Be quick to make both mental calculations and calculations using just pen and paper is very useful when you take a math exam and also exams of other scientific subjects, especially if timing is important, such as in GCSEs and in tests in general. In fact:
Here I list some of the most famous tricks with examples to show their efficiency. (Do not have to read them all at once)
1. To add a number to another one, or to subtract a number from another one, sometimes it is easier to round a number to the nearest ten, then add or subtract to the result the complement to nearest ten of the rounded number.
25 + 9 = 25 + (10 − 1) = (25 + 10) − 1 = 35 − 1 = 34
191 − 37 = 191 − (40 − 3) = (191 − 40) + 3 = 151 + 3 = 154 29 + 15 = (30 − 1) + 15 = (30 + 15) − 1 = 45 − 1 = 44
124 · 11 = 1240 + 124 = 1364
Note that often you should use more than one trick in a calculation. Those are just a few of the possible tricks; you can also invent new tricks when you need. At first glance, maybe you do not see great advantages in using them, but I am sure you will change idea after a bit of practice. You can become confident with certain particular operations if you associate numbers with something else, for example you know that a football match is made up two times of 45 minutes each, for a total of 90 minutes, that there are 24 hours in a day and 12 is midday, etc.
To conclude, I want to show you two complete reasonings to solve two exer- cises from GCSEs. They are quite long and technical to be read as if they were tales. I suggest you to take pen and paper, then read slowly, stopping from time to time when you do not understand a passage and to try to re- peat the passages without reading them. Important: Do not memorize as if it were a poem!
How to estimate
207 · 148 49
Firstly note that:
148 ∼ 150 = 3 49 50
Butif50·3=150,then49·3=(50−1)·3=150−3=147. So: 148=147+ 1 =3+ 1