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"Addition and Subtraction of Integers" PPT on Integers and Their Addition and Subtraction (Lesson 2)
Part One Content: Basic Knowledge Key Points
Knowledge point 1: The rule of bracket removal
1.-The result of deformation of (a+b-c) is (A)
A.-a-b+c B.-a+b-c
C.a-b+c D.-a-b-c
2. Among the following deformations, which one is incorrect (B)
A.a-( b-c+d )=a-b+c-d
B.a-b-( c-d )=a-b-c-d
C.a+b-( -c-d )=a+b+c+d
D.a+( b+c-d )=a+b+c-d
3. Simplify:
(1)x-(x-y);
PPT on addition and subtraction of integers, part 2: improvement of comprehensive abilities
7. The following formulas must be true (C)
A.3(x+8)=3x+8
B.-x-6=-(x-6)
C.a2-2( a-3 )=a2-2a+6
D.6x+5=6( x+5 )
8. (Adapted) Among the following formulas, the correct one is (C)
A.3x2-2x+5y=3x2-( 2x+5y )
B.3x2-2x+5y=3x2-( 5y-2x )
C.5x-3( 4x-y2 )=5x-12x+3y2
D.5x-3( 4x-y2 )=5x-12x-y2
9. The following sets of integers: ①x-y and -x-y; ②x+y and -x-y; ③x+1 and 1-x; ④-x+y and x-y. Among them, the opposite numbers are (B)
A.①②④ B.②④ C.①③ D.③④
Addition and subtraction of integers PPT, the third part: Expansion, exploration and breakthrough
19.Read the following materials:
Calculation:1+2+3+4+…+99+100.
If adding them one by one is obviously too complicated, we carefully observe the characteristics of this formula and find that using the arithmetic law of addition can simplify the calculation and improve the calculation speed.
1+2+3+…+99+100=( 1+100 )+( 2+99 )+…+( 50+51 )=101×50=5050.
According to the method provided in the reading material, calculate: a+( a+m )+( a+2m )+( a+3m )+…+( a+100m ).
Solution: a+( a+m )+( a+2m )+( a+3m )+…+( a+100m )
=101a+( m+2m+3m+…+100m )
=101a+( m+100m )+( 2m+99m )+( 3m+98m )+…+( 50m+51m )
=101a+101m×50
=101a+5050m.
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