Elementary school mathematics algorithm

Additive commutative law

When two numbers are added, the positions of addends are exchanged, and their sum is unchanged, that is, A+B = B+A.

associative law of addition

Add three numbers, first add the first two numbers, then add the third number; Or add the last two numbers first, and then add the first number, and their sum remains the same, that is, (a+b)+c=a+(b+c).

Commutative law of multiplication

When two numbers are multiplied, the position of the exchange factor remains unchanged, that is, a× b = b× a.

Multiplicative associative law

Multiply three numbers, first multiply the first two numbers and then multiply the third number; Or multiply the last two numbers first, and then multiply them with the first number, and their products are unchanged, that is, (a×b)×c=a×(b×c).

Powder companion

When the sum of two numbers is multiplied by a number, you can multiply the two addends by this number, and then add the two products, that is, (a+b) × c = a× c+b× c.

The essence of subtraction

If you subtract several numbers from a number continuously, you can subtract the sum of all subtractions from this number, and the difference remains unchanged, that is, a-b-c=a-(b+c).

algorithm

Integer addition calculation rule

The same numbers are aligned from the low order. When the numbers add up to ten, they will advance to the previous number.

Calculation rules of integer subtraction

The same numbers are aligned from the lower number. If the number of digits is not reduced enough, the number of digits from the last digit is reduced by ten, and then it is combined with the number of digits in the radix and then reduced.

Calculation rules of integer multiplication

First, multiply the number on each bit of one factor by the number on each bit of another factor, then multiply the number on which bit of the factor, align the end of the multiplied number with which bit, and then add the multiplied numbers.

Calculation rules of integer division

Divide from the high order of the dividend, which is a few digits, depending on the first few digits of the dividend; If the division is not enough, look at another place and the quotient is written on the dividend. If any number is not quotient 1, a "0" placeholder should be added. The remainder of each division should be less than the divisor.

Decimal multiplication rule

First, calculate the product according to the calculation rules of integer multiplication, and then look at the factor * * *, how many decimal places there are, just count a few from the right side of the product and point to the decimal point; If the number of digits is not enough, make up with "0".

Calculation rules of fractional division with divisor as integer

First of all, according to the law of integer division, the decimal point of quotient should be aligned with the decimal point of dividend; If there is a remainder at the end of the dividend, add "0" after the remainder to continue the division.

? Divider is a calculation rule of fractional division.

First, move the decimal point of the divisor to make it an integer, then move the decimal point of the divisor to the right by several digits (the number of digits is not enough, make up "0"), and then calculate according to the division rule that the divisor is an integer.

Calculation method of addition and subtraction of fractions with the same denominator

Add and subtract fractions with denominator, only add and subtract numerators, and the denominator remains the same.

Calculation method of addition and subtraction of fractions with different denominators

Divide first, and then calculate according to the addition and subtraction law of fractions with the same denominator.

? Fraction addition and subtraction calculation method

Add and subtract the integer part and the decimal part respectively, and then combine the obtained numbers.

? Calculation rules of fractional multiplication

Fractions are multiplied by integers, and the product of the multiplication of fractions and integers is taken as the numerator, and the denominator remains unchanged; Fractions are multiplied by fractions, the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator.

Calculation rules of fractional division

The number A divided by the number B (except 0) is equal to the reciprocal of the number A multiplied by the number B.