Fast calculation can not only simplify the calculation process, but also improve the calculation efficiency.
Therefore, in the learning process, we not only need to master the calculation rules, but also need to learn some calculation skills.
"First calculate gather together enough.
When adding, if the items in the formula can be grouped properly, the calculation process will be greatly simplified. If the two numbers add up, if they can add up to exactly ten, one hundred, one thousand, ten thousand ... then calculate first.
For example,1+9 =10,3+7 =10,2+8 =10,4+6 =10,5+5 =10.
Another example is:12+88 =100,35+65 =100,21+79 =100,44+56 =100.
In the above formula, 1 is called the "complement" of 9; 79 is called the "complement" of 2 1, and 44 is also called the "complement" of 56, which means that two numbers are "complements" of each other.
Example 1. Calculation 53+55+47
Solution: The original formula =(53+47)+55.
= 155
Calculate 23+39+6 1
Solution: Original formula =23+(39+6 1)
=23+ 100
= 123
For those that cannot be rounded directly, one of the numbers can be split and rounded again.
Example 2. Calculating 87+ 15
Solution: The original formula =87+ 13+2.
=(87+ 13)+2
= 100+2
= 102
Calculation 54+79
Solution: The original formula =33+2 1+79.
=33+(2 1+79)
=33+ 100
= 133
Calculate 65+ 18+27
Solution: The original formula =60+2+3+ 18+27.
=60+(2+ 18)+(3+27)
=60+20+30
= 1 10
For numbers that are not directly rounded up, you can round up first and then subtract the rounded number.
Example 3. Calculation: 38+29+ 19
Solution: The original formula = (38+2)+(29+1)+(19+1)-4.
=40+30+20-4
=90-4
=86
arithmetic series
Arithmetic continuous number (arithmetic progression) is equal to the difference between two adjacent numbers, which is called arithmetic continuous number, also known as arithmetic progression, such as:
1,2,3,4,5,6,7,8,9
1,3,5,7,9
2,4,6,8, 10
3,6,9, 12, 15
4,8, 12,16,20, etc. Is an arithmetic continuous number.
1, when the number of arithmetic continuous numbers is odd, their sum is equal to the middle number multiplied by the number.
Example 4. Calculate 1+2+3+4+5+6+7+8+9.
Solution: Original formula =5×9 (middle number is 5, ***9)
=45
Calculate1+3+5+7+9+11+13.
Solution: The original formula =7×7 (the middle number is 7 and the number * * * is 7).
=49
Calculate 2+4+6+8+ 10.
Solution: The original formula =6×5 (the middle number is 6, ***5).
=30
2. When the number of arithmetic consecutive numbers is even, their sum is equal to the sum of the first number and the last number multiplied by half of the number.
Example 5. Calculate1+2+3+4+5+6+7+8+9+10.
*** 10 number, the half number is 5, the first number is 1, and the last number is 10.
Solution: The original formula =( 1+ 10)×5.
= 1 1×5
=55
Calculate1+3+5+7+9+1+13+15.
***8 numbers, half of which is 4, the first number is 1, and the last number is 15.
Solution: The original formula =( 1+ 15)×4.
= 16×4
=64
Calculate 2+4+6+8+ 10+ 12.
***6 numbers, half of which is 3, the first number is 2 and the last number is 12.
Solution: The original formula =(2+ 12)×3.
= 14×3
=42
Benchmark number method
First, observe which numbers of each addend are close, then add each addend according to the close numbers, then add up the ones with less calculation and subtract the ones with more calculation.
Example 6. Calculate 23+22+24+18+19+17.
Through observation, it was found that all the additions were close to 20.
Solution: The original formula =20×6+3+2+4-2- 1-3.
= 120+9-6
= 123
Calculation103+102+101+99+98.
All the additions are close to 100.
Solution: The original formula =100× 5+3+2+1-2.
=500+3
=503
Clever calculation in subtraction
1, first add up several "complements" of each other, and then subtract them from the minuend.
Example 7. Calculation 400-63-37
Solution: Original formula = 400-(63+37)
=400- 100
=300
Calculation 1000-90-80- 10-20.
Solution: Original formula =1000-(90+80+10+20)
= 1000-200
=800
2. Subtract those minuets whose mantissa is the same as the minuend.
Example 8. Calculation 4622-(622+ 149)
Solution: Original formula =4000- 149.
=385 1
3. Use "complement" to round first, and then calculate (pay attention to subtract the extra number and add the extra number).
Example 9. Calculation 505-397
Solution: The original formula = 500+5-400+3 (plus 3 minus).
= 108
Calculation 523-289
Solution: The original formula =523-300+ 1 1 (added 1 1).
=223+ 1 1
=234
Calculate 358+997
Solution: The original formula = 358+ 1000-3 (minus the extra 3).
= 1355
Addition-subtraction mixed operation
1, the rule of removing brackets and adding brackets
In a formula with only addition and subtraction operations, if there is a "+"sign in front of the brackets, the operation symbols in the brackets will remain unchanged whether the brackets are removed or added; If there is a "-"sign in front of the bracket, whether the bracket is deleted or added, the operation symbol in the bracket will change, and "+"will change to "-"and "-"will change to "+".
Example 10. Calculate 200-20- 10-30
Solution: Original formula = 200-( 10+20+30)
=200-60
= 140
Calculation 100-40+30
Solution: Original formula = 100-(40-30)
= 100- 10
=90
2. Use the symbol "move"
Example 1 1. Calculate 545+47- 145+53.
Solution: The original formula = 545- 145+47+53.
=(545- 145)+(47+53)
=400+ 100
=500
Note: The operation symbol before each number is the symbol of this number, such as +47,-145, +53. Although there is no symbol before 545, it should be +545.
3. Two numbers with the same number but opposite signs can be directly "cancelled".
Example 12. Calculate 18+2- 18+4.
Solution: The original formula = 18- 18+2+4.
=6