"Integral Form" PPT Courseware 3

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"Integral Form" PPT Courseware 3

Are you smart enough to list the following algebraic expressions?

(1) If a car travels c kilometers at a speed of 60 kilometers per hour, the driving time of the car is _______ hours.

(2) The width and height of the cuboid are acm, and the length is bcm. Then its volume is ________ cubic centimeters.

(3) A hectare of afforestation was planted in the first year, and the area increased by 10% in the second year compared with the first year. Then the afforestation area in the second year increased by ____ hectares compared with the first year.

(4)The opposite of the cube of x is _______.

Observe the algebraic expression above

60c a2b 10%a -x3

What are their characteristics in terms of the operations they contain?

Definition

These algebraic expressions are all algebraic expressions composed of multiplying numbers and letters (or letters and letters). Such algebraic expressions are called monomials.

A single number or letter is also a monomial

Discuss: If you try to divide the factors in the monomial – 5ab3 into two parts, how should you divide them appropriately?

The numerical factors in a monomial are called the coefficients of the monomial.

For example: the coefficient of 5mn is _____; the coefficient of -6x²y is _____;

The coefficient of 3/5xy is _____; the coefficient of 2πr is _____.

How many different letter factors are there in the other part ab3 besides the coefficient of the monomial –5ab3? What are the exponents of each letter?

In a monomial, the sum of the exponents of all letters is called the degree of the monomial.

For example: the degree of a2 is ____; the degree of 1/2ab is ____;

The degree of -m2a2b is ____; the degree of 2πr is ____;

Example 1: Use algebraic expressions and indicate their coefficients and degrees.

(1) The turnover of a store in August was m yuan, and the turnover in September increased by 25% compared with August. How much yuan was the turnover in September?

(2) The original price of a certain brand of car is a yuan/car, and it is now sold at a 10% discount. If b cars of this kind are sold within a week, how many yuan is the sales this week?

(3) A rectangular parallelepiped-shaped part has the base side lengths acm and bcm respectively. The height is hcm. What is the volume of this part in cubic centimeters?

Variation training

1. If the degree of -5xym is 4, then m=________.

2. The monomials 2x3y4 and -1/7y2zn have the same degree, then n=________.

3. Try to write a monomial so that its coefficient is -3 and its degree is 5. It can be written as ________.

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Update Time: 2024-11-17

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