| A fully comprehended problem when solved at nice | | | | knows only one arithmatical operatio i.e. "ADDITION" |
| speed and 100% accuracy is what makes you | | | | and for all other operations it just manipulates it adding |
| proficient in Mathematics. TRUE? Your proficiency in | | | | skill?). |
| mathematics requires three things: | | | | Any way... the above example can also be solved as |
| 1. Comprehension | | | | follows: |
| 2. Speed | | | | 89 x 8 |
| 3. Accuracy | | | | = (80 + 9) x 8 Now we have used “80+9” in |
| 1.Comprehension | | | | place of “90-1” |
| Can you find a solution without knowing the problem? | | | | = 640 + 72 |
| Certainly not! How can you find a solution, if you are | | | | = 712 |
| not clear about the problem itself? As in real life, in | | | | Example 2 |
| mathematics too, the solution of a problem lies in | | | | 65 x 12 |
| grasping the problem properly. If you are able to see | | | | = (60 + 5) x 12 |
| through a problem, you can certainly see though its | | | | = 720 + 60 |
| solution. | | | | = 780. |
| 2.Speed | | | | OR |
| Speed means your calculating speed. Higher the | | | | 65 x 12 |
| speed, more proficient you are! If you want to be | | | | = 65 x (10+2) |
| more skilled in math, you will have to improve upon you | | | | = 650+130 |
| calculating speed. | | | | = 780 |
| 3.Accuracy | | | | Example 3 |
| The calculations you have done MUST be 100% | | | | 34 x 9 |
| accurate to reach the right solution. If you have | | | | = (30 + 4) x 9 |
| comprehended the problem properly and solved it at a | | | | = 270 + 36 |
| nice speed but you are not 100% accurate in | | | | = 306 |
| calculations then all will be a waste | | | | Example 4 |
| All the above three pre-requisits of your efficiency can | | | | 312 x 14 |
| be sharpened with practice and labor. A little more | | | | = (300 + 10 +2) x 14 |
| hardwork can do wonders. | | | | = 4200+140+28 |
| Shortcuts are double edged knife. Generally in life | | | | = 4368 |
| shortcuts are dangerous. But at certain places these | | | | With a little practice you will be devising your own |
| shortcuts can make your life pleasantly easy. Using | | | | ways of such manipulations to get the answer quickly |
| shortcuts in math can enhance your calculating speed | | | | and accurately. |
| as well as accuracy. This article gives to shortcuts | | | | The above mentioned methods make the things |
| while you are multiplying. | | | | simpler and more accurate, the only thing required is |
| Applying Tactics in Multiplication | | | | applying these tactics regularly while doing such |
| While multiplying, we may also use certain tactics to | | | | calculations. So start using this method in your real life |
| find the answer quickly. | | | | to improve your calculating speed. |
| Example 1 | | | | Can you multiply 68 by 62 in exactly 2.5 seconds ? |
| 89 x 8 | | | | Yes! You can. |
| For making the above calculation simple we may do | | | | Can you calculate 120342 x 11 in exactly 5 seconds ? |
| as mentioned below | | | | Yes! You can. |
| 89 x 8 | | | | Is 1000020708 divisible by 18 ? |
| = (90 -1) x 8 | | | | Yes! you can reply in just 2 seconds! |
| = 720 – 8 | | | | 0.5 is what % of 75 ? |
| = 712. | | | | There are many more shortcuts available for these |
| But avoid using a minus sign as far as possible while | | | | type of questions and you will be able to solve all |
| bifurcating a number. Remember, adding is always | | | | these applying least or at the most very simple |
| easier as well as less prone to mistakes than | | | | calculations. |
| subtraction. (By the way, do you knwo that computer | | | | |