I. Decimal multiplication

1, the calculation rule of decimal multiplication: first calculate the product by integer multiplication, and then put the decimal point on the product point. (how to point the decimal point? ) Look at a factor * * *, how many decimal places there are, just count a few from the right side of the product and point to the decimal point. There are not enough decimal places in the product. How to point to the decimal point? ) add 0 in front of it, and then point the decimal point.

2. Law of product change caused by factor change:

If one factor remains the same, another factor will expand (or shrink) several times, and the product will also expand (or shrink) the same multiple.

(2) The two factors are expanded at the same time by a certain multiple, and the product expansion multiple is equal to the product of the two factors multiplied by the multiple. For example, the first factor is expanded 5 times, the second factor is expanded 10 times, and the product is expanded (5× 10=50 times).

③ When one factor contracts and the other factor expands, it depends on whether the multiple of contraction is larger or the multiple of expansion is larger. The greater the shrinkage, the smaller the product. If the expansion ratio is large, the product will expand. The multiple of contraction or expansion is equal to the quotient of large number divided by decimal number.

For example, one factor is reduced by 20 times and the other factor is increased by 10 times. Because 20 > 10, the product decreases, and it decreases (20÷ 10=2 times). Another example is that one factor is expanded by 30 times and the other factor is reduced by 6 times, because 30 > 6000.

3, the size of the factors and the relationship between the product:

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.

Second, fractional division.

1, the calculation rule of dividing decimal by integer: ① Divide by integer; ② The decimal point of quotient should be aligned with the decimal point of dividend; ③ The integer part is not divided enough, the quotient is 0, and the decimal point; If there is a remainder, add 0 and divide it.

2. Calculation rules for dividing a number into decimals: first move the decimal point of the divisor to make it an integer, move the decimal point of the divisor to the right by several digits, and move the decimal point of the dividend by several digits to the right. When the number of digits of the dividend is not enough, it shall be supplemented by 0 at the end of the dividend, and then calculated by fractional division with the divisor as an integer.

3. The changing law of dividend, divisor and quotient;

(1) The dividend and divisor are multiplied (or divided) by the same number (except 0) at the same time, and the quotient remains unchanged;

(2) The dividend is constant. If the divisor is expanded (or reduced) several times, the quotient will also be reduced (or expanded) by the same multiple;

(3) If the divisor remains the same, the dividend will be expanded (or reduced) several times, and the quotient will also be expanded (or reduced) by the same multiple.

4. The relationship between dividend and business:

Divide a number (except 0) by a number greater than 1, and the quotient is less than the dividend;

Divide a number (except 0) by a number less than 1 (except 0), and the quotient is greater than the dividend.

5. The decimal part of a number, starting from a certain number, and one or several numbers appear repeatedly in turn, is called cyclic decimal. The fractional part of the cyclic decimal, which appears repeatedly in turn, is called the cyclic segment of this cyclic decimal.

6. 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.

7. Digital black hole refers to the situation that natural numbers fall into a cycle after some operation.

Third, the object of observation

1. When observing an object, you can see at most three faces and at least one face at a time.

Fourth, simple equations.

1, the algorithm is expressed in letters:

Additive commutative law: a+b=b+a Addition Law: (a+b)+c= a+(b+c)

Multiplicative commutative law: ab=ba Multiplicative associative law: (ab)c= a(bc)

Multiplication and distribution law: (a+b)c= ac+bc

2. Use letters to express the formula:

Circumference of a square: C= 4a Area of a square: S=a2.

Circumference of rectangle: C=2(a+b) Area of rectangle: S=ab.

3. An equation with unknowns is called an equation. 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.

4, the relationship between the four parts of the operation:

(1), addend+addend = addend = and-another addend.

(2), minuend-minuend = difference minuend = difference+minuend = minuend-difference.

(3), factor x factor = product factor = product ÷ another factor.

(4), dividend/divisor = quotient dividend = quotient x divisor = dividend/quotient

5, the main steps to solve the problem of column equation:

(1) Write the solution and set it; (2) Find out the equal relationship between the quantities in the questions; (3) List the equations according to the equivalence relation;

④ Solving the equation; ⑤ Test and answer.

Example: 6 x = 3.5

6—x+x=3.5+x

3.5+x=6

3.5+x—3.5=6—3.5

X=2.5

Verb (abbreviation for verb) The area of a polygon.

1, the area of parallelogram = base × height is represented by letters: S=ah.

The base = area ÷ height of parallelogram is expressed in letters: a = s ÷ h.

The height = area ÷ base of parallelogram is represented by letters: h = s ÷ a.

(Parallelograms with equal bases and equal heights have equal areas)

2. The area of triangle = base × height ÷2 is represented by letters: S=ah÷2.

The base of a triangle = area ×2÷ height is represented by letters: a = 2s ÷ h.

The height of triangle = area ×2÷ The base is represented by letters: H = 2s ÷ a..

(Triangles with equal bases and equal heights have equal areas)

3. A triangle is half the area of a parallelogram with equal base and equal height;

If the product (area) of triangle and parallelogram are equal, the height is twice that of parallelogram;

If the equal product (area) of triangle and parallelogram is high, the base is twice that of parallelogram.

4. Trapezoidal area = (upper bottom+lower bottom) × height÷ 2 is expressed by letters: S=(a+b)h÷2.

The height of trapezoid = area ×2÷ (upper bottom+lower bottom) is expressed by letters: h =2 S ÷(a+b).

The upper bottom of the trapezoid = area ×2 ÷ height-the lower bottom is represented by letters: a = 2s ÷ h-b.

Trapezoidal bottom = area ×2 ÷ height-the upper bottom is represented by letters: b = 2s ÷ h-a.

5. Calculation formula for the number of logs and steel pipes:

Total number of roots = (number of top roots+number of bottom roots) × number of layers ÷2

Number of layers = number of roots at the bottom-number of roots at the top+1

Statistics and possibility of intransitive verbs

1. Arrange a set of data from small to large (or from large to small) in turn, and the middle number (or the average of the two most intermediate data) is the median of this set of data. The advantage of median is that it is not affected by too large or too small data.

2. Paving on a plane without overlapping or gaps is called dense paving. Common patterns that can be densely laid include triangle, rectangle, square, trapezoid, regular hexagon and so on. , but can't be densely covered, including circles and regular pentagons.

Fill in the blanks.

1.2 hours = () minutes 0.208m = () cm

3500kg = () tons, 4m, 5cm = () meters.

860 square centimeters = () square decimeter = 5.03 hectares = () square meters.

0.28 square meters = () square decimeter 3 meters 4 centimeters = () meters.

4 jiao = () yuan 3 meters 5 cm = () meters

0.58m2 = () square decimeter 6005g = () kilogram () gram.

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 greater than the original number ().

Divide a number (except 0) by a number greater than 1, and the quotient is greater than the original number ().

Divide a number (except 0) by a number less than 1, and the quotient is greater than the original number ().

7.8÷0. 1○7.8 3.5×7.28○7.28 2.7○2.7÷0.8

15×0.6○ 15× 1 3.6÷ 1.2○3.6 0.82×0.99○0.82

3.57÷ 1.05○3.57 5.85÷0.9○5.85 2.75× 1.0 1○2.75

4.95÷0.9○4.95 1× 1.009○ 1.009 3.6× 1.45○3.6

When an object is on the table, we can see at most () faces from different angles, and at least () faces.

Use a, b and c to represent three numbers, and write the law of addition and association ().

Use a, b and c to represent three numbers, and write the multiplication and division method ().

A story book has 98 pages, averaging x pages a day. Six days later, there are () pages left.

You can definitely spell a () with two identical right triangles.

The area of triangle is 24 square meters, and the area of parallelogram with equal base and equal height is () square meters.

The area of the trapezoid is 50 square decimeters, the sum of the upper and lower bottoms is 16 meters, and the height is ().

The base of the parallelogram is 6.5 meters, the height is 4 meters, and the area of the triangle with the same height as the base is () square meters.

The price of the math contest is one yuan, so you should pay () yuan for five such books.

9.954 keep a decimal place is ().

First, think about it. I'll fill it out. (20 points)

The product of 1 and 5.04×2. 1 is () decimal place, and the quotient of 22.6÷0.33 is about ().

2. One decimal place () and two decimal places () will be reserved.

Please fill in ""or "=" in the box below.

3.25×0.98 3.25 A ÷0.97 A (A≠0)

0.75 ÷ 0.5 0.75× 24. A classmate's ID number is 510402199703155221. This classmate was born on () of (), and her gender is ().

5. Kobayashi buys four pens, one yuan each; I bought five more exercise books at B yuan each. The amount of money paid by a * * * can be expressed by formula (); When a = 0.5 and b = 1.2, Party A * * * shall pay RMB ().

6. Move the decimal point of a decimal to the right by two places to get a new number. The difference between this new number and the original number is 44.55, and the original number is ().

7. Master Wang processes one part and 20 parts in 5 minutes. On average, Master Wang takes () minutes to process 1 part, and 1 minute can process () such parts.

8. The three sides of a right triangle are 3 cm, 4 cm and 5 cm respectively, and the area of this right triangle is () square cm.

9. The upper bottom, lower bottom and height of the right-angled trapezoid are 10dm, 12dm and 8dm respectively, and its area is () square decimeter; Draw the largest square in the trapezoid, and the area of the square is () square decimeter.

10. There are six balls in the box, which are marked with the numbers 1, 2, 3, 4, 5 and 6 respectively. Touch any one, there are () possibilities, the possibility of each result is (), the possibility of being singular is (), and the possibility of being less than 3 is ().

1, 2.5 hectares = () m2, 2300 cm2 = () m2.

8050g = () Kg 160m2 = () square decimeter = () square meter.

2. The product of1.36× 0.2 has () decimal places.

3. The business cycle decimal of11÷ 6 is (), and the exact percentile is ().

4. If the circumference of an equilateral triangle is one meter, then the length of each side is () meters.

5. When A = 4, B = 0.3, and C = 5, the value of c÷a-b+C is (), and that of c÷a-b is ().

6. Fill in >, 70

2. Two trapezoids () can be combined into a parallelogram.

A, identical B, equal area C, equal bottom and equal height

Xiao Qiang is one year old, Xiaohong is two years older than Xiao Qiang, and Xiao Qiang is () years younger than Xiaohong in three years.

A, (a-3) years old B, 2 years old C, 5 years old D, (a+3) years old

4. The triangle has an area of S square centimeters, a height of 4 centimeters and a base of () centimeters.

a，2s÷4 B，2S ÷ 2 ÷ 4c，S4D，4s÷2[ elf

5, in two identical rectangles, the area of the shadow part ()

Jiayi

1. Each empty bottle can hold 2.5 kilograms of salad oil. Miss Wang needs at least () bottles to put 25.5 kilograms of salad oil in such bottles.

a、 10 B、 1 1 C、 12

2, the following graphics can't close shop is ()

A, regular pentagon b, regular hexagon c, regular triangle

3. A box of 15 balls, including 5 red balls, 2 green balls, 7 black balls and yellow balls 1 ball. If you touch any ball from the box, the possibility of finding the red ball is (), and the possibility of finding the yellow ball is ().

a、 1/ 15 B、2/ 15 C、7/ 15 D、5/ 15

4. The teacher's home is in Building 06, Unit 3, 08th Floor, Happiness Community. If F is used to represent a happy community, then the teacher's home number is ().

a . f—06—3—08—3b . f—3—06—3—08c . f—6—3—8—35÷0 . 50 . 75×24。 A classmate's ID number is 5 10402 1997036545.

5. In the picture on the right, two triangles A and B are drawn in two equilateral squares (indicated by shading), and their areas are compared by ().

A, A has a large area, B has a large area, and C is equal.

Error-prone multiple choice questions set

1, the area of the triangle is 63 square decimeters, the height is 7 decimeters, and the bottom is ().

A.4.5 B. 18

2. Divide a parallelogram into two trapeziums at will, and the () in these two trapeziums is always equal.

A. Height B. Area C. Sum of upper and lower bottoms

3, a triangle, the bottom is unchanged, the height is expanded by 5 times, and its area is ().

A. Zoom in 5 times B. Zoom in 25 times C. Zoom out 25 times

4. Divide the trapezoid into parallelogram and triangle, where () is equal.

A. Height B. Area C. Sum of upper and lower bottoms

5. The base reduction of parallelogram is 10 times and the height expansion is 10 times. The area of this parallelogram is ().

A is equal to the original B. It is reduced by 10 times and C. It is expanded by 10 times.

6. Circle three equal-length iron wires into rectangles, squares and parallelograms to form the area of the figure, ().

A. square is big B. rectangle is big C. parallelogram is big

7. Draw the largest triangle in a parallelogram with an area of 42 square meters. The area of this triangle is ().

A.2 1 m2 B. 30 m2 C. 14 m2

8. Triangle and parallelogram are equal in height and area. The base of parallelogram is 15cm, and the base of triangle is long.

() centimeters.

① 10 ② 15 ③30 ④20

9. It is known that the area of a trapezoid is 42.5dm2, the upper bottom is 3dm, the lower bottom is 7dm, and the height is ().

①42.5×2÷(3+7) ② 42.5÷(3+7) ③42.5÷(3+7-3)

10, if the base and height of a parallelogram are divided by 2, its area is larger than the original ().

① 2 times smaller, 2 times larger and 3 times smaller.

1 1, the first factor (excluding 0) enlarges 10 times, and the second factor (excluding 0) reduces 100 times, and the product ().

① magnification 10 times; ② Decrease 100 times; ③ Decrease 10 times.

12, two triangles with equal base and height ()

① Same shape, ② Equal perimeter and ③ Equal area.

13, the divisor decimal point is shifted to the right by two places. To reduce the quotient by 10, the decimal point of the divisor should be ().

A.b. move two places to the left.

C. Move one bit to the right D. Move one bit to the left

A number ÷0.4= B number ×0.4, then the size relationship between A and B is ()

A.a is as big as B.

C.b number is very large.

14, the solution of the equation "38X=0" is ().

A.x = 38 b.x = 0 C. I can't be sure.

15, A number ÷0.4= B number ×0.4, then the size relationship between A and B is ().

A.a is as big as B.

C.b number is very large.

16, the quotient of dividing two numbers is 0.07. If the dividend is enlarged by 10 times and the divisor remains the same, then the quotient ().

A, unchanged. B, also expanded by 10 times. C, reduced by 10 times. D, not sure.

17. In the following formula, the inequality of 9.7× 100. 1 is ().

a、9.7× 100+9.7×0. 1 B 、( 100+0. 1)×9.7

c、9.7+9.7× 100 D、0.97+9.7× 100

18, Xiao Ming uses 16 small squares to set the graph, and at most () different rectangles can be set.

A 2 B 3 C 4

19, the quotient of dividing two numbers is 3.5, the dividend and divisor are expanded by 10 times, and the quotient is ().

a、35 B、3.5 C、0.35 D、350

20. Mom is one year old and Xiaoying is one year old (a-25). 10 years later, the difference between mom and Xiaoying is ().

A, a, b, 25, c, 10, d and 15.

2 1, if 4.6X>4.6, then ()

A X> 1 B X< 1 C X= 1

22. In the picture on the right, the two sides of the parallelogram are 6 cm and 4 cm respectively, and the height is 5 cm, so its area is ().

A 30 square centimeters B 20 square centimeters c cannot be determined

23, 8.8 x12.5 is not equal to ().

a 10× 12.5- 1.2× 12.5 B 8× 12.5× 1. 1

c 8× 12.5+0.8× 12.5D 0.8× 12.5+ 12.5× 1 1

24. A pile of circular steel pipes, with five at the top and nine layers of 13 and * * at the bottom, has a difference of 1 between every two adjacent layers, and this pile of steel pipes has ().

a 163 B 8 1 C 72D 144

25. The quotient of dividing two numbers is 1.5. If the dividend is enlarged by 10 times and the divisor is reduced by 10 times, the quotient is ().

① 1.5 ② 15 ③ 150