Modern mathematics competition is still a problem-solving competition, but it is mainly held among students (especially senior high school students). The purpose is to discover and cultivate talents. The following are the clever math problems I have compiled. I hope everyone will read it carefully!
First,? Round up? Calculate first
1. Calculation: (1)24+44+56
(2)53+36+47
Solution: (1)24+44+56=24+(44+56)
=24+ 100= 124
Think of it this way: because 44+56= 100 is an integer, let's add them up first.
(2)53+36+47=53+47+36
=(53+47)+36= 100+36= 136
Think of it this way: because 53+47= 100 is an integer, first move +47 together with the symbol to the front of +36; Then calculate the sum of 53+47.
2. Calculation: (1)96+ 15
(2)52+69
Solution: (1) 96+15 = 96+(4+11)
=(96+4)+ 1 1= 100+ 1 1= 1 1 1
Think of it this way: 15 is divided into 15=4+ 1 1, because 96+4= 100 can be rounded up first.
(2)52+69=(2 1+3 1)+69
=2 1+(3 1+69)=2 1+ 100= 12 1
Think of it this way: because 69+3 1= 100, 52 is divided into the sum of 2 1 and 3 1, and then 3 1+69= 100 is rounded up first.
3. Calculation: (1) 63+18+19
(2)28+28+28
Solution: (1) 63+18+19
=60+2+ 1+ 18+ 19
=60+(2+ 18)+( 1+ 19)
=60+20+20= 100
Think of it this way: 63 divided by 63=60+2+ 1 because 2+ 18 and 1+ 19 can be rounded up first.
(2)28+28+28
=(28+2)+(28+2)+(28+2)-6
=30+30+30-6=90-6=84
Think of it this way: because 28+2=30 can be rounded up, but in the end, we have to subtract the extra three twos.
Second, change the operation order: in only? +? 、? -? In the mixed formula of numbers, the operation order can be changed.
Calculation: (1) 45-18+19
(2)45+ 18- 19
Solution: (1) 45-18+19 = 45+19-18.
=45+( 19- 18)=45+ 1=46
Think of it this way: move+19 with the symbol, and move to the front of-18. Then calculate 19- 18= 1.
(2)45+ 18- 19=45+( 18- 19)
=45- 1=44
Think of it this way: plus 18, minus 19 equals minus 1.
Third, calculate the sum of arithmetic continuous numbers.
A string of numbers with equal difference between two adjacent numbers is called arithmetic hyphen, also called 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 and so on are arithmetic hyphens.
1. When the number of arithmetic hyphens is odd, their sum is equal to the middle number multiplied by the number, abbreviated as:
(1) calculation: 1+2+3+4+5+6+7+8+9.
=5? The median number of 9 is 5.
=45 ***9 digits
(2) Calculation: 1+3+5+7+9
=5? The median number of 5 is 5.
=25 *** There are five numbers.
(3) Calculation: 2+4+6+8+ 10
=6? The median number of 5 is 6.
=30 *** There are five numbers.
(4) Calculation: 3+6+9+ 12+ 15.
=9? The median number of 5 is 9.
=45 *** There are five numbers.
(5) Calculation: 4+8+ 12+ 16+20.
= 12? The median number of 5 is 12.
=60 *** There are five numbers.
Fourth, the benchmark method
(1) calculation: 23+20+19+22+18+21.
Solution: After careful observation, the size of each addend is close to 20. You can first add up each addend according to 20, and then add up the less calculated ones and subtract the more calculated ones.
23+20+ 19+22+ 18+2 1
=20? 6+3+0- 1+2-2+ 1
= 120+3= 123
All six addends add 20, and the total is 20? 6= 120.23 is less if it is calculated by 20? 3? , so plus? 3? ; 19 overcharged by 20? 1? , so reduce it again? 1? And so on.
(2) Calculation:102+100+99+101+98.
Solution: Method 1: After careful observation, we can see that each addend is close to 100, so we choose 100 as the benchmark number and use the benchmark number method to calculate skillfully.
102+ 100+99+ 10 1+98
= 100? 5+2+0- 1+ 1-2=500
Method 2: After careful observation, the five numbers can be rearranged as follows: (In fact, some addends move with signs)
102+ 100+99+ 10 1+98
=98+99+ 100+ 10 1+ 102
= 100? 5=500
It can be found that this is a summation problem of arithmetic connected numbers, the middle number is 100, and the number is 5.
;