"Basic Properties of Equations" PPT Courseware 2

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"Basic Properties of Equations" PPT Courseware 2

What is the equation?

An equation that uses the equal sign "=" to express an equal relationship is called an equation.

Let us discuss the properties of equations together!

think

(1) Can we get x+5=y+5 from x=y?

(2) Can we get a=b from a+2=b+2?

(3) Can we get -3a=-3b from a=b?

(4) Can we get x/9=y/9 from x=y? Why?

(5) Can we get x=y from 2x+1=2y+1? Your basis?

Come into today’s study with questions!

communication and discovery

Think about the following questions and discuss them with your classmates.

(1) Xiaoying is a year old this year and Xiaoliang is b years old this year. How old will they be in c years?

Answer: Xiaoying is (a+c) years old; Xiaoliang is (b+c) years old

(2) If Xiaoying and Xiaoliang are the same age, (i.e. a=b), will they still be the same age in c years? What about C years ago? Why?

What conclusion do you find from (2)? Can you express it as an equation?

Basic properties of equation 1

If a=b, then a+c=b+c, ​​a-c=b-c

Add (or subtract) the same algebraic expression to both sides of the equation, and the result is still an equation.

Basic properties of equation 2. If a=b, then ac=bc

Similarly, if a=b, then a/c=b/c (c≠o)

If both sides of the equation are multiplied by the same number (or divided by the same number that is not 0), the result is still an equation.

In conclusion

1. Both sides of the equation must participate in operations, and they must perform the same operation.

2. The numbers added, subtracted, multiplied or divided on both sides of the equation must be the same number or the same formula.

3. Both sides of the equation cannot be divided by 0, that is, 0 cannot be used as a divisor or denominator.

consolidate new knowledge

1 Answer the following questions:

(1) Can we get the equation x=y from the equation x+5=y+5? Why?

(2) Can we get the equation x=y from the equation -2x=-2y? Why?

(3) Can we get the equation a+3=b+3 from the equation a=b? Why?

2 Fill in the appropriate numbers or integers in the following brackets so that the equation still holds:

(1) If x+3=10, then x=10-( )

(2) If 2x-7=15, then 2x=15+( )

(3) If 4a=-12, then a=( )

3. Which of the following deformations conforms to the properties of equation ( )

A. If 2x-3=7, then 2x=7-3

B. If 3x-2=1, then 3x=1-2

C. If -2x=5, then x=5+2

D. If -1/3X=1, then X=-3

Expand and improve

1. Choose:

Among the following equations, what can be obtained by deforming equation 2x-3=x+2 is ( )

(A)2x-1=x (B) x-3=2

(C)3x=3+2 (D)x+3=-2

2. After learning the properties of equations, Xiaohong found that using the properties of equations can make complex equations simpler, which made her very excited, so she wrote an equation: 3ａ+ｽb-2＝ 7ｽa+ｽ-2, and begin to use the properties of equality to transform this equation. The process is as follows:

3ａｽｂ＝7ａｽb (add 2 to both sides of the equation)

3ａ＝7a (subtract b from both sides of the equation)

3=7 (divide both sides of the equation by a at the same time)

At this point of transformation, Xiao Hong was immediately dumbfounded: He actually came up with such an equation! So Xiaohong started to check her transformation process, but she couldn't find any mistakes.

Smart classmate, can you make Xiaohong's frown relax in sudden enlightenment?

Enlightenment and reflection

What did you learn in this lesson?

(1) The properties of Eq.

Property of Equality 1: If the same number (or formula) is added (or subtracted) to both sides of the equation, both sides of the equation are still equal.

Property of Equality 2: If both sides of the equation are multiplied by the same number or divided by the same number that is not 0, both sides of the equation are still equal.

(2) Application of equation properties.

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