, it is necessary to check whether the numbers and symbols from horizontal copying to draft vertical copying are correct.

Third, it is necessary to check whether the number of the draft is copied vertically, whether it is copied correctly on the horizontal type, whether the decimal point is in the right place, and whether there is any omission.

Four orders of operations.

Of the four operations, addition and subtraction are called first-level operations, and multiplication and division are called second-level operations. An equation that contains two or more operations is often referred to as a hybrid operation. The mixed operations of addition, subtraction, multiplication, and division are also called four mixed operations.

In the four mixed operations, the specified order of calculations is called the order of operations. The mathematically prescribed order of four operations is as follows:

1) Sibling operations in an equation, if only sibling operations are included, they should be performed in order from left to right. That is, mixed operations with only addition and subtraction, or only multiplication and division, in the order of operation from left to right.

2) Level 1 to 2 operations.

In an equation, if there are both first-level and second-level operations, then the second-level operation should be calculated first, and then the first-level operation. That is, "multiplication and division first, then addition and subtraction", referred to as "multiplication and division first, then addition and subtraction".

3) Parenthetical operations.

If you want to change the order of operations mentioned above, you need to use parentheses. There are three commonly used parentheses: small parentheses, denoted as parentheses in ( ), denoted as [ ; Braces, denoted as When using parentheses, pull on both sides and add them in the middle.

Use parentheses first, then braces, and finally curly braces.

In an equation, if there are several parentheses, you should first calculate the multiplication or division in the parentheses, then the addition or subtraction in the parentheses, and finally the braces. When calculating, the formula inside the parentheses should be calculated in the order mentioned above, and then the resulting result should be calculated in the same order as the numbers outside the parentheses.

When addition, subtraction, multiplication and division are mixed together, multiplication and division are calculated first, and then addition and subtraction are calculated, and the order of parentheses is calculated first.

Addition, subtraction, multiplication and division are calculated first, multiplication and division are calculated first, and then addition and subtraction.

Addition, subtraction, multiplication and division are the basic four operations, and the symbol is "+ In the absence of parentheses, the order of operation is multiplication and division first, then addition and subtraction. Those with parentheses should be counted in parentheses first, and then outside the parentheses. If there are addition, subtraction, multiplication and division operations in parentheses, the multiplication and division in the parentheses are calculated first, and then the addition and subtraction in the parentheses are calculated.

1. Addition. +" is the plus sign, and the number of the sail surface before and after the plus sign is the plus number, and "= is the equal sign, and the number after the equal sign is the and.

100 (plus) + (plus) 300 (plus) = (equal to the width of the sign) 400 (and).

2. Subtraction touches.

is a minus sign, the minus sign is preceded by the subtracted number, followed by the minus number, "= is the equal sign, and the number after the equal sign is the difference.

3. Multiplication. "is a multiplier sign, and the numbers before and after the multiplication sign are called factors," = is an equal sign, and the numbers after the equal sign are called products.

10 (multiplier) 200 (factor) = (equal) 2000 (product).

4. Division. "is the division sign, the division sign is preceded by the dividend, followed by the divisor," = is the equal sign, and the number after the equal sign is the quotient.

100 (dividend) 2 (divisor) = 50 (quotient).

1000 (subtracted) - (minus) 300 (minus) = (equal to sign) 700 (difference).

Four Operations:

One. The Law of Additive Operations:

1. The two additions exchange positions, and the sum is invariant, which is called the additive commutative law.

The formula is: a+b=b+a

2. Add the first two numbers first, or add the last two numbers first, and keep invariant, which is called the law of addition and combination.

The formula of the word only travel silver mother is: (a+b) +c=a+(b+c).

Two town tours. The Law of Multiplication:

1. Swap the positions of two factors, and the product is unchanged, which is called the multiplicative commutative law.

The formula is: a+b=b+a

2. Multiply the first two numbers first, or multiply the last two numbers first, and the product remains the same, which is called the multiplicative associativity law.

The letter formula is: (a b) c=a (b c).

3. The sum of two numbers and one number refers to the multiplication, you can first multiply them with this number, and then add them, which is called the multiplicative distributive law.

The alphabetical formula is: (a+b) c=a c+b c or a (b+c) =a b+a c

Extension: (a-b) c=a c-b c

or a (b-c) = a b-a c

Three. Subtraction simple operation:

1. If you subtract two numbers from a number in a row, you can use this number to subtract the sum of these two numbers.

The letter formula is: (a b) c=a (b c).

2. If you subtract two numbers from a number in a row, you can use this number to subtract the latter number first and then subtract the previous number.

The letter formula is: a-b-c=a—c-b

Four. Simple division arithmetic:

1. A number is divided by two numbers consecutively, and this number can be divided by the product of these two numbers.

The letter formula is: (a b) c=a (b c).

2. A number is divided by two numbers consecutively, and this number can be used to divide the next number and then divide the previous number.

The letter formula is: a-b-c=a—c-b