"Algebraic Expressions" PPT courseware 3

Description

"Algebraic Expressions" PPT courseware 3

Knowledge review

1. Writing format using letters to express numbers

When multiplying numbers and letters, when the multiplication sign is omitted, the numbers should be written in front of the letters. For example, n×2 should be written as 2n, not n2;

When multiplying letters by letters, the multiplication sign can be omitted, or "·" can be used. When multiplying numbers, you must use the multiplication sign "×"

Expressions for addition or subtraction followed by units should be enclosed in parentheses.

Division operations should be written in fraction form, with the division sign replaced by a fraction line.

When multiplying mixed numbers by letters, the mixed numbers should be written in the form of improper fractions

2. Use letters to express quantitative relationships:

1. The Atlantic Ocean is the second largest ocean in the world. According to measurements, the width of his things increases by 4 centimeters every year, and after n years it will increase by _____ centimeters.

2. The length and width of the rectangle are a and b respectively, the side length of the square is c, and the sum of the areas of the rectangle and the square is _____.

3. Xiaoliang walked s meters in t seconds, and his speed is _____ meters/second.

4. Xiaobin spent 166 yuan to buy pens. After buying n pens with a unit price of 5 yuan, the remaining money was _____ yuan.

learning target:

1. Understand the concepts and meanings of algebraic expressions.

2. Be able to list algebraic expressions.

3. Able to skillfully convert natural language into mathematical language

Explore new knowledge

Operation symbols include addition, subtraction, multiplication, division, exponentiation, etc.

These formulas are composed of numbers, letters representing numbers, and operation symbols (addition, subtraction, multiplication, division, exponentiation, etc.). Formulas like this are called algebraic formulas.

A single number or letter is also called an algebraic expression. Such as: 5, -7, a, m, etc.

Characteristics of algebraic expressions

(1) Numbers, numbers and letters, letters and letters are connected with operation symbols (addition, subtraction, multiplication, division, exponentiation, etc.).

(2) The algebraic expression does not contain units, including “=”, “≠”, “≤”, “≥”, “�”, “�”, etc.

(3) A single number or letter is also an algebraic expression

Appreciation of examples

Example 1. Let the letter a represent the number A, and use algebraic expression to represent the number B in the following questions:

(1) The number B is 3 greater than the number A (2) The sum of the two numbers A and B is 10

(3) Number A is 5 times that of number B. (4) Number B is 2 less than the square of number A.

Example 2 is represented by algebraic expression:

(1) The sum of 3 times x and 2 times y;

(2) 3 times the difference between x and 5.

(1)3x+2y (2)3(x－5)

Languages ​​that use words to express quantitative relationships such as "the sum of 3 times x and 2 times y" and "3 times the difference between x and 5" are called natural languages. Through Examples 1 and 2, we transform them into mathematical language. It can be seen that mathematical language is simpler and clearer than natural language when describing problems.

Basic self-test

1. Multiple choice questions:

(1) Which of the following conclusions is correct ( )

A.a is an algebraic expression, 1 is not an algebraic expression B.1 is an algebraic expression, a is not an algebraic expression

C. Neither 1 nor a is an algebraic expression D. 1 and a are both algebraic expressions

(2) The meaning of algebraic formula 2(m+n) is ( )

A.The sum of 2m and n B.The sum of 2 times m and n

C. 2 times the sum of m and n D. 2 times the sum of m and n

2. Use algebraic expression:

(1) The difference between 2 times x and half of y (2) The sum of n times x and -1

3. Express the following algebraic expressions in natural language:

(1)5-4a (2)(a+b)(a-b)

Compliance in court

1. Use algebra to express "the sum of the product of two numbers a and b and c" should be ( )

A. a(b+c) B. a+bc C. (a+b) c D. ab+c

2. Use language to describe the incorrect expression of algebraic expression 1/m-3 ( )

A. A number that is 3 less than the reciprocal of m

B. The difference between the reciprocal of m and 3

C. The difference between the quotient of 1 divided by m and 3

The reciprocal of the difference between D, m and 3

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Update Time: 2024-07-04

This template belongs to Mathematics courseware Qingdao Edition Seventh Grade Mathematics Volume 1 industry PPT template

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