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Simple operation of primary school mathematics (turn)
First, a simple calculation method

1, algorithm

Add:

Additive commutative law a+b=b+a

Additive associative law (a+b)+c=a+(b+c)

Multiplication:

Multiplicative commutative law a×b=b×a

Multiplicative associative law (a×b)×c=a×(b×c)

Multiplication and distribution law (a+b)×c=a×c+b×c

Subtraction:

The nature of subtraction a-b-c=a-(b+c)

Department:

The nature of division a÷b÷c=a÷(b×c)

2. Add (delete) brackets

Parentheses are preceded by+,× and invariant symbols; The brackets are preceded by-,,and the symbol should be changed.

Sign and change rules:+change-,-change+; Change, change.

Step 3 move the position

Move with the number: when moving, move with the symbol in front of the number.

Second, problem-solving skills.

Some students, you test his arithmetic rules, and he knows it backwards, but when they encounter specific problems, like a tiger biting a hedgehog, they don't know where to start. In the final analysis, I still don't know all kinds of simple calculation methods and specific application scenarios.

Next, I will specifically talk about what kind of simple calculation method is used under what circumstances.

First of all, we need to know two concepts: peer operation and two-level operation.

Addition and subtraction are first-order operations, and multiplication and division are second-order operations. If an expression only contains addition, subtraction or multiplication and division, we say it is the same level operation; An expression, if it includes both addition and subtraction and multiplication and division (usually multiplication and addition or multiplication and subtraction), is called secondary operation.

Ⅰ. Two-stage operation

You can only use the multiplication distribution law!

Example 1, 25×(4+8)

=25×4+25×8

= 100+200

=300

Parentheses, multiply separately, and then add.

Example 2, 17×23-23×7

=23×( 17-7)

=23× 10

=230

No brackets, seek the same number.

Give the same number and write the rest in brackets. If the middle is+,write it as+,if the middle is-,write it as-.

Example 3, 99×38+38

=38×99+38× 1

=38×(99+ 1)

=38× 100

=3800

Example 4, 88×20 1-88

=88×20 1-88× 1

=88×(20 1- 1)

=88×200

= 17600

It is a two-stage operation, but it is not a standard form, and can be transformed into a standard form through appropriate deformation. The first step can be omitted after proficiency.

Ⅱ. Operation at the same level

1, including addition only.

Additive commutative law and the law of association are used comprehensively to piece together a piece that can be rounded and put it in brackets.

Example 5,5+137+45+63+50

=(5+45+50)+( 137+63)

= 100+200

=300

2. Only multiplication is included.

Using multiplicative commutative law and associative law synthetically, a piece that can be rounded up is pieced together and enclosed in brackets.

Example 6,8× 25×125× 4

=( 125×8)×(25×4)

= 1000× 100

= 100000

3. Continuous reduction

The essence of subtraction

Example 7,347-148-52

=347-( 148+52)

=347-200

= 147

4. Even division

The essence of division

Example 8, 16000÷ 125÷8

= 16000÷( 125×8)

= 16000÷ 1000

= 16

Step 5 have brackets

Remove brackets

Example 9,740 ℉ (37× 4)

=740÷37÷4

=20÷4

=5

Pay attention to changing the number.

6. Same mantissa

shift position

Example10,445+87-45

=445-45+87

=400+87

=487

III. Multiply two numbers and then divide them.

Multiplication of two numbers is only directly applicable to the multiplication and exchange law, which can not make the calculation simple, and needs to be converted into the same-order operation or the second-order operation through division.

1, there is a number close to the whole hundred (the whole ten is almost the same as the whole thousand).

Break a number close to the whole hundred into "whole hundred+several" or "whole hundred-several".

Example 1 1, 87×99

=87×( 100- 1)

=87× 100-87× 1

=8700-87

=86 13

For example, 12,103x12.

=( 100+3)× 12

= 100× 12+3× 12

= 1200+36

= 1236

2. A number is 25 or 125.

25 in the case of 4, 125 in the case of 8.

Example13,25× 28

=25×(4×7)

=25×4×7

= 100×7

=700

For example, 14 and 125×72.

= 125×(8×9)

= 125×8×9

= 1000×9

=9000

Can also be divided into two levels of operation.

125×72

= 125×(80-8)

= 125×80- 125×8

= 10000- 1000

=9000

Third, error-prone analysis.

1, the multiplication and distribution law only multiplies the first number.

Examples: 15, 125×(80+8)

Wrong solution:

125×(80+8)

= 125×80+8

= 10000+8

= 10008

Positive solution:

125×(80+8)

= 125×80+ 125×8

= 10000+ 1000

= 1 1000

2. Operations at the same level are divided into two levels.

Example16,25× 32

Wrong solution:

25×32

=25×(4×8)

=25×4+25×8

= 100+200

=300

Positive solution:

25×32

=25×(4×8)

=25×4×8

= 100×8

=800

3. I forgot to bring my number to move.

Example17,253-87+53

Wrong solution:

253-87+53

=253-53+87

=200+87

=287

Positive solution: just calculate in the order of operation.

4. Add (delete) brackets,-,and forget to change the symbol.

Example18,3700 ÷ 25× 4

Wrong solution:

3700÷25×4

=3700÷(25×4)

=3700÷ 100

=37

Positive solution: just calculate in the order of operation.

5. An error occurred while disassembling the project.

Example19,37× 99

Wrong solution:

37×99

=37×(99+ 1)

=37× 100

=3700

Positive solution:

37×99

=37×( 100- 1)

=37× 100-37× 1

=3700-37

=3663

Fourth, expand and upgrade.

Two-level operation, no brackets, no same sign.

Example 20,46× 32+27× 64

=46×32+54×32

=32×(46+54)

=32× 100

=3200

Find the multiple, and transform it into the standard form of the multiplication and distribution law by using the changing law of the product.