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Junior one mathematics knowledge points
Junior one mathematics is the first high school mathematics stage that students are exposed to, and it is also an important stage of basic mathematics knowledge. This paper will introduce the basic knowledge points of junior one mathematics, including integers, rational numbers, fractions, decimals, algebraic expressions, equations, proportions and similarities, geometric figures and so on.

integer

Integer is the most basic number in mathematics, including positive integer, negative integer and 0. We can add, subtract, multiply and Divison integers by the following steps:

1. addition: add the absolute values of two integers, and then determine the sign of the result according to the signs of the two numbers.

For example: (-3)+5=2, (-3)+(-5)=-8, 3+(-5)=-2, 5+(-5)=0.

2. subtraction: add the reciprocal of the minuend, that is, a-b=a+(-b).

For example: 5-3=2, (-5)-(-3)=-2, 3-(-5)=8, (-5)-5=- 10.

3. Multiplication: Multiply the absolute values of two integers, and then determine the sign of the result according to the signs of the two numbers.

For example: (-3)×5=- 15, (-3)×(-5)= 15, 3×(-5)=- 15, 5×(-5)=-25.

4. Division: Divide the dividend by the divisor, and then determine the sign of the result according to the signs of the two numbers.

For example: (-15)÷5=-3, (-15) ÷ (-5) = 3,15 ÷ (-5) =- 3,5 ÷ (-5).

rational number

Rational number is a general term for integers and fractions, including positive rational number, negative rational number and 0. We can add, subtract, multiply and Divison rational numbers through the following steps:

1. addition: change the denominators of two rational numbers into the same denominator, and then add the molecules.

For example: (-3/4)+(5/4)=2/4= 1/2, (-3/4)+(-5/4)=-8/4=-2, 3/4+(-5/4) =-2/.

2. subtraction: add the reciprocal of the minuend, that is, a-b=a+(-b).

For example: 5/4-3/4=2/4= 1/2, (-5/4)-(-3/4) =-2/4, 3/4-(-5/4) = 8.

3. Multiplication: Multiply the numerator and denominator of two rational numbers respectively, and then divide them.

For example: (-3/4) × (5/4) =-15/16, (-3/4) × (-5/4) =15/6, 3/4.

4. Division: the dividend is multiplied by the reciprocal of the dividend, and then divided by the dividend.

For example: (-15/4) ÷ (5/4) =-15/20 =-3/4, (-15/4) ÷ (-5/4) =/kloc-.

mark

Fraction is a representation in mathematics, which consists of a numerator and a denominator. The denominator represents the number of equal parts, and the numerator represents the number of equal parts. We can add, subtract, multiply and divide fractions by the following steps:

1. addition: change the denominator of two fractions into the same denominator, and then add the numerator.

For example: 3/4+5/4=8/4=2, 3/4+ 1/2=5/8, 1/3+2/3= 1.

2. subtraction: add the reciprocal of the minuend, that is, a-b=a+(-b).

For example: 5/4-3/4=2/4= 1/2, 3/4- 1/2= 1/4, 2/3- 1/3.

3. Multiplication: Multiply the numerator and denominator of two fractions respectively, and then divide them.

For example: 3/4×5/4= 15/ 16, 3/4× 1/2=3/8, 1/3×2/3=2/9.

4. Division: the dividend is multiplied by the reciprocal of the dividend, and then divided by the dividend.

For example: 3/4÷5/4=3/5, 3/4÷ 1/2=3/2, 1/3÷2/3= 1/2.

decimal

Decimal system is the representation of fractions. The numerator is divided by the denominator to get a decimal point, and the number after the decimal point represents the equal part of the fraction. We can add, subtract, multiply and divide decimals by the following steps:

1. addition: align the decimal points of two decimal places, and then add the numbers in the corresponding positions.

For example: 0.75+0.25= 1, 0.75+0.5= 1.25, 0.333+0.667= 1.

2. subtraction: add the reciprocal of the minuend, that is, a-b=a+(-b).

For example: 0.75-0.25=0.5, 0.75-0.5=0.25, 0.667-0.333=0.334.

3. Multiplication: Multiply two decimal places and keep the corresponding decimal places.

For example: 0.75×0.25=0. 1875, 0.75×0.5=0.375, 0.333×0.667=0.222.

4. Division: Divide the dividend by the divisor, and then keep the corresponding decimal places.

For example: 0.75÷0.25=3, 0.75 ÷ 0.5 =10.5, 0.667÷0.333=2.

algebraic expression

Algebraic expression is a representation in mathematics, which consists of variables and constants and can be added, subtracted, multiplied and divided. We can add, subtract, multiply and Divison algebraic expressions by the following steps:

1. Addition: Add the coefficients of similar items, and then merge the results.

For example: 3x+4x=7x, 2y+3y=5y, 2x+3y+4x+5y=6x+8y.

2. subtraction: add the reciprocal of the minuend, that is, a-b=a+(-b).

For example: 4x-3x=x, 3y-2y=y, 2x+3y-4x-5y=-2x-2y.

3. Multiplication: Multiply each term of two algebraic expressions, and then merge the results.

For example: (3x+2) (4x-5) =12x2-7x-10, (2y-3) (3y+4) = 6y 2+5y- 12, (2x+3y) (4x.

4. Division: Divide the dividend by the divisor, and then merge the results.

For example: (12x2-7x-10)/(3x+2) = 4x-5, (6y 2+5y- 12)/(2y-3) = 3y+4, (8x 2+).

equation

Equation is a form of equation, which consists of unknown and known numbers. The unknown can be solved by deformation.