Number pairs are used to indicate positions, for example, the third column and the second row are indicated as (3,2). Usually expressed as (column, row)

Unit 2: Fractional Multiplication

1, the fractional multiplication of integers has the same meaning as integer multiplication, and it is a simple operation to find the sum of several identical addends. (For example, 75×4 indicates how many four 75s are or how many four times 75s are. )

2. Multiplying a number by a fraction means finding a fraction of this number. (For example, 6×43 means how much is 43 of 6; 65×52 indicates what 52 of 65 is. )

3. Calculation rules of fractional multiplication: the product of numerator multiplication is numerator, and the product of denominator multiplication is denominator. (If you can cut the point, cut the point first)

4. Multiply a number by a true fraction, and the product is less than this number (for example, 5× 21￠ 5;

Multiply a number by 1 and the product is equal to this number (for example, 54×1~ 54);

Multiply a number by a false fraction greater than 1, and the product is greater than this number (for example, 53× 45 ~ 53).

5. Two numbers whose product is 1 are reciprocal. The reciprocal of 1 is 1, and 0 has no reciprocal. Unit 3: Fractional Division

1, the meaning of fractional division is the same as integer division, that is, knowing the product of two factors and one of them to find the other factor. 2. Calculation rule of fractional division: Divided by divisor (except 0) equals the reciprocal of dividend multiplied by divisor.

3. When a number is divided by the true fraction, the quotient is greater than this number (for example, 4 ÷ 2 1 ×4); Divided by a number greater than 1

The quotient is less than this number (for example, 3 ÷ 23 ? 3).

The division of two numbers is also called the ratio of two numbers. In the ratio of two numbers, the number before the comparison sign is called the first term of the ratio, and the number after the comparison sign is called the last term of the ratio. compare

The quotient obtained by dividing the former term by the latter term is called the ratio.

The ratio is usually expressed in fractions, and can also be expressed in decimals or integers. According to the relationship between fraction and division, two

The ratio of numbers can also be written as a fraction. (For example, 3:2 can also be written as 23, which is still pronounced as "3 to 2")

5, the relationship between ratio and division, fraction:

Compared with the previous paragraph.

The latter ratio

Division dividend quotient

Fraction numerator fraction line denominator fraction value

6. The basic nature of the ratio: the first term and the second term of the ratio are multiplied or divided by the same number at the same time (except 0), and the ratio remains unchanged.

7. The "golden ratio" (0.6 18: 1) gives people an advantage.

The visual feeling of beauty. Many architectural works and artistic works are designed according to the golden ratio.

Unit 4: Circle

1, circle: A circle is a closed plane figure surrounded by curves.

2. The point of the center of the circle is called the center of the circle (represented by the letter O).

3. The line segment connecting the center of the circle and any point on the circle is called the radius (represented by the letter R).

4. The line segment whose two ends pass through the center of the circle is called the diameter (represented by the letter D).

5. A circle with the same length has countless radii. A circle has countless diameters and equal lengths.

6. In the same circle or in the same circle, the length of the diameter is half.

Twice the diameter.

7. The circle is an axisymmetric figure. The straight line with each diameter is the symmetry axis of the circle, and the circle has countless symmetry axes. In the symmetrical figure we have learned before, the rectangle

A shape has two axes of symmetry and a square has four axes of symmetry.

An isosceles triangle has 1 symmetry axes and is an equilateral triangle.

There are three axes of symmetry, and the isosceles trapezoid has 1 axes of symmetry.

8. The ratio of the circumference to the diameter of a circle is called pi. The circumference of a circle is always equal to π times the diameter and 2π times the radius.

Circumference c=πd or c=2πr Area s=πr2.

9. Ring area = π (R2-R2), outer circle radius = inner circle radius+1 ring width.

Outer circle diameter = inner circle diameter+width of two rings 10, runway width ×2π= runway spacing.

1 1, rectangles, squares and circles with equal areas, with the shortest circumference of the circle and the longest circumference of the rectangle; Rectangular, square and circular with equal perimeters, the circular area is the largest and the rectangular area is the smallest. Unit 5: Percentage

1, percentage: The number indicating that one number is the percentage of another number is called percentage, also called percentage or percentage. Percent means the multiple ratio of two numbers, so there is no unit name. 2. General formula: Wheat flour yield =

The weight of wheat

Flour weight × 100%

Product qualification rate = total number of products

Number of qualified products × 100%

Attendance of employees = number of people who should attend.

Actual attendance × 100%

Peanut oil yield = weight of peanut kernel × weight of peanut oil × 100%

Compliance rate = total number of students × 100% of students who meet the standards.

100% number of germinated seeds, total number of seeds tested for germination rate, 100% attendance rate, attendance rate, actual number.

100% survival rate of living trees Total number of trees planted

100% qualified quantity qualified rate total production quantity

Shooting percentage = total number of shots × 100%

100% sales price-purchase price (cost)

Profit rate, purchase price (cost), 100% growth, original growth rate? Profit selling price-purchase price

Rice yield = rice weight × 100%

(Note: The flour yield, rice yield, oil yield, germination rate, attendance rate, survival rate and qualified rate shall not exceed 100%. )

Time x speed = distance efficiency x time = total workload x quantity = total output

Distance ÷ speed = total time work ÷ efficiency = total time output ÷ single output = quantity

Distance/Time = Speed/Total Work/Time = Work Efficiency Total Output/Quantity = Single Output

3. Taxation: Taxes are mainly divided into consumption tax, value-added tax, business tax and personal income tax. pay

Our tax is called tax payable.

The ratio of taxable amount to income is called tax rate.

4. Bank deposit methods include demand deposit, lump-sum deposit and withdrawal, and lump-sum deposit and withdrawal. The money deposited in the bank is called Ben

Gold; The extra money paid by the bank when withdrawing money is called interest;

The ratio of interest to principal is called interest rate.

Interest: principal × interest rate × time (according to state regulations, deposit interest should be taxed at the rate of 5%. )

Unit 6: Statistics

Commonly used statistical charts are: bar statistical charts and broken line systems.

Chart, fan-shaped statistical chart.

Commonly used statistics are: single statistics and composite statistics.

Rice.

Bar chart: You can clearly see the number of each part. Broken line statistical chart: not only can you clearly see

How many parts, we can see the change of the number of each part. Fan chart: better understand the relationship between the number of parts and the total number.

Relationship.

Fraction percentage application problem

A general solution to the application of fractions and percentages 1. Solve the problem of fractional multiplication

1, what is the score of a number? (Single)

The bit "1" is known) unit "1"× fraction = the quantity corresponding to the fraction.

2. How much is a number more than the unit "1"? (The unit "1" is known) Unit "1"× (1+fraction) = the amount corresponding to the fraction. 3. How much smaller is a number than the unit "1"? (The unit "1" is known) Unit "1"× (1-fraction) = the amount corresponding to the fraction. Second, solve the problem of fractional division.

1. What fraction of a number is known? How did you find this number? (The unit "1" is unknown) Quantity ÷ Number corresponding score = Unit "1"

2. Given that one number is a few points more than another, how do you find this number? (unit "1" unknown) Quantity ÷( 1+ score) = unit "1"

As we all know, one number is a little less than another. How did you find this number? (Unit "1" unknown) Quantity ÷( 1- score) = Unit "1" Third, solve the percentage problem.

1, the question of percentage: What percentage is one number in another?

Another number, a number × 100%= percentage

2. Find out how much one number is more (less) than another.

Difference ÷ Unit "1" = how much (less) percentage corresponds to quantity ÷ unit "1"-1or1-corresponding quantity ÷ unit "1".

3. Find the percentage of a number (known unit "1"). Unit "1"× percentage = the amount corresponding to the score.

What percentage of a number is known? Find this number. (Unknown unit "1") Quantity ÷ Percentage corresponding to quantity = Unit "1"4. What is more (less) than a number?

Unit "1"× (1+percentage) = the amount corresponding to the score.

5. What is the number that is known to be more (less) than a number? Find this number.

Quantity ÷( 1+ corresponding score) = unit "1"6. Discount original price × discount = current price 7. Tax revenue × tax rate = tax payable 8. Interest principal × interest rate × time = interest interest × tax rate = interest tax.

Interest tax = after-tax interest principal and interest = principal+after-tax interest