Unit 1: A Preliminary Understanding of Negative Numbers

Positive and negative numbers are numbers with opposite meanings. 0 is neither positive nor negative, positive is greater than 0 and negative is less than 0.

0 is greater than any negative number.

Unit 2: Calculation of Polygon Area

1. area of parallelogram = base × high letter formula: S = a h 2. Area of triangle = base × height ÷2 letter formula: S = a h÷2 3. Trapezoidal area = (upper bottom+lower bottom) × height ÷2 letter formula: S = (a+b). Two identical triangles can form a parallelogram.

5. A parallelogram can be divided into two identical trapezoids; Two identical trapezoids can form a parallelogram.

6. The areas of triangles with equal bases and equal heights are equal; The area of a triangle is half that of a parallelogram with equal base and equal height.

7. Length units: millimeter (mm), centimeter (cm), decimeter (dm), meter (m) and kilometer (km).

Propulsion rate:10101010008. Area unit:

Measure and calculate the land area, usually in hectares. Square land with side length 100 m and area 1 hectare (hm).

Measure and calculate a large area of land, usually in square kilometers. A square piece of land with a side length of 1 000m and an area of1km2. 1 km2 = 1000000 m2

Area unit: square centimeter (cm2) square decimeter (dm2) square meter (m2) hectare (hm2) square kilometer (km2)

Yield:100100100001009. Weight unit: grams (kilograms) tons (tons).

Prepayment rate: 1000 1000

10. unit of volume: milliliter (mL) liter (l)

Prepayment rate 1000

Unit 3: the meaning and nature of decimals

1. Fractions with denominators of 10, 100 and 1000 can all be expressed in decimals, with one decimal place representing a few tenths, two decimals representing a few percent and three decimals representing a few thousandths.

2. The first digit to the right of the decimal point is ten digits, and the counting unit is one tenth (0.1); The second digit to the right of the decimal point is the percentile, and the counting unit is one percent (0.01); The third digit to the right of the decimal point is one thousandth, and the counting unit is one thousandth (0.001); The propulsion rate between every two adjacent counting units is 10.

4. Add 0 or remove 0 at the end of the decimal, and the size of the decimal remains the same, which is the essence of the decimal. According to the nature of decimals, decimals can usually be simplified by removing the 0 at the end of decimals.

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5. To rewrite a number into a number with "ten thousand" as the unit, just add a decimal point to the lower right corner after the ten thousand digits (the fifth from the left), and then add the word "ten thousand" to the end of the number. To rewrite a number into a number with the unit of "100 million", just add a decimal point in the lower right corner after this hundred million digits (the ninth on the left), and then add the word "100 million" at the end of the number. The 0 at the end of the decimal part is generally omitted.

Unit 4: Decimal addition and subtraction

Decimal addition and subtraction calculation method: same digit alignment; Decimal point alignment; The decimal point in sum should be aligned with the decimal point in addend; The decimal point in the difference should be aligned with the decimal point of the minuend and the minuend. From the lowest point: you must enter one at the age of ten or above; If it is not enough, it should be reduced by 1 to 10.

Unit 5: Fractional Multiplication and Division

1. The meaning of decimal times integer (decimal times integer and integer times have the same meaning, and they are all seeking.

A simple operation of the sum of several identical addends) for example: 0.3×4 (that is, what is the sum of four 0.3? Or 4 times 0.3? )

2. The calculation method of decimal times integer is to multiply the integer to calculate the product, and then look at the factor.

There are several decimal places, and the decimal point is counted from the unit of the product to the left. 3. Multiply an integer by a decimal (meaning to find a few tenths, a few percent and a few thousandths of this number)

how much is it? )

4. The calculation method of integer multiplication by decimal is to calculate the product by integer multiplication first, and then look at the factor.

There are several decimal places in the product, and then count several decimal places from the product to the left.

5. The calculation method of decimal multiplication is to calculate the product by integer multiplication, and then look at the factors.

If a * * * has several decimal places, the decimal point should be counted from the unit of product to the left; When the number of digits is insufficient, the number of digits must be supplemented by "0". 6. Multiply a decimal by 10, 100, 1000, as long as the decimal point of this decimal is moved to the right by one, two or three places; Move the decimal point of a decimal to the right by one, two or three places, and the decimal will be enlarged by 10 times, 100 times and 1000 times. When a number (except 0) is multiplied by a number greater than 1, the product is greater than the original number, and vice versa.

7. Meaning of decimal divided by integer: The meaning of decimal divided by integer is the same as that of integer division. 8. Decimals divided by integers are calculated as integers. The decimal point of quotient should be aligned with the decimal point of dividend.

9. The calculation method of fractional division of divisor is to move the divisor decimal point back first, move the divisor decimal point to the right by several digits (that is, turn the divisor into an integer first), and move the divisor decimal point to the right by several digits (if the number of digits is not enough, make up with 0), and then calculate it according to the fractional division of divisor as a voucher.

10. Divide a decimal by 10, 100, 1000. Just move the decimal point of this decimal to the left by one, two or three places. Moving the decimal point of a decimal to the left by one, two or three places will reduce the decimal by 10 times, 100 times and 1000 times.

1 1. If the divisor remains the same, the quotient will decrease (or increase) by the same factor;

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

Divider and divisor are multiplied (or divided) by the same number (except 0) at the same time, and the quotient remains unchanged. -Constant business rules.

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12. Decimal multiplication and division generally adopts rounding method to retain decimals, and sometimes we can choose to use "one-in-one method" and "mantissa method" to retain integers according to the actual situation.

13. Finite decimals: decimals with limited decimal places are called finite decimals; The number of decimal places is infinite, which is called infinite decimal.

14. Cyclic decimal: the decimal part of the decimal system is a number or several numbers repeated in turn. Such a small tree is called a cyclic decimal; These numbers that appear in turn are called cyclic segments of these decimals. The representation of circular cross section is: if it is a circular decimal number, click a point on this number; if it is a two-digit cycle, click a point on these two numbers, and click a point on the first and last position of a three-digit or more digital cycle.

15. The rounding method is used to approximate rounding decimals.

16. The calculation method of decimal mixed operation is the same as that of integer mixed operation. Unit 6: Statistical tables and charts

The bar chart can directly see the quantity.

Unit 7 Problem Solving Strategies (Enumeration and Graphic Method) k 1. Length+width of rectangle = half the circumference of rectangle.

2. When the perimeter of the rectangle is constant, the greater the difference between length and width, the smaller the area of the rectangle; Conversely, the smaller the difference between length and width, the larger the area of this rectangle.

3. When the area of a rectangle is constant, the greater the difference between length and width, the longer the perimeter of the rectangle; On the contrary, the smaller the difference between length and width, the shorter the circumference of this rectangle. Unit 8: using letters to represent numbers

1. Using letters to represent numbers is concise, easy to remember and easy to use.

2. Multiplication signs between numbers and letters and between letters can be written and expressed; It can also be omitted, but when omitting the multiplication sign, the number must be written before the letter. For example, 5× a = 5. A = 5× y× 7 = 7× y.

The most important thing to note is that letters can represent not only numbers, but also some relationship between two quantities.

4. Find the value of algebraic expression

Example 1. Write the formula first, and then substitute the numerical value into the formula for calculation.

1. Find the area of a parallelogram with a base length of 5cm and a height of 2.4cm (1) s=ah÷2 (2) s=ah÷2.

=5×2.4÷2 =69 (square centimeter)

Example 2. Read 10 1 page 5 questions.