Calculating skills
Please ask yourself a simple question. What part of mathematics do you use most in you daily life? By which method do you solve problems when you are shopping or dealing with other basic things? I think for most of us it is calculating. It is simple enough that everyone is able to comprehend and apply calculating. As a result, there is need for us to improve this skill. Here are some basic calculating skills with the help of some basic knowledge of algebra or someexperience in using numbers. zedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some expericzedge of algebra or some experic/
Multiplication Skills
In many cases,we’re toubled by the problem of calculation.For example,we may get confused when calculating the price of a certain amount of things.Following are some skills of multiplication,they might help you to some extent when doing the calculation.
1、If the tens digits of the two operation numbers are the same,and the sum of the units is 10,(Like 23 and 27),then we can calculate their product in the following way——Firstly,add 1 to the tens digit and then multiply the tens digit by it.Secondly,calculate the product of the unit digits.Finally,combine them.For example,23 multiplied by 27 is 621,the process could be like this——2×（2+1）=6,3×7=21.Put them together,the result is 621.
Here is the explanation——
When a＋b＝10，（A×10＋a）（A×10＋b）= A×A×100+A×（a+b）×10+ab=A×(A＋１)×100＋ab
2、If the units digits of the two operation numbers are the same,and the sum of the tens is 10,The process is——Firstly,calculate the product of the tens digits,and then add it to the units digit.Secondly,calculate the product of the units digits.Finally combine them.For example,18 multiplied by 98 can be calculated like this——17=1×9+8,64=8×8,so the result is 1764.And 17=2×8+1,01=1×1, so 21×81=1701.
The explanation is——
When A+B=10，（A×10+a）（B×10+a）=（AB+a）×100+a^2
3、If the tens digits of the two operation numbers are consecutive,and the sum of the units is 10(Like 32 and 28),then what is their product?
Firstly,find the bigger one of the two tens digits.Multiply it by itself,then subtract 1.Secondly,find the bigger units digit of the two number,multiply it by itself.Then 100 subtracts it,we can get another number.Combine them together,we can get the exact result.For example,32×28=896， 3 is the bigger one of the tens digits.8=3×3-1.And 2 is the bigger units digit of the two number.96=100-2×2. As a result, the product is 896.Take another one as an example, 47×53=2491,it follows the same rule.
The explanation is——
（A×10+a）×[(A-1)×10＋(10-a)]=(A^2-1)×100+(100-a^2)
4、If the tens digit and the units digit of the first number are the same,and the sum of the tens digit and the units digit of the second number is 10(Like 66 and 37).We can calculate the product like this——Firstly add 1 to the tens digit of the second number.And then calculate the product of the tens digit of the first number and it.Secondly calculate the product of the two unit digits.And then combine them.For example,66×37—— 24=6×(3+1),42=6×7,we can get the result:2442.
The explanation:when a+b=10，（A×10＋A）（a×10＋b）=A(a＋1)×100＋Ab
There are many other quick ways of calculating the product.Although calculating is the basis of math,there’re also many mathematicial principles behind it.As long as we use them correctly,we’re able to increase our calculation speed.
Division skils /If the divisor is double-digit,we can use some method to improve our calculation speed
1.If the top digits of dividend and the divisor is the same , in addition the dividend the first two is not enough. At this time, the first digit of quotient was 8 or 9.
EX.5742÷58=99，4176÷48=87
2.When the first two digits of the number of interim dividend consisting of less than the divisor and the first three digits of the number of provisional composition of the divisor and greater than or equal to 10 times of the divisor,the quotient can be a digit of "9."
Generally, if the dividend is m, the divisor is n, only when 9n ≤ m <10n, n divide m is 9. This is the gist of the method.
EX. 4508÷49=92，6480÷72=90
3.When the divisor is 11, 12 ...... 18 and 19, and in addition to the first two digit of the dividend is not enough to be divided by dividor, you can use method to know the first digit of the quotient according to the difference between the divisor and the first two digit of the dividend. If the difference is 1 or 2, first digit of the quotient is 9; difference is 3 or 4, 8 is first digit of the quotient; the difference is 5 or 6, then 7; the difference is 7 or 8, the first digit of the quotient is 6; the difference is 9, then 5. If not accurate, as long as subtract 1.
EX. 1476÷18=82（the difference between 18 and 14 is 4，so the first digit of the quotient is 8）；
1278÷17=75（the difference between 17 and 12 is 5，the first digit of the quotient is 7）。
Power skills
In face, we can learn much from some formulas we’ve learnt before.
1.We can learn from a2=(a+b)(a-b)+b2
Example:
152=(15+5)x(15-5)+52
532=(53+3)x(53-3)+32
2.Then how about we do it the same to 3-digit numbers?
Like:
8632=900x?+372
But what exactly is ? seems to be a little hard to know quickly.
Let’s think,because the difference between 900 and 863 is the same as that between 900 and ?, so 900+? must be twice as much as 863.
?-800=63x2-100=26
8632=900x826+372
372=40x34+3^2
3.How about cube? we know that
a3=aa2=a(a2-b2)+ab2=a(a+b)(a-b)+ab2
Either a+b or a-b is times as much as 10, it would be the best if they both are.
EX 133=10x13x16+13x32 Is it way easier?
So, these are some basic skills to quickly speed up your calculating. In fact, those ways are just under the nose of us, we ignore them in our daily lives. When we find them, it turns out that math is just like magic, or game. Through those games, we see, understand the world.
Group members:
Zeyu Xu 13122674
Weitao Zhu 13122041
Chao Hu 13121197
After the presentation, we see both our advantages and disadvantages.
We think even though what we are talking about has no further mathematical meaning, these skills can be really useful. Maybe obviously they are some formulas, but when we actually apply these skills, formulas will never come to our mind. What we want is to make people think about what they can do to improve their calculating skills, which haven’t been improved since basic calculating skills were taught. Maybe what we have presented may be thought to aim at primary school students, which we don’t deny. But sometimes primary school students can do better in calculating than us.
At the same time, we realize the lack preparation of this presentation. The progress went too slowly, and there were no such thing as interaction with other students. What’s more, our presentation lacks innovation. Maybe it’s because time’s limited. We could have add more color to our presentation.
Calculating is full of sparkles. It allows us to think in a different way. What we want is we can learn to improve our methods when we are doing mathematics, and that’s joyful.