1. Fast calculation by directly using the multiplicative associative law

By using the law of multiplicative association, the product of two factors can be calculated first, which makes the calculation simple. In order to calculate quickly, we can memorize some commonly used multiplication formulas, such as: 25× 4 = 100, 125× 8 = 1000, 12× 5 = 60. ...

Example 1 Calculate 236×4×25

Solution: 236×4×25

=236×(4×25)

=236× 100

=23600

2. Fast calculation of simultaneous application of multiplicative commutative law and associative law.

Multiply several factors, first exchange the positions of the factors, so that the products of the factors are integer ten, integer hundred and integer thousand, and it is simpler to calculate by grouping according to the law of association.

Example 2 125×2×8×25×5×4

Solution: The original formula = (125× 8 )× (25× 4 )× (5× 2).

= 1000× 100× 10

= 1000000

3. Simple calculation is made directly by using the multiplication and distribution law.

Example 3 Calculation:

( 1) 175×34× 175×66

(2)67× 12+67×35+67×52+67

Solution: (1) According to the multiplication distribution law:

Original formula = 175× (34+66)

= 175× 100

= 17500

(2) After 67 is regarded as 67× 1, it is simplified by multiplication and division.

Original formula = 67× (12+35+52+ 1)

=67× 100

=6700

4. Divide one factor into two factors, and use exchange method and combination method to calculate skillfully.

Example 4 Calculate (1)28×25.

(2)48× 125

(3) 125×5×32×5

Solution: (1) Original formula = 4× 7× 25.

=7×(4×25)

=7× 100

=700

(2) The original formula = 6× 8×125 = 6× (8×125)

=6× 1000

=6000

(3) The original formula = 125× 8× 4× 5× 5.

=( 125×8)×(4×25)

= 1000× 100

= 100000

5. Use the multiplication table to calculate indirectly.

Example 5 Calculate (1)26×99.

(2) 1236× 199

(3)7 13× 10 1

Solution: (1) from 99 = 100- 1,

Original formula = 26× (100- 1)

=26× 100-26× 1

=2600-26

=2574

(2) From 199 = 200- 1,

Original formula = 1236× (200- 1)

= 1236×200- 1236× 1

=247200- 1236

=246000-36

=245964

(3) The original formula = 713× (100+1)

=7 13× 100+7 13× 1

=7 1300+7 13

=720 13

6. Clever calculation of the product of several common special factors

(1) The product of any natural number multiplied by 0 is equal to 0.

Example 6 Calculate1326+427× 9× 42× 0-315.

Solution: The original formula = 1326+0-3 15.

= 10 1 1

(2) In the multiplication formula, any number is multiplied by 1 to get the original number.

Example 7 8736× 49+8736× 40-8736× 88

Solution: According to multiplication and division method and distribution method,

Original formula = 8736× (49+40-88)

=8736× 1

=8736

(3) Find the product of a number multiplied by 5.

Example 8 Calculation 12864732×5

Solution: When a number is multiplied by 5, it is actually multiplied by half of 10, so you can add a 0 (enlarge 10 times) at the end of the multiplicand then divide the obtained number by 2 (halve).

Original formula = 128647320 ÷ 2

=64323660

(4) Find the product of a number multiplied by 1 1.

Example 913254638×11

Solution: arrange the multiplicand in turn, write the first two digits of this number, and then add the two adjacent numbers in the middle (enough 10 to enter 1), which is the product of this number multiplied by 1 1.

13254638× 1 1= 14580 10 18

The students summed up this quick calculation multiplied by 1 1 into one sentence, which is called "pulling on both sides and adding in the middle".

(5) Find the product of ten times ten.

Example 10 calculation 18× 12.

Solution: If both factors are ten digits, you can add the digits of one factor to the digits of the other factor, multiply it by 10, and add the products of the digits of the two factors.

Original formula = (18+2) × 10+2× 8.

=200+ 16

=2 16