Answers to Chinese language review for primary school graduation
Volume and surface area
The area of a triangle = base × height ÷ 2. Formula S= a×h÷2
The area of a square = side length × side length Formula S= a2
The area of a rectangle = length × width Formula S= a×b
The area of the parallelogram = base × height formula S = a × h
The area of the trapezoid = (upper base + lower base) × height ÷ 2 formula S = (a + b) h ÷2
Sum of interior angles: The sum of interior angles of a triangle = 180 degrees.
The surface area of the cuboid = (length × width + length × height + width × height) × 2 Formula: S = (a × b + a × c + b × c) × 2
< p>Surface area of the cube = Edge length × Edge length × 6 Formula: S = 6a2Volume of the cuboid = Length × Width × Height Formula: V = abh
Cuboid (or cube ) = base area × height formula: V = abh
Volume of the cube = edge length × edge length × edge length formula: V = a3
Perimeter of the circle = diameter ×π formula: L＝πd＝2πr
The area of a circle = radius × radius × π formula: S＝πr2
The surface (side) area of the cylinder: the surface (side) area of the cylinder ) area is equal to the perimeter of the base multiplied by the height. Formula: S=ch=πdh=2πrh
Surface area of a cylinder: The surface area of a cylinder is equal to the circumference of the base multiplied by the height plus the area of the circles at both ends. Formula: S=ch+2s=ch+2πr2
The volume of a cylinder: The volume of a cylinder is equal to the base area times the height. Formula: V=Sh
The volume of the cone = 1/3 base × area height. Formula: V=1/3Sh
Arithmetic
1. Commutative law of addition: When two numbers are added, the positions of the addends are exchanged, and the sum remains unchanged.
2. Associative law of addition: a + b = b + a
3. Commutative law of multiplication: a × b = b × a
4. Multiplication Associative law: a × b × c = a × (b × c)
5. Distributive law of multiplication: a × b + a × c = a × b + c
6 , Properties of division: a ÷ b ÷ c = a ÷ (b × c)
7. Properties of division: In division, the dividend and divisor expand (or shrink) by the same multiple at the same time, and the quotient is not Change. O divided by any number that is not O is O. Simple multiplication: For multiplications with O at the end of the multiplicand and multiplier, you can multiply the ones before the O first. Zeros do not participate in the operation. Several zeros are dropped and added to the end of the product.
8. Division with remainder: dividend = quotient × divisor + remainder
Equations, algebra and equations
Equation: the value on the left side of the equal sign and An equation in which the values on the right side of the equal sign are equal is called an equation. Basic properties of equations: If both sides of the equation are multiplied (or divided) by the same number at the same time, the equation still holds.
Equation: An equation containing unknown numbers is called an equation.
Linear equation of one variable: An equation that contains an unknown number and the degree of the unknown is linear is called a linear equation of one variable. Learn the examples and calculations of linear equations of one variable. That is, give an example of the formula with χ and calculate it.
Algebra: Algebra is the use of letters instead of numbers.
Algebraic expression: An expression represented by letters is called an algebraic expression. For example: 3x =ab+c
Fraction
Fraction: Divide the unit "1" evenly into several parts, and the number that represents such a part or several points is called a fraction.
Comparison of fractions: Compared with fractions with the same denominator, the one with the larger numerator is larger and the one with the smaller numerator is smaller. When comparing fractions with different denominators, first make the common denominator and then compare; if the numerators are the same, the one with the larger denominator will be smaller.
The rules for adding and subtracting fractions: When adding and subtracting fractions with the same denominator, only add and subtract the numerators, leaving the denominator unchanged. To add and subtract fractions with different denominators, first add and subtract the common denominators.
To multiply a fraction by an integer, use the product of the numerator of the fraction and the integer as the numerator, and the denominator remains unchanged.
To multiply a fraction by a fraction, use the product of the numerators as the numerator, and the product of the denominators as the denominator.
The rules for adding and subtracting fractions: When adding and subtracting fractions with the same denominator, only add and subtract the numerators, leaving the denominator unchanged. To add and subtract fractions with different denominators, first add and subtract the common denominators.
The concept of reciprocal: 1. If the product of two numbers is 1, we say one is the reciprocal of the other. These two numbers are reciprocals of each other. The reciprocal of 1 is 1, and there is no reciprocal of 0.
Dividing a fraction by an integer (other than 0) is equal to multiplying the fraction by the reciprocal of the integer.
The basic properties of fractions: the numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, the size of the fraction
The division method of fractions: divide by a number (except 0), which is equal to multiplying the reciprocal of this number.
Proper fraction: The fraction whose numerator is smaller than the denominator is called a proper fraction.
Improper fractions: A fraction whose numerator is greater than the denominator or whose numerator and denominator are equal is called an improper fraction. An improper fraction is greater than or equal to 1.
Mixed numbers: Writing improper fractions in the form of integers and proper fractions is called mixed numbers.
Basic properties of fractions: If the numerator and denominator of a fraction are multiplied or divided by the same number (except 0) at the same time, the size of the fraction remains unchanged.
Quantity relationship calculation formula
Unit price × quantity = total price 2. Unit output × quantity = total output
Speed × time = distance 4. Work efficiency × time = total amount of work
Addend + addend = sum one addend = sum + another addend
Minuend - Minuend = Difference Minuend = Minuend - Difference minuend = subtrahend + difference
Factor × factor = product one factor = product ÷ another factor
Divisor ÷ divisor = quotient divisor = dividend ÷ quotient dividend = quotient × Divisor
Unit of length:
1 kilometer = 1 kilometer 1 kilometer = 1000 meters
1 meter = 10 decimeters 1 decimeter = 10 centimeters 1 Centimeter = 10 millimeters
Area unit:
1 square kilometer = 100 hectares 1 hectare = 10,000 square meters
1 square meter = 100 square decimeters 1 Square decimeter = 100 square centimeters 1 square centimeter = 100 square millimeters
1 mu = 666.666 square meters.
Unit of volume
1 cubic meter = 1000 cubic decimeters 1 cubic decimeter = 1000 cubic centimeters
1 cubic centimeter = 1000 cubic millimeters
1 liter = 1 cubic decimeter = 1000 ml 1 ml = 1 cubic centimeter
Unit of weight
1 ton = 1000 kilograms 1 kilogram = 1000 grams = 1 kilogram = 1 Shijin
ratio
What is ratio: The division of two numbers is called the ratio of the two numbers. For example: 2÷5 or 3:6 or 1/3. The first and last terms of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged.
What is proportion: The formula that expresses the equality of two ratios is called proportion. For example, 3:6=9:18
The basic property of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.
Solving the proportion: Finding the unknown items in the proportion is called solving the proportion. For example, 3:χ=9:18
Positive proportion: two related quantities, one quantity changes, and the other quantity also changes. If the corresponding ratio of the two quantities ( That is to say, if the quotient k) is certain, these two quantities are called directly proportional quantities, and their relationship is called a directly proportional relationship. For example: y/x=k (k is certain) or kx=y
Inverse proportion: two related quantities, if one quantity changes, the other quantity will also change. If these two quantities The product of two corresponding numbers in is constant, these two quantities are called inversely proportional quantities, and their relationship is called an inversely proportional relationship. For example: x×y = k (k is certain) or k / x = y
Percent
Percent: A number that expresses what percentage of another number a number is, called percentage. Percentage is also called percentage or percentage.
To convert a decimal into a percentage, just move the decimal point two places to the right and add a percent sign at the end. In fact, to convert a decimal into a percentage, just multiply the decimal by 100%. To convert a percentage to a decimal, simply remove the percent sign and move the decimal point two places to the left.
To convert a fraction into a percentage, usually first convert the fraction into a decimal (when division cannot be completed, usually three decimal places are retained), and then convert the decimal into a percentage. In fact, to convert a fraction into a percentage, you first need to convert the fraction into a decimal and then multiply it by 100%.
To convert a percentage into a fraction, first rewrite the percentage into a fraction, and then reduce the ratio that can be reduced to the simplest fraction.
You must learn to convert decimals into fractions and fractions into decimals.
Multiples and Divisors
Greatest common divisor: The common divisor of several numbers is called the common divisor of these numbers. There are a finite number of common factors. The largest one is called the greatest common divisor of these numbers.
Least common multiple: The common multiple of several numbers is called the common multiple of these numbers. There are an infinite number of common multiples. The smallest one is called the least common multiple of these numbers.
Co-prime numbers: Two numbers whose common divisor is only 1 are called co-prime numbers. Two adjacent numbers must be mutually prime. Two consecutive odd numbers must be relatively prime. 1 is relatively prime to any number.
Common fraction: converting fractions with different denominators into fractions with the same denominator that are equal to the original fraction is called a common fraction. (Use the least common multiple for common fractions)
Reduction: Divide the numerator and denominator of a fraction by a common factor at the same time. The fraction value remains unchanged. This process is called reduction.
Simplest fraction: A fraction whose numerator and denominator are coprime numbers is called the simplest fraction. At the end of the fraction calculation, the number must be converted into the simplest fraction.
Prime number (prime number): If a number has only two divisors, 1 and itself, such a number is called a prime number (or prime number).
Composite number: If a number has other divisors besides 1 and itself, such a number is called a composite number. 1 is neither a prime number nor a composite number.
Prime factors: If a prime number is a factor of a certain number, then the prime number is the prime factor of the number.
Decomposing prime factors: Expressing a composite number in terms of prime factors is called decomposing prime factors.
Characteristics of multiples:
Characteristics of multiples of 2: Each bit is 0, 2, 4, 6, 8.
Characteristics of multiples of 3 (or 9): The sum of the numbers in each digit is a multiple of 3 (or 9).
Characteristics of multiples of 5: Each bit is 0, 5.
Characteristics of multiples of 4 (or 25): the last two digits are multiples of 4 (or 25).
Characteristics of multiples of 8 (or 125): the last three digits are multiples of 8 (or 125).
Characteristics of multiples of 7 (11 or 13): The difference (big-small) between the last three digits and the remaining digits is a multiple of 7 (11 or 13).
Characteristics of multiples of 17 (or 59): The difference (big-small) between the last 3 digits and 3 times the remaining digits is a multiple of 17 (or 59).
Characteristics of multiples of 19 (or 53): The difference (big-small) between the last 3 digits and 7 times the remaining digits is a multiple of 19 (or 53).
Characteristics of multiples of 23 (or 29): The difference (big-small) between the last 4 digits and 5 times the remaining digits is a multiple of 23 (or 29).
For two numbers in a multiple relationship, the greatest common divisor is the smaller number, and the least common multiple is the larger number.
For two numbers that are mutually prime, their greatest common divisor is 1 and their least common multiple is their product.
When two numbers are divided by their greatest common divisor, the resulting quotients are relatively prime.
The product of two numbers and their least common multiple is equal to the product of the two numbers.
The common divisor of two numbers must be the divisor of the greatest common divisor of the two numbers.
1 is neither a prime number nor a composite number.
Use 6 to divide prime numbers greater than 3, and the result must be 1 or 5.
Odd and even numbers
Even numbers: Numbers whose ones digit is 0, 2, 4, 6, or 8.
Odd numbers: numbers whose units digit is not 0, 2, 4, 6, or 8.
Even number ± even number = even number Odd number ± odd number = odd number Odd number ± even number = odd number
The sum of an even number of even numbers is an even number, and the sum of an odd number of odd numbers is an odd number.
Even number × even number = even number Odd number × odd number = odd number Odd number × even number = even number
The sum of two adjacent natural numbers is an odd number, and the product of adjacent natural numbers is an even number.
If one of the numbers in the multiplication is an even number, then the product must be an even number.
Odd number ≠ even number
Divisible
If c|a, c|b, then c|(a±b)
If , then b|a, c|a
If b|a, c|a, and (b, c)=1, then bc|a
If c|b, b|a, then c|a
Decimals
Natural numbers: Integers used to represent the number of objects are called natural numbers. 0 is also a natural number.
Pure decimal: a decimal whose ones digit is 0.
With decimals: decimals with each digit greater than 0.
Recurring decimal: A decimal, starting from a certain digit of the decimal part, a number or several numbers appear repeatedly in sequence. Such a decimal is called a recurring decimal. Such as 3. 141414
Non-repeating decimal: A decimal, starting from the decimal part, does not have a number or several digits that repeatedly appear in sequence. Such a decimal is called a non-repeating decimal. Such as 3. 141592654
Infinitely recurring decimal: A decimal, from the decimal part to an infinite number of digits, one number or several numbers appear repeatedly in sequence. Such a decimal is called an infinitely recurring decimal. Such as 3. 141414...
Infinite non-recurring decimals: A decimal, starting from the decimal part to an infinite number of digits, without a number or several digits repeating in sequence, such a decimal is called infinite non-recurring decimal.
Such as 3. 141592654……