Conceptual questions for the fifth grade of primary school mathematics in the last semester
1. Multiplication of decimals
1. Calculation rules for multiplication of decimals: first calculate the product by multiplication of integers, and then Add decimal points to the points. (How to point the decimal point?) To see how many decimal places there are in the factor, count the number from the right side of the product and put the decimal point. (The product you multiply does not have enough decimal places, how do you add a decimal point?) You need to add 0 in front, and then add a decimal point.
2. Changes in factors cause changes in the product:
① If one factor remains unchanged and the other factor expands (or shrinks) several times, the product will also expand (or shrink) by the same amount. multiples.
② Two factors are expanded by a certain multiple at the same time, and the multiple of the product expansion is equal to the product of the expansion multiples of the two factors. For example: the first factor is expanded by 5 times, the second factor is expanded by 10 times, and the product is expanded (5×10=50 times).
③If one factor reduces and the other factor expands, it depends on whether the reduction factor is greater or the expansion factor is greater. If the multiple of reduction is large, the product will shrink; if the multiple of expansion is large, the product will expand. The multiple of reduction or expansion is equal to the quotient of a large number divided by a small number.
For example: one factor is reduced by 20 times, and the other factor is expanded by 10 times. Because 20>10, the product must be reduced, reduced (20÷10=2 times). Another example: one factor is expanded 30 times, and the other factor is reduced 6 times. Because 30>6, the product needs to be expanded, expanded (30÷6=5 times).
3. The relationship between factors and products:
When a number (except 0) is multiplied by a number greater than 1, the product is larger than the original number;
A When a number (except 0) is multiplied by a number less than 1, the product is smaller than the original number.
2. Decimal division
1. Calculation rules for dividing decimals by integers: ① Divide according to the method of integer division; ② The decimal point of the quotient must be aligned with the decimal point of the dividend; ③ The integer part If it is not enough to divide, add 0 as the quotient and put the decimal point; ④ If there is a remainder, add 0 and divide again.
2. Calculation rules for dividing a number by a decimal: first move the decimal point of the divisor to make it an integer, then move the decimal point of the divisor a few places to the right, and the decimal point of the dividend also move a few places to the right. When the number of digits in the dividend is not enough, pad the end of the dividend with 0, and then perform the calculation according to the decimal division method where the divisor is an integer.
3. The changing rules of dividend, divisor and quotient:
① If the dividend and divisor are multiplied (or divided) by the same number (except 0) at the same time, the quotient remains unchanged; < /p>
②The dividend remains unchanged, and the divisor expands (or shrinks) by several times, and the quotient shrinks (or expands) by the same multiple;
③The dividend remains unchanged, and the dividend expands (or shrinks) by how many times times, the quotient also expands (or shrinks) by the same multiple.
4. The relationship between the dividend and the quotient:
When a number (except 0) is divided by a number greater than 1, the quotient is smaller than the dividend;
A number (Except 0) divided by a number less than 1 (except 0), the quotient is greater than the dividend.
5. In the decimal part of a number, starting from a certain digit, one number or several numbers appear repeatedly in sequence. Such decimals are called recurring decimals. The decimal part of a recurring decimal, the numbers that appear repeatedly in sequence, are called the recurring section of the recurring decimal.
6. The number of digits in the decimal part is a finite decimal, which is called a finite decimal. A decimal that has infinite digits in the decimal part is called an infinite decimal.
7. Digital black hole refers to a situation in which natural numbers fall into a cycle after undergoing certain operations.
3. Observing objects
1. When observing an object, you can see at most three sides at a time and at least one side.
4. Simple equations
1. Use letters to express the laws of operation:
Commutative law of addition: a+b=b+a Associative law of addition: (a +b)+c= a+(b+c)
Commutative law of multiplication: ab=ba Associative law of multiplication: (ab)c= a(bc)
Distributive law of multiplication: (a+b)c= ac+bc
2. Use letters to express the formula:
Perimeter of the square: C= 4a Area of ??the square: S=a2
Perimeter of the rectangle: C=2 (a+b) Area of ??the rectangle: S=ab
3. An equation containing unknown numbers 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 finding solutions to equations is called solving equations.
4. The relationship between the various parts of the four arithmetic operations:
①. Addend + addend = sum and addend = sum - another addend
② , Minuend - Minuend = Difference Minuend = Difference + Minuend Minuend = Minuend - Difference
③, Factor × factor = product factor = product ÷ another factor
④. Dividend ÷ divisor = quotient Divisor = quotient × divisor Divisor = dividend ÷ quotient
5. The main steps to solve problems with equations:
①Write the solutions and assumptions ; ② Find the equality relationship between the quantities in the question; ③ List the equations based on the equivalence relationship;
④ Solve the equation; ⑤ Check and answer.
Example: 6—x=3.5
Solution: 6—x+x=3.5+x
3.5+x=6
3.5+x—3.5=6—3.5
X=2.5
5. Area of ??polygon
1. Area of ??parallelogram = base × height Represented by letters: S=ah
The base of a parallelogram = area ÷ height is expressed by letters: a=S÷h
The height of a parallelogram = area ÷ base is expressed by letters: h =S÷a
(The areas of parallelograms with equal bases and equal heights are equal)
2. The area of ??a triangle = base × height ÷2 expressed in letters: S=ah÷2< /p>
The base of a triangle = area × 2 ÷ height expressed in letters: a = 2S ÷ h
The height of a triangle = area × 2 ÷ base expressed in letters: h = 2S ÷ a < /p>
(The areas of triangles with equal bases and equal heights are equal)
3. A triangle is half the area of ??a parallelogram with equal bases and equal heights;
Triangles and parallelograms, etc. If the products (areas) of a triangle and a parallelogram have the same base, then the height is twice the height of the parallelogram;
If the triangle and the parallelogram have the same product (area), then the base is twice the height of the parallelogram.
4. The area of ??the trapezoid = (upper base + lower base) × height ÷ 2 expressed in letters: S = (a + b) h ÷ 2
The height of the trapezoid = area ×2÷(upper base + lower base) expressed by letters: h =2 S ÷(a+b)
The upper base of the trapezoid = area × 2 ÷height - lower base expressed by letters: a = 2 S ÷h -b
The lower base of the trapezoid = area × 2 ÷height - the upper base is represented by letters: b =2 S ÷h -a
5. Calculate logs , The formula for the number of steel pipe stacks:
Total number of pipes = (number of top pipes + number of bottom pipes) × number of layers ÷ 2
Number of layers = number of bottom pipes - number of top pipes + 1
6. Statistics and Possibility
1. Arrange a set of data from small to large (or from large to small), and find a number in the middle (or the largest number). The average of the two middle data) is the median of this set of data. The advantage of the median is that it is not affected by large or small data.
2. No matter what graphics are laid on the plane without overlap or gaps, it is called dense paving. Common shapes that can be densely tiled include triangles, rectangles, squares, trapezoids, regular hexagons, etc., while shapes that cannot be densely tiled include circles, regular pentagons, etc.
1. Fill in the blanks.
1.2 hours = ( ) minutes 0.208 meters = ( ) centimeters
3500 kilograms = ( ) tons 4 meters 5 centimeters = ( ) meters
860 square centimeters = ( ) square decimeter 5.03 hectare = ( ) square meter
0.28 square meter = ( ) square decimeter 3 meters 4 centimeters = ( ) meter
4 jiao = ( ) yuan 3 meters 5 centimeters = ( ) meters
0.58 square meters = ( ) square decimeters 6005 grams = ( ) kilograms ( ) grams
A number (except 0) multiplied by more than 1 Number, the product is the ratio of the original number ( ).
When a number (except 0) is multiplied by a number less than 1, the product is the ratio of the original number ( ).
When a number (except 0) is divided by a number greater than 1, the quotient is greater than the original number ( ).
When a number (except 0) is divided by a number less than 1, 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 2.75×1.01○2.75
4.95÷0.9○4.95 1×1.009○1.009 3.6×1.45○3.6
An object is in On the table, when we observe it from different angles, we can see at most ( ) faces and at least ( ) faces.
Use a, b, c to represent three numbers and write the additive associative law ( ).
Use a, b, c to represent three numbers and write the distributive law of multiplication ( ).
A storybook has 98 pages. On average, I read x pages every day for 6 days, and there are ( ) pages left.
Using two identical right triangles, they can definitely form one ( )
The area of ??a triangle is 24 square meters, and the area of ??a parallelogram with the same base and height is ( ) square meters.
The area of ??a trapezoid is 50 square decimeters, the sum of its upper and lower bases is 16 meters, and the height is ( ).
The base of a parallelogram is 6.5 meters and the height is 4 meters. The area of ??a triangle with the same base and height is ( ) square meters.
The price of a book "Mathematics Competition" is a yuan. If you buy 5 such books, you will pay ( ) yuan.
9.954 to one decimal place is ( ).
1. Think carefully and I will fill it in. (20 points)
1. The product of 5.04×2.1 is ( ) decimal places, and the quotient of 22.6÷0.33, with one decimal place, is approximately ( ).
2. Keeping to one decimal place is ( ), and keeping to two decimal places is ( ).
3． Fill in the following with "》" "《" or "="
3.25×0.98 3.25 A ÷0.97 A (A≠0)
0.75÷0.5 0.75×2 4 ． The ID card number of a classmate is 510402199703155221. The classmate was born on ( ) year ( ) month ( ), and his gender is ( ).
5. Xiaolin bought 4 pens, each worth a yuan; and bought 5 exercise books, each worth b yuan. The amount of money a *** pays can be expressed by the formula ( ); when a=0.5, b=1.2, a *** should pay ( ) yuan.
6. Move the decimal point of a decimal number two places to the right to obtain a new number, which differs from the original number by 44.55. The original number is ( ).
7. Master Wang processes one kind of parts and processes 20 of them in 5 minutes. Then Master Wang takes ( ) minutes to process 1 part on average and can process ( ) parts of this kind in 1 minute.
8. The three sides of a right triangle are 3 cm, 4 cm and 5 cm respectively. The area of ??this right triangle is ( ) square centimeters.
9. The upper base, lower base and height of a right-angled trapezoid are 10dm, 12dm and 8dm respectively, and its area is ( ) square decimeters; draw the largest square within the trapezoid, and the area of ??the square is ( ) Square decimeters.
10. The box contains 6 small balls marked with the numbers 1, 2, 3, 4, 5, and 6. Touch one at will, there are ( ) possibilities, the possibility of each result is ( ), the possibility of being an odd number is ( ), and the possibility of being less than 3 is ( ).
1. 2.5 hectares = ( ) square meters 2300 square centimeters = ( ) square meters
8050 grams = ( ) kilograms 160 square centimeters = ( ) square decimeters = ( ) square meters Meters
The product of 2 and 1.36×0.2 has ( ) decimal places.
3. The commercial recurring decimal representation of 11÷6 is ( ), and the accuracy to the percentile is ( ).
4. If the perimeter of an equilateral triangle is a meter, then the length of each side is ( ) meters.
5. When a=4, b=0.3, c=5, the value of ab+c is ( ), and the value of c÷a-b is ( ).
6. Fill in ○ with >, < or =.
1.2÷0.8 ○1.2×0.8 1.1×0.99 ○1.1
7. When the turntable is turned, the possibility that the pointer stops in the red area is ( ); if it is turned 100 times, it is estimated that it will stop There will be approximately ( ) times in the green area.
8. According to 51.2×8=409.6, write the product of the following questions.
5.12×0.8＝( ) 0.512×80＝( )
9. The area of ??a triangle is 18 square meters, its height is 9 meters, and its base is ( ) rice.
10. The three sides of a right triangle are 6 cm, 8 cm and 10 cm respectively. The area of ??this triangle is ( ) square centimeters, and the height of the hypotenuse is ( ) centimeters.
2. Choice
1. Which of the following formulas is not an equation ( ).
A. 1.5a＋6=9 B. 2x÷4=2.5 C. 6x＋4x＞70
2. Two ( ) trapezoids can be combined into a parallelogram.
A. Identical B. Equal areas C. Equal bases and equal heights
3. Xiaoqiang is a year old this year, Xiaohong is 2 years older than Xiaoqiang, and in three years Xiaoqiang will be better than Xiaoqiang Hong Xiao ( ) years old.
A, (a-3) years old B, 2 years old C, 5 years old D, (a+3) years old
4. The area of ??the triangle is s square centimeters, and the height is 4 centimeters, then the base is ( ) centimeters
A. 2s÷4 B. s÷2÷4 C. s÷4 D. 4s÷2[Little Elf
5. In two identical rectangles, the area of ??the shaded part ( )
A and B
1. Each empty bottle can hold 2.5 kilograms of salad oil. Teacher Wang needs to put 25.5 kilograms of salad oil into it. To put salad oil in such a bottle, at least ( ) such bottles are needed.
A, 10 B, 11 C, 12
2. Among the following figures, the ones that cannot be densely paved are ( )
A. Regular pentagon B , regular hexagon C, regular triangle
3. There are 15 balls in a box, including 5 red balls, 2 green balls, 7 black balls, and 1 yellow ball. From the box Randomly draw a ball here, the possibility of drawing a red ball is ( ), and the possibility of drawing a 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, Floor 08, No. 3, Xingfu Community. If F is used to represent Xingfu Community, then the number of the teacher’s home is ( )
A .F—06—3—08—3 B. F—3—06—3—08 C. F—6—3—8—35÷0.5 0.75×2 4. The ID card number of a classmate is 510402199703155221. The classmate was born on ( ) year ( ) month ( ), and his gender is ( ).
5. In the picture on the right, two triangles A and B (indicated by shading) are drawn in two squares with equal side lengths. Their areas are compared ( )
A. The area of ??A is larger. B. The area of ??B is larger. C. Equal
Error-prone multiple choice question set
1. The area of ??a triangle is 63 square decimeters and the height is 7 points. Meter, its base is ( )
A. 4.5 B. 18C． 9
2. Divide a parallelogram into two trapezoids arbitrarily. ( ) in these two trapezoids are always equal.
A. High B． Area c. The sum of the upper and lower bases
3. A triangle, with the base unchanged and the height expanded 5 times, its area ( ).
A. Expand 5 times B. Expand 25 times C. Reduce 25 times
4. Divide a trapezoid into a parallelogram and a triangle. The ( ) in these two figures are equal.
A. High B． Area c. The sum of the upper and lower bases
5. The base of a parallelogram is reduced 10 times and the height is expanded 10 times. The area of ??this parallelogram is ( ).
A. Equal to the original B. Reduce 10 times C. Expand 10 times
6. Surround three wires of the same length into a rectangle, a square and a parallelogram to form a figure. area, ( ).
A. Square is big B. Rectangle is big C. Parallelogram is big
7. Draw the largest triangle within a parallelogram with an area of ??42 square meters. The area of ??this triangle is ( ).
A.21 square meters B. 30 square meters C.14 square meters
8. The height and area of ??a triangle and a parallelogram are equal. The base of the parallelogram is 15cm. The base length of the triangle
( ) cm.
①10 ②15 ③30 ④20
9. It is known that the area of ??the trapezoid is 42.5dm2, the upper base is 3dm, the lower base is 7dm, and its height is ( )
< p>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 If both are divided by 2, its area will be smaller than the original ( )
① 2 times smaller ② 4 times smaller ③ 4 times smaller
11. The first factor (except 0) is 10 times smaller times, the second factor (except 0) shrinks 100 times, product ( )
①Expand 10 times ②Reduce 100 times ③Reduce 10 times
12. The bottom and the height are equal Two triangles ( )
①The shape is the same ②The perimeter is equal ③The area is equal
13. Move the decimal point of the divisor two places to the right to make the quotient smaller by 10 digits. The decimal point of the dividend answer( ).
A. Move two places to the right B. Move two places to the left
C. Move one position to the right D. Move one position to the left
The number of A ÷ 0.4 = the number of B × 0.4 Then the relationship between A and B is ( )
A. A large number B. Same size
C. The number B is large
14. The solution to the equation "38X=0" is ( ).
A. p>A. A large number B. Same size
C. Number B is large
16. The quotient of dividing two numbers is 0.07. If the dividend is expanded 10 times and the divisor remains unchanged, then the quotient ( )
A. remains unchanged. B. Also expanded 10 times. C. Shrunk 10 times. D. Unable to determine.
17. In the following calculation, the result that is not equal to 9.7×100.1 is ().
A. 9.7×109.7×0.1 B, (100.1)×9.7
C, 9.7+9.7×100 D, 0.97+9.7×100
18, used by Xiao Ming 16 small squares are arranged into figures, and up to ( ) different rectangles can be arranged
A 2 B 3 C 4
19. The quotient of dividing two numbers is 3.5. The dividend and divisor are both expanded 10 times, and the quotient is ( ).
A, 35 B, 3.5 C, 0.35 D, 350
20. The mother is a years old this year, and the child is (a-25) years old this year. After 10 years, the mother and the child will be Welcome phase difference ( ).
A, a year old B, 25 years old C, 10 years old D, 15 years old
21. If 4.6X>4.6, then ( )
A X> 1 B
A 30 square centimeters B 20 square centimeters C Unable to determine
23. What is not equal to 8.8×12.5 is ( )
A 10×12.5-1.2 ×12.5 B 8×12.5×1.1
C 8×12.5+0.8×12.5 D 0.8×12.5+12.5×11
24. A pile of circular steel pipes, with 5 on the top layer , there are 13 steel pipes on the bottom floor and 9 floors on top. Each adjacent floor differs by 1 pipe. This pile of steel pipes has ( ) steel pipes
A 163 B 81 C 72 D 144
25. The quotient of dividing two numbers is 1.5.
If the dividend is expanded 10 times and the divisor is reduced 10 times, the quotient is ( )
① 1.5 ② 15 ③ 150