Unit 1 Decimal Multiplication

1, decimal times integer: meaning-a simple operation to find the sum of several identical addends. For example, 1.5×3 indicates how many times 1.5 or how many three 1.5 are. Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; Look at a factor * * *, how many decimal places there are, and count the decimal points from the right side of the product.

2. Decimal multiplied by decimal: meaning-that is, what is the fraction of this number. For example, 1.5×0.8 (the integer part is 0) is to find eight tenths of 1.5. 1.5× 1.8 (integer part is not 0) is 1.8 times of 1.5.

Calculation method: first expand the decimal into an integer; Calculate the product according to the law of integer multiplication; Look at a factor * * *, how many decimal places there are, and count the decimal points from the right side of the product. Note: In the calculation results, the 0 at the end of the decimal part should be removed, and when the decimal part is not enough, it should be occupied by 0.

3. Rule: a number (except 0) is multiplied by a number greater than 1, and the product is greater than the original number; A number (except 0) is multiplied by a number less than 1, and the product is less than the original number.

4. There are generally three methods to find the divisor: rounding method; Become law; Tailing method.

5. Calculate the amount of money and keep two decimal places, indicating that the calculation is completed. Keep one decimal place, indicating that the angle has been calculated.

6. The order of four decimal operations is the same as that of integers.

7. Arithmetic rules and properties: additive commutative law: a+b=b+a additive associative law: (a+b)+c=a+(b+c) multiplicative commutative law: a×b=b×a multiplicative associative law: (a×b)×c=a×(b×c) multiplicative distribution.

Subtraction: Subtraction property: a-b-c=a-(b+c) Division: Division property: a \b \c = a \b×c c.

8. In order to determine the position of an object, you need to use several pairs (first column: vertical, then horizontal). Two problems can be solved by using number pairs: first, given a number pair, the point where the object is located is marked on the way of coordinates. The second is to give a point in the coordinates, which can be expressed by several pairs.

9. Significance of fractional division: Know the product of two factors and one of them, and find the operation of the other factor. For example, 0.6÷0.3 means that the product of two known factors is 0.6, one factor is 0.3, and what is the other factor?

10, the calculation method of decimal divided by integer: decimal divided by integer, and then divided by integer. The decimal point of quotient should be aligned with the decimal point of dividend. The integer part is not divided enough, quotient 0, decimal point. If there is a remainder, add 0 and divide it.

165438+ Note: If the number of digits in the dividend is not enough, make up the dividend with the 0 at the end.

12. In practical application, the quotient obtained by fractional division can also be rounded to a certain number of decimal places as needed to obtain the approximate number of quotients.

13, the change law of division: ① quotient invariance: the dividend and divisor are expanded or reduced by the same multiple at the same time (except 0), and the quotient remains unchanged. (2) The divisor is constant, the dividend is enlarged (reduced), and the quotient is enlarged (reduced). (3) The divisor is constant, the divisor decreases, but the quotient expands; The dividend is constant, the divisor is enlarged, but the quotient is reduced.

14, cyclic decimal: the decimal part of a number. Starting from a certain number, one number or several numbers appear repeatedly in turn. Such decimals are called cyclic decimals. Circular part: the decimal part of a circular decimal, which is a number that appears repeatedly in turn. For example, the period of 6.3232 is 32. Abbreviation 6.32.

15, the number of digits in the decimal part is a finite decimal, which is called a finite decimal. The number of digits in the decimal part is infinite decimal, which is called infinite decimal. Decimals are divided into finite decimal and infinite decimal.

16. There are three situations when the incident occurs: possible, impossible and certain.

17, possible events, probability. By adding the number of copies of several possible situations as the denominator and taking a single possibility as the numerator, the possibility of the corresponding event can be obtained.

18. In the formula containing letters, the multiplication sign in the middle of the letters can be recorded as ""or omitted. The plus sign, minus sign, division sign and multiplication sign between numbers cannot be omitted.

19, you can write A A or a, where a is read as the square 2a of a, which means a+a, especially 1A = A, and "1" is not written here.

20. Equation: An equation with an unknown number is called an equation (★ Conditions that the equation must meet: there must be an unknown number, and both are indispensable). The value of the unknown that makes the left and right sides of the equation equal is called the solution of the equation. The process of solving an equation is called solving an equation.

2 1, principle of solving equation: balance. The equation still holds when the left and right sides of the equation add, subtract, multiply and divide the same number (except 0) at the same time.

22. 10 quantitative relationship: addition: sum = addend+addend; One addend = sum-another addend subtraction: difference = minuend-meimei = difference+meimei = minuend-difference multiplication: product = factor × factor = product ÷ another factor division: quotient =

All equations are equations, but all equations are not necessarily equations.

24. The test process of the equation: the left side of the equation =.

25. The solution of the equation is a number; Calculation process of solving equations. = the right side of the equation, so X=… is the solution of the equation.

26. Formula: Polygon area formula Variant of area formula Square area = side length x side length S positive =aXa=a2 Known: square area.

Find side length = length x width s length =aXb Known: area and length of rectangle, width = area of bottom x height s flat =aXh Known: area and bottom of parallelogram, height h = area of s flat ÷ area of triangle = bottom x width height ÷2S 3 =aXh÷2.

Known: the area and bottom of triangle, find the height H=S 3x2 ÷ a trapezoid trapezoid area = (upper bottom+lower bottom) x height ÷2S step =(a+b)2 Known: the sum of trapezoid area and upper and lower bottom, find the height = area ×2÷ (upper bottom+lower bottom) upper bottom = area ×

When the combined figure is convex, the areas of two or three simple figures are added and calculated. When the combined pattern is concave, the largest simple pattern area is used to subtract the smaller simple pattern area for calculation.

27. Derivation of parallelogram area formula: A parallelogram can be transformed into a rectangle through cutting and translation; The length of a rectangle is equivalent to the base of a parallelogram; The width of the rectangle is equivalent to the height of the parallelogram; The area of a rectangle is equal to the area of a parallelogram, because the area of a rectangle = length times width, so the area of a parallelogram = bottom times height.

28. Derivation of triangle area formula: Two identical triangles can be rotated to form a parallelogram, and the bottom of the parallelogram is equivalent to the bottom of the triangle; The height of parallelogram is equivalent to the height of triangle; The area of parallelogram is equal to twice the area of triangle, because the area of parallelogram = base times height, so the area of triangle = base times height ÷2.

29. Derivation of trapezoidal area formula: rotation.

30. Two identical trapezoids can be combined into a parallelogram. The base of parallelogram is equivalent to the sum of the upper and lower bases of trapezoid; The height of parallelogram is equivalent to the height of trapezoid; The parallelogram area is equal to twice the trapezoid area, because the parallelogram area = bottom times height, so the trapezoid area = (upper bottom+lower bottom) times height ÷2.

3 1, the parallelogram with equal base and equal height has the same area; Triangles with equal bases and equal heights have equal areas; The area of a parallelogram with equal base and equal height is twice that of a triangle.

32. The rectangular frame is drawn as a parallelogram with a constant perimeter and a smaller area.

33. Calculation of combined graphic area: It must be converted into a simple graphic that has been learned. When the combined figure protrudes, it is divided into several simple figures with dotted lines, and the areas of the simple figures are added up for calculation. When the combined figure is concave, the largest simple figure is composed of dotted lines, and the largest simple figure area is subtracted from several smaller simple figure areas for calculation.