I. 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 to simplify the decimal; When the number of decimal places is not enough, use 0 to occupy the place.
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 usually three ways to find the approximate value:
(1) rounding method; (2) into law; (3) Tailing method
5. Calculate the amount of money, and keep two decimal places, indicating that the calculation has reached the point. 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, operation law and nature:
Addition: additive commutative law: a+b=b+a Addition Law: (a+b)+c=a+(b+c).
Multiplication: multiplication commutative law: a× b = b× a.
The law of multiplicative association: (a×b)×c = a×(b×c)4 or 0.4 see 2.5, 8 or 0.8 see 1.25.
Multiplication and distribution law: (a+b)×c=a×c+b×c or a×c+b×c=(a+b)×c(b= 1, b) omitted.
Variants: (a-b)×c=a×c-b×c or a× c-b× c = (a-b )× c.
Subtraction: Subtraction property: a-b-c=a-(b+c)
Division: nature of division: a÷b÷c=a÷(b×c)
Second, the area of the polygon.
1, formula
Rectangular: perimeter = (length+width) × 2; Area = length × width;
Square: perimeter = side length × 4; Area = side length × side length;
Parallelogram: area = base × height;
Triangle: area = base × height ÷ 2;
Trapezoid: area = (upper bottom+lower bottom) × height ÷ 2;
2, the method of unit conversion
Larger and smaller, multiplication rate; From small to large, divided by the forward speed.
3, the ratio between commonly used units
1 km = 1 000m1m = 10 decimeter.
1 decimeter = 1 0cm1cm =10mm
1 km2 = 1 00ha1hectare =10000m2
1 m2 = 100 square decimeter 1 square decimeter = 100 square centimeter
4, the relationship between graphics
(1), parallelogram can be transformed into rectangle; Two identical triangles can form a parallelogram. Two identical trapezoids can be combined into a parallelogram.
(2) The parallelogram with equal base and equal height has the same area; The area of a triangle with equal base and height is equal.
(3) The area of a parallelogram with equal base and equal height is twice that of a triangle. If a triangle and a parallelogram have the same area and the same base, the height of the triangle is twice that of the parallelogram. If the area and height of triangle and parallelogram are equal, the base of triangle is twice that of parallelogram.
(4) Draw the rectangular frame into a parallelogram with the same perimeter and smaller area.
5. Find the method of combining graphic regions
(1) Observe carefully to determine which basic graphics can be divided or supplemented into which areas can be calculated.
(2) Find out the data needed to calculate these basic graphic areas.
(3) Calculate the areas of these basic figures respectively, and then add and subtract.