Multiplication of decimals and multiplication of integers
Publish: 2021-04-23 04:11:51
1. What's the difference between decimal multiplication and integer multiplication
the meaning of multiplying a number by a decimal is different from that of integer multiplication. It is a further extension of the meaning of integer multiplication. It can be understood as how many tenths, percentages, thousandths... Of the number. For example, 2.5 × 0.6 means what is six tenths of 2.5, 2.5 × 0.98 is the 98 percent of 2.5.
summarizes how to master the multiplication and division of decimals.
when a decimal is multiplied by an integer, first calculate the proct according to the integer multiplication rule, and then look at how many decimals there are in the multiplicand, count out a few digits from the right side of the proct, and point the decimal point.
divisor is the decimal division of an integer:
(1) remove according to the integer division rule, The decimal point of quotient should be aligned with the decimal point of divisor 2) If there is a remainder at the end of the divisor, fill in zero after the remainder, and then continue to divide.
divisor is a decimal division of decimals:
(1) first look at how many decimals there are in the divisor, then move the decimal point of the divisor to the right several places, if there are not enough places, use zero to make up 2) Then divide the object according to the decimal division of integer divisor
1. Know that the shape of the observed object is different in different positions.
2. Correctly identify the shape of the simple object observed from the front, side and back
the meaning of multiplying a number by a decimal is different from that of integer multiplication. It is a further extension of the meaning of integer multiplication. It can be understood as how many tenths, percentages, thousandths... Of the number. For example, 2.5 × 0.6 means what is six tenths of 2.5, 2.5 × 0.98 is the 98 percent of 2.5.
summarizes how to master the multiplication and division of decimals.
when a decimal is multiplied by an integer, first calculate the proct according to the integer multiplication rule, and then look at how many decimals there are in the multiplicand, count out a few digits from the right side of the proct, and point the decimal point.
divisor is the decimal division of an integer:
(1) remove according to the integer division rule, The decimal point of quotient should be aligned with the decimal point of divisor 2) If there is a remainder at the end of the divisor, fill in zero after the remainder, and then continue to divide.
divisor is a decimal division of decimals:
(1) first look at how many decimals there are in the divisor, then move the decimal point of the divisor to the right several places, if there are not enough places, use zero to make up 2) Then divide the object according to the decimal division of integer divisor
1. Know that the shape of the observed object is different in different positions.
2. Correctly identify the shape of the simple object observed from the front, side and back
2. The same points: 1. Decimal multiplication and integer multiplication algorithm is the same. 2. The operation order is the same (from right to left). Differences: 1. Decimal multiplication factor end alignment, integer multiplication factor alignment. 2. The decimal point should be added in the calculation of decimal multiplication.
3.
It's not the same
the meaning of multiplying decimal by integer is the same as that of integer multiplication, but the meaning of multiplying decimal by decimal is different from that of integer multiplication
Multiplication of decimal by integer: it has the same meaning as multiplication of integer, which is a simple operation to find the sum of several identical addendsthe meaning of multiplying a number by a decimal: different from the meaning of integer multiplication, it is a further extension of the meaning of integer multiplication. It can be understood as how many tenths, percentages, thousandths... Of the number are
extended data:
calculation method of multiplying decimal by decimal:
(1) expand decimal to integer first
(2) calculate the proct according to the rule of integer multiplication(3) if you look at how many decimal places there are in the factor, you can count the decimal points from the right side of the proct. When the number of decimal places of the proct is not enough, make up the decimal point with 0
note: in the calculation result, the 0 at the end of the decimal part should be removed to simplify the decimal part; When the number of decimal places is not enough, use 0 to occupy the place
significance of decimal division: the significance of decimal division is the same as that of integer division, which is the operation of finding another factor by knowing the proct of two factors and one of them
4. Multiplication can be done according to the integer multiplication, and then add the decimal places of two numbers to get the decimal places of the proct
in division, the decimal points of two numbers are shifted to the right at the same time to become integer division.
in division, the decimal points of two numbers are shifted to the right at the same time to become integer division.
5. After multiplication, add the decimal places of the two numbers to get the decimal places of the proct.
in division, move the decimal points of the two numbers to the right at the same time to become integer division
in division, move the decimal points of the two numbers to the right at the same time to become integer division
6. The same point is: the decimal multiplication and division method and the integer multiplication and division method are done according to the integer multiplication and division method; The difference is that after the multiplication of decimals to calculate the proct, we need to see how many decimals there are in the factor, so we can count out the number of decimals from the right side of the number, and point the decimal point; Before you divide a decimal, you must first change the divisor into an integer. Note: decimal multiplication: align the last place, multiply according to the integer multiplication, after calculating the proct, to see how many decimal places there are in the factor, count out a few decimal places from the right side of the number, and point the decimal point. Note: decimal multiplication: align the last place, multiply according to the integer multiplication, after calculating the proct, to see how many decimal places there are in the factor, count out a few decimal places from the right side of the number, and point the decimal point
note for decimal division: first expand the divisor to an integer, and the divisor will also expand the corresponding multiple. The decimal point of the quotient should be aligned with the decimal point of the divisor. The quotient is written on the top of the division, and the remainder is smaller than the divisor. If you want to see if this step has been divided, it depends on whether there is quotient and remainder in this step. In addition, we need to take the decimal point up first, and take down the number to which place we divide it.
note for decimal division: first expand the divisor to an integer, and the divisor will also expand the corresponding multiple. The decimal point of the quotient should be aligned with the decimal point of the divisor. The quotient is written on the top of the division, and the remainder is smaller than the divisor. If you want to see if this step has been divided, it depends on whether there is quotient and remainder in this step. In addition, we need to take the decimal point up first, and take down the number to which place we divide it.
7. The meaning of decimal multiplication: (the old teaching materials are separated for reference)
(1) decimal multiplication by integer: the same meaning as integer multiplication, which is a simple operation to find the sum of several identical addends. For example: 2.5 × 6
denotes the sum of 6 2.5 or 6 times of 2.5.
(2) the meaning of multiplying a number by a decimal is different from that of integer multiplication. It is a further extension of the meaning of integer multiplication. It can be understood as how many tenths, percentages, thousandths... Of the number. For example, 2.5 × 0.6 means what is six tenths of 2.5, 2.5 × 0.98 means 98% of 2.5
(1) decimal multiplication by integer: the same meaning as integer multiplication, which is a simple operation to find the sum of several identical addends. For example: 2.5 × 6
denotes the sum of 6 2.5 or 6 times of 2.5.
(2) the meaning of multiplying a number by a decimal is different from that of integer multiplication. It is a further extension of the meaning of integer multiplication. It can be understood as how many tenths, percentages, thousandths... Of the number. For example, 2.5 × 0.6 means what is six tenths of 2.5, 2.5 × 0.98 means 98% of 2.5
8. Multiplication can be done according to the integer multiplication, and then add the decimal places of two numbers to get the decimal places of the proct
in division, the decimal points of two numbers are shifted to the right at the same time to become integer division
integer multiplication rule:
1) from the right, multiply the number on each bit of the second factor by the first factor, and the end of the number will be aligned with which bit of the second factor to which bit of the first factor
2) then add up the multiplications
(multiplication of 0 at the end of an integer: you can multiply the number before 0 first, and then see how many zeros there are at the end of each factor, and then add several zeros at the end of the multiplied number.)
decimal multiplication rule:
1) calculate the proct according to the rule of integer multiplication
2) if you look at how many decimal places there are in the factor, you can count the decimal places from the right side of the number
3) there is a 0 at the end of the decimal part of the number, so it is generally necessary to remove the 0
division rules of integers
1) starting from the quotient of the divisor, first look at how many digits the divisor has, and then try to divide the first few digits of the divisor by the divisor. If it is smaller than the divisor, try to divide more digits
2) write the quotient on the divisor
3) after each division, the remaining number must be smaller than the divisor
8. Divisor is the decimal division rule of integer:
1) according to the rule of integer division, the decimal point of quotient should be aligned with the decimal point of divisor
2) if there is a remainder at the end of the divisor, fill in zero after the remainder, and then continue to divide.
in division, the decimal points of two numbers are shifted to the right at the same time to become integer division
integer multiplication rule:
1) from the right, multiply the number on each bit of the second factor by the first factor, and the end of the number will be aligned with which bit of the second factor to which bit of the first factor
2) then add up the multiplications
(multiplication of 0 at the end of an integer: you can multiply the number before 0 first, and then see how many zeros there are at the end of each factor, and then add several zeros at the end of the multiplied number.)
decimal multiplication rule:
1) calculate the proct according to the rule of integer multiplication
2) if you look at how many decimal places there are in the factor, you can count the decimal places from the right side of the number
3) there is a 0 at the end of the decimal part of the number, so it is generally necessary to remove the 0
division rules of integers
1) starting from the quotient of the divisor, first look at how many digits the divisor has, and then try to divide the first few digits of the divisor by the divisor. If it is smaller than the divisor, try to divide more digits
2) write the quotient on the divisor
3) after each division, the remaining number must be smaller than the divisor
8. Divisor is the decimal division rule of integer:
1) according to the rule of integer division, the decimal point of quotient should be aligned with the decimal point of divisor
2) if there is a remainder at the end of the divisor, fill in zero after the remainder, and then continue to divide.
9. Decimal multiplication is the same as integer multiplication. The method is the same, except that the multiplier and multiplicee of primary multiplication have several decimal places in total. We should count several decimal places from right to left in the proct and point the decimal point. Fractional multiplication is the multiplication of the numerator by the numerator, the multiplication of the denominator by the denominator by the denominator, and finally the simplest fraction.
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