"Algebraic Formulas" PPT Courseware 2

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"Algebraic Formulas" PPT Courseware 2

Use letters to express quantitative relationships

⒈ The perimeter of a square with side length a cm is ______cm and the area is ______cm.

⒉ The speeds of Xiaohua and Xiaoming are x meters/second and y meters/second respectively. After 6 minutes, they have traveled a total of ______ meters.

⒊ After the temperature rises from 2℃ to t℃, it is ______.

4. Xiaobin spent 166 yuan to buy pens and bought n pens with a unit price of 5 yuan. The remaining money was ______ yuan. He could buy at most ______ pens of this kind.

Can you express it algebraically?

(1) The difference between 3 times x and 2;

(2) The square of the sum of a and b;

(3) The square root of 2a;

(4) The square of the two numbers a and b;

(5) The square of the difference between the two numbers a and b;

(6) The product of the sum of two numbers a and b and their difference;

Describe in words the meaning of the following algebraic expressions

1. (1) a+b; (2) 2(a+b); (3) 2a+3b

Solution: (1) The sum of a and b

(2) 2 times the sum of a and b

(3) The sum of 2 times a and 3 times b

Note:

The order of operational relations in algebraic expressions is usually related to language description. Generally, it is: read first, write first, and calculate first, read first.

2. (1) (a+b)2 (2) a2+b2

Solution: (1) The square of the sum of a and b;

(2) The sum of the squares of the two numbers a and b.

How to express the algebraic expressions (a-b)2 and a2-b2 in literal language?

Math Applications

Please explain the algebraic expression a+2.

Solution: (1) There is a student in a certain class, and there are 2 new students transferred this semester. This class has a total of (a+2) students in this semester.

(2) The radius of a circle is a cm. If the radius is increased by 2 cm, the radius of the circle is (a+2) cm.

self practice

column algebra

The ticket prices for a certain park are: 10 yuan per adult ticket and 5 yuan per student ticket. There are x adults and y students in a tour group. How much ticket fee should the tour group pay?

Solution: The ticket fee payable by this tour group is (10x+5y) yuan

think about it

What else can the algebraic expression (10x+5y) represent?

(1) If x (m/s) is used to represent Xiao Ming’s running speed, and y (m/s) is used to represent Xiao Ming’s walking speed, then (10x+5y) represents the distance traveled by him running for 10 seconds and walking for 5 seconds;

(2) If x and y represent the number of 1 yuan and 50 cent coins respectively, then (10x+5y) represents the total number of cents of x 1 yuan coins and y 50 cent coins.

Can you give other examples?

What else can the algebraic expression 10x+5y represent?

1. The teacher has x pieces of 10 yuan and y pieces of 5 yuan, then 10x+5y represents how much money the teacher has.

2. A car drove at a speed of x kilometers/hour for 10 hours, and then drove at a speed of y kilometers/hour for 5 hours. Then 10x+5y represents the distance traveled by the car.

3. A certain mathematics material costs 10 yuan each, and each English material costs 5 yuan. Xiao Ming bought x mathematics materials and y English materials, then 10x+5y represents how much money was shared.

practise

In a certain place, people found that there is an approximate relationship between the number of times a certain kind of cricket chirps and the temperature: divide the number of times a cricket chirps in 1 minute by 7, and then add 3 to approximately get the temperature of the place at that time (ºC ).

Use an algebraic expression to express the temperature of the place at that time

Challenge yourself and explore the rules

Fill in the blanks according to the rules:

1) 4, 7, 10, 13, ...the fifth item is ____, and the nth item is ___

2) 1, 8, 27, 64, …the fifth item is ____, and the nth item is ___

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For more information about the "Algebraic Expressions" PPT courseware, please click the Algebraic Expressions ppt tab.

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Update Time: 2024-09-14

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

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