1. The significance of fractional multiplication: a simple operation to find the sum of several identical fractions.
2. The significance of fractional division: know the product of two multipliers and one of them, and find the operation of the other multiplier.
3. The algorithm of fractional multiplication:
(1) Fraction multiplied by integer: numerator multiplied by integer, denominator unchanged.
(2) Fractional multiplication: numerator multiplies numerator, denominator multiplies denominator, and what can be reduced is reduced first.
4. The algorithm of fractional division:
(1) A number divided by an integer (except 0) is equal to this number multiplied by the reciprocal of this integer.
(2) A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.
(3) dividing by a number (except 0) is equal to multiplying the reciprocal of this number.
If the product of two numbers is 1, then we call one of them the reciprocal of the other. For example, the reciprocal of 1/2 is 2, and the reciprocal of 2 is 1/2. These two numbers are reciprocal. The reciprocal of 1 is 1, and 0 has no reciprocal.
6. Practical problems of fractional multiplication and division
(1) Find the fraction of a number and multiply it.
(2) Know the fraction of a number, find this number, divide it, or solve the equation.
Second, the mixed operation of fractions
1. The order of fractional mixing operations is the same as that of integer mixing operations: multiply first, then divide, then add and subtract, and the bracketed ones are counted in the brackets first, and then counted outside the brackets.
2. Operating rules:
(1) Multiplicative Distribution Law:
(2) Multiplicative associative law:
(3) Multiplicative commutative law:
Using the algorithm, you can simply perform the mixed operation of fractions.
Third, the understanding, surface area, volume and volume of cuboids.
1. A cuboid has six faces, generally rectangular (in special cases, two opposite faces are square), and the areas of the opposite faces are equal; There are 8 vertices, 12 edges, and 12 edges can be divided into 3 groups: 4 long, 4 wide and 4 high.
2. A cube has six faces, all of which are squares with equal areas; There are 8 vertices, 12 sides, and each side has the same length.
3. Cubes are special cuboids. (Length, width and height are equal)
4. The sum of the sides of a cuboid = (length+width+height) ×4
5. Sum of cube sides = side length × 12
6. The total area of six faces of a cuboid is called its surface area. The areas of two opposite sides of a cuboid are equal, and the areas of the front and back sides are equal to length × height; Left and right area = width × height; Up and down area = length × width
7. Surface area of cuboid = (length× width+length× height+width× height) ×2
8. cuboid volume = length × width × height
9. Volume of cube = side length × side length × side length
10. cuboid (cube) volume = bottom area × height
Four. per cent
1. Percentage indicates the percentage of one number to another. Percentage is also called percentage, percentage.
Writing 22%, reading 22%
2. Reciprocity of percentages and decimals:
(1) Decimal percentage: move the decimal point to the right by two places and add a percentage sign.
(2) Decimal point: If the percentage sign is removed, the decimal point of the number before the percentage sign will be moved to the left by two places.
3. Reciprocity of percentage and score:
(1) Fractional percentage: divide the numerator by the denominator, and then convert the quotient of division into percentage. Or the decimal part is a fraction with the letter 100, and then rewritten as a percentage.
(2) Percentage score: write the percentage as a score, and the denominator is 100, and the quotation that can be reduced is divided into the simplest score.
4. Excellent rate = excellent number ÷ total number.
5. Pass rate = number of people passing through ÷ total number of people.
6. Qualified rate = number of qualified products ÷ total number of products
7. Attendance rate = attendance ÷ total number
8. Hit rate = hit times ÷ total times
9. Germination rate = number of germinated seeds/total number of seeds
10. Survival rate = number of surviving trees ÷ total number of planted trees.
1 1. Flour yield = flour weight/wheat weight.
12. Oil yield = pressed oil weight/peanut kernel weight.
Verb (abbreviation for verb) statistics
1. Bar chart can clearly show the quantity of various kinds of land for comparison.
2. The fan-shaped statistical chart can intuitively show the percentage of each quantity in the total.
3. The broken-line statistical chart can display the change of quantity intuitively.
4. Average value = total quantity/total number of copies
5. Arrange a set of data from small to large (or from large to small), and the middle number is called the median of this set of data.
6. The number with the highest frequency in a set of data is called the mode of this set of data.
The concept formula of the second volume of fifth grade mathematics
I. Fractional multiplication and fractional division
1. The significance of fractional multiplication: a simple operation to find the sum of several identical fractions.
2. The significance of fractional division: know the product of two multipliers and one of them, and find the operation of the other multiplier.
3. The algorithm of fractional multiplication:
(4) Fraction and integer multiplication: numerator and integer multiplication, denominator unchanged.
(5) Fractional multiplication: numerator multiplies numerator, denominator multiplies denominator, and what can be reduced is reduced first.
4. The algorithm of fractional division:
(1) A number divided by an integer (except 0) is equal to this number multiplied by the reciprocal of this integer.
(2) A number divided by a fraction is equal to the number multiplied by the reciprocal of the fraction.
(6) Dividing by a number (except 0) is equal to multiplying the reciprocal of this number.
If the product of two numbers is 1, then we call one of them the reciprocal of the other. For example, the reciprocal of 1/2 is 2, and the reciprocal of 2 is 1/2. These two numbers are reciprocal. The reciprocal of 1 is 1, and 0 has no reciprocal.
6. Practical problems of fractional multiplication and division
(1) Find the fraction of a number and multiply it.
(2) Know the fraction of a number, find this number, divide it, or solve the equation.
Second, the mixed operation of fractions
1. The order of fractional mixing operation is the same as that of integer mixing operation: multiply first, then divide, then add and subtract, and those with brackets are counted in brackets first, and those without brackets are counted again.
2. Operating rules:
(1) Multiplicative Distribution Law:
(2) Multiplicative associative law:
(3) Multiplicative commutative law:
Using the algorithm, you can simply perform the mixed operation of fractions.
Third, the understanding, surface area, volume and volume of cuboids.
1. A cuboid has six faces, generally rectangular (in special cases, two opposite faces are square), and the areas of the opposite faces are equal; There are 8 vertices, 12 edges, and 12 edges can be divided into 3 groups: 4 long, 4 wide and 4 high.
2. A cube has six faces, all of which are squares with equal areas; There are 8 vertices, 12 sides, and each side has the same length.
1 1. Cube is a special cuboid. (Length, width and height are equal)
12. Sum of sides of cuboid = (length+width+height) ×4
13. Sum of sides of cube = side length × 12.
14. The total area of six faces of a cuboid is called its surface area. The areas of two opposite sides of a cuboid are equal, and the areas of the front and back sides are equal to length × height; Left and right area = width × height; Up and down area = length × width
15. Surface area of cuboid = (length× width+length× height+width× height) ×2.
16. The total area of six faces of a cube is called its surface area, and the areas of all six faces are equal.
17. Surface area of cube = side length × side length ×6.
18. The size of the space occupied by an object is called the volume of the object. Commonly used unit of volume are: cubic centimeter, cubic decimeter and cubic meter.
1 m3 = 1000 cubic decimeter 1 cubic decimeter = 1000 cubic centimeter 1 m3 = 1000000 cubic centimeter.
19. The volume of an object that a container can hold is called the volume of the container. The commonly used unit of volume are liters and milliliters.
1 l = 1 cubic decimeter 1 ml = 1 cubic centimeter
20. Mutualization between adjacent volume units.
Low-level unit and high-level unit
2 1. unit of volume is used to calculate the volume of objects, and unit of volume is generally used to calculate the volume of liquids and gases.
22. cuboid volume = length × width × height
23. The volume of the cube = side length × side length × side length
24. cuboid (cube) volume = bottom area × height
Four. per cent
1. Percentage indicates the percentage of one number to another. Percentage is also called percentage, percentage.
Writing 22%, reading 22%
2. Reciprocity of percentages and decimals:
(1) Decimal percentage: move the decimal point to the right by two places and add a percentage sign.
(2) Decimal point: If the percentage sign is removed, the decimal point of the number before the percentage sign will be moved to the left by two places.
3. Conversion between percentage and score:
(1) Fractional percentage: divide the numerator by the denominator, and then convert the quotient of division into percentage. Or the decimal part is a fraction with the letter 100, and then rewritten as a percentage.
(2) Percentage score: write the percentage as a score, and the denominator is 100, and the quotation that can be reduced is divided into the simplest score.
13. Excellent rate = excellent number ÷ total number.
14. Pass rate = number of people passing ÷ total number of people.
Verb (abbreviation for verb) statistics
1. Bar chart can clearly show the quantity of various kinds of land for comparison.
7. The fan-shaped statistical chart can intuitively show the percentage of each quantity in the total.
8. Line charts can visually show the changes in quantity.
9. Average value = total quantity/total number of copies
10. Arrange a set of data from small to large (or from large to small), and the middle number is called the median of this set of data.
1 1. The number with the highest frequency in a set of data is called the mode of this set of data.