"Addition and Subtraction of Integers" PPT Courseware 8

Description

"Addition and Subtraction of Integers" PPT Courseware 8

Activity one:

Xiao Hong and Xiao Ming each wrote a formula on their own pieces of paper.

Xiaohong: 2x-3y Xiaoming: 5x+4y

question:

(1) Xiaohong said, find their sum. can you help her?

(2) Xiao Ming said, find the difference between 5x+4y and 2x-3y.

Can you still help him?

The addition and subtraction of integers is usually performed first (removing brackets) and then (merging similar terms).

Do it:

The seventh grade (1) class is divided into three groups to participate in social welfare activities on Sundays. The first group has m students; the number of the second group is 10 less than twice the number of the first group; the number of the third group is the second half of the group. How many students are there in class 7 (1)?

Try your hand:

1. Calculation: 2b3 + (3ab2 – a2b) -2(ab2 +b3)

Solution: 2b3 + (3ab2 – a2b) -2(ab2 +b3)

= 2b3 + 3ab2 – a2b -2ab2 -2b3

= ab2 – a2b

2. Find the sum of polynomials 2x2 -3x-1 and -x2 +3x-5.

3. Find the difference between polynomials 2a2 +3a-1 and 4a2 -4a+2.

Let's discuss

There is such a question: "It is known that A=2a2+2b2-3c2, B=3a2-b2-2c2, C=c2+2a2-3b2, when a=1, b=2,

When c=3, find the value of A-B+C." One student said that b=2 and c=3 given in the question are redundant. Does what he said make sense? Why?

Solution: A-B+C=(2a2+2b2-3c2)- (3a2-b2-2c2)+(c2+2a2-3b2)

=2a2+2b2-3c2 - 3a2+b2+2c2+c2+2a2-3b2

=(2a2-3a2+2a2)+(2b2+b2-3b2)+(-3c2+2c2+c2)

=a2

Because A-B+C is simplified to a2 and does not contain the letters b and c, its value has nothing to do with b and c.

knowledge consolidation

1. One side of the rectangle is 2a+3b, and the other side is smaller than it by b-a. Find the perimeter of this rectangle?

2. It is known that A=x3+x2+x+1, B=x+x2 calculation

(1)A+B (2)B+A (3)A-B (4)B-A

Through calculation, you can find the results of (1) and (2). What is the relationship between the results of (3) and (4)?

3. (1) It is known that the difference between a certain polynomial and 3x2-6x+5 is 4x2+7x-6, find this polynomial.

Solution: (3x2- 6x+5) + ( 4x2+7x - 6)

(2) If the sum of two polynomials is 2x2+xy+3y2, and one addition is x2-xy, find the other addition.

Solution: (2x2+xy+3y2) –(x2-xy)

=2x2 +xy + 3y2 –x2 +xy

=x2+2xy+3y2

Sprint:

(1) Add 2x2-x3-5-3x4 to a polynomial to get 3x4-5x3-3. Find this polynomial.

(2) It is known that A+B=3x2-5x+1, A-C=-2x+3x2-5, when x=2, find the value of B+C.

The value of the algebraic formula (x2+ax-2y+7)-(bx2-2x+9y-1) has nothing to do with the value of the letter x. Find the values ​​of a and b.

Solution: (x2+ax-2y+7)-(bx2-2x+9y-1)

=x2+ax-2y+7-bx2+2x-9y+1=(1-b)x2+(a+2)x-11y+8

∵The value of the algebraic formula (x2+ax-2y+7)-(bx2-2x+9y-1) has nothing to do with the value of the letter x,

∴1-b=0, a+2=0, the solution is a=-2, b=1.

Answer: a=-2, b=1.

Comment:

This is a comprehensive problem that is solved by adding and subtracting integers. First, simplify the given algebraic expression by removing brackets and merging similar terms, and then list the equations according to the meaning of the question to find the values ​​of a and b.

Thinking: If the value of the algebraic formula (2x2+ax-5y+b)-(2bx2-3x+5y-1) has nothing to do with the value of the letter x, find the algebraic formula 3(a2-ab-b2)-(4a2+ab+b2 ) value.

What did you gain from this class?

summary:

1. Rules for addition and subtraction of integers.

2. List the general steps to solve practical problems.

3. To evaluate more complex formulas, simplify them first and then substitute the values ​​into the calculation.

Keywords: teaching courseware for adding and subtracting integers, download the Hebei Education Edition seventh-grade mathematics PPT courseware for the first volume, downloading seventh-grade mathematics slide courseware, downloading PPT courseware for adding and subtracting integers, .PPT format;

For more information about the PPT courseware "Addition and Subtraction of Integers", please click on the Addition and Subtraction of Integers ppt tab.

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Update Time: 2024-06-29

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