1. Addition, subtraction, multiplication and division are called four operations.
2. In the formula without brackets, if there is only addition, subtraction or multiplication and division, it should be calculated from left to right.
3. In the formula without brackets, if there are multiplication, division and addition and subtraction, calculate the multiplication and division first and then the addition and subtraction.
4. If there are brackets in the formula, count the inner side of brackets first, and then the outer side of brackets; The calculation order of large, medium and small brackets is small → medium → large. The calculation order in brackets follows the above calculation order of 1, 2 and 3.
Knowledge point 2: 0 operation
1.0 is not divisible; The letter means: none, a÷0 is the wrong expression.
2. Add 0 to a number to get the original number; The letter means: A+0 = A.
3. Subtract 0 from a number to get the original number; The letter means: a-0 = a.
4. If you subtract yourself from a number, the difference is 0; Letter: A-A = 0
5. Multiplying a number by 0 still gets 0; Letter: a×0 =0
Divide 6.0 by any number other than 0 to get 0; Letter means: 0÷a =0(a≠0)
Knowledge point 3: Operation law
1. additive commutative law: In the addition operation of two numbers, the positions of two addends are interchanged and the sum is unchanged. Letters indicate:
a+b=b+a
2. The law of addition and association: When three numbers are added, first add the first two numbers and then add another addend; Or add the last two numbers first, then add another addend, and the sum remains the same. Letters indicate:
(a+b)+c=a+(b+c)
3. Law of Multiplication and Interchange: In the multiplication operation of multiplying two numbers, the positions of the two multipliers are interchanged and the product remains unchanged. Letters indicate:
a×b=b×a
4. Multiplication and association law: When three numbers are multiplied, the first two numbers are multiplied first, or the last two numbers are multiplied first, and the product remains unchanged. Letters indicate:
(a×b)×c=a×(b×c)
5. Multiplication and distribution law: when two numbers are added (or subtracted) and then multiplied by another number, it is equivalent to multiplying this number by two addends (subtractions) respectively, and then adding (subtracting) the two products to keep this number unchanged. Letters indicate:
①(a+b)×c=a×c+b×c
a×c+b×c=(a+b)×c
②a×(b-c)=a×b-a×c
a×b-a×c=a×(b-c)
6. The law of continuous decline:
(1) A number minus two numbers in a row equals the sum of the two numbers after subtracting this number, and this number remains unchanged; Letters indicate:
a-b-c=a-(b+c)
a-(b+c)=a-b-c
(2) In the addition and subtraction of three numbers, the positions of the two numbers remain unchanged after the exchange. Letters indicate:
a-b-c=a-c-b
a-b+c=a+c-b
7. Law of division:
(1) When a number is divided by two numbers in a row, it is equal to the product of the two numbers after the number is divided, and this number remains unchanged. Letters indicate:
a÷b÷c=a÷(b×c)
a \(b×c)= a \b \c
(2) In the multiplication and division of three numbers, the positions of the two numbers remain unchanged after the exchange. Letters indicate:
a \b \c = a \c \b
a \b×c = a×c \b
Knowledge point 4: Simple calculation example
First, the common multiplication operation:
1. Integer: 25× 4 = 100, 125× 8 = 1000.
2. Decimal system: 0.25× 4 = 1, 0. 125× 8 = 1.
Second, a simple example of additive commutative law:
50+98+50
=50+50+98
= 100+98
= 198
Third, a simple example of additive associative law:
488+40+60
=488+(40+60)
=488+ 100
=588
Fourth, simple examples of multiplication and method of substitution:
0.25×56×4
=0.25×4×56
= 1×56
=56
Five, simple examples of multiplication and association law:
99×0. 125×8
=99×(0. 125×8)
=99× 1
=99
Six, with a simple example of additive commutative law and the law of association:
65+28.6+35+7 1.4
=(65+35)+(28.6+7 1.4)
= 100+ 100
=200
Seven, a simple example of using multiplicative commutative law and associative law:
25×0. 125×4×8
=(25×4)×(0. 125×8)
= 100× 1
= 100
Eight, a simple example of multiplication and distribution law:
1. Decomposition formula
25×(40+4)
=25×40+25×4
= 1000+ 100
= 1 100
2. Combined type
135× 12.3- 135×2.3
= 135×( 12.3-2.3)
= 135× 10
= 1350
3. Special case 1
99×25.6+25.6
=99×25.6+25.6× 1
=25.6×(99+ 1)
=25.6× 100
=2560
4. Special Example 2
45× 102
=45×( 100+2)
=45× 100+45×2
=4500+90
=4590
5. Special Example 3
99×26
=( 100- 1)×26
= 100×26- 1×26
=2600-26
=2574
6. Special Example 4
5.3×8+35.3×6-4×35.3
=35.3×(8+6-4)
=35.3× 10
=353
Nine, continuous subtraction simple operation example:
528-6.5-3.5
=528-(6.5+3.5)
=528- 10
=5 18
528-89- 128
=528- 128-89
=400-89
=3 1 1
52.8-(40+ 12.8)
=52.8- 12.8- 150
=40-40
=0
X. Examples of simple division and join operations:
3200÷25÷4
=3200÷(25×4)
=3200÷ 100
=32
XI. Other simple examples:
256-58+44
=256+44-58
=300-58
=242
250÷8×4
=250×4÷8
= 1000÷8
= 125