Algebra

$\frac{1}{1 \times 4} + \frac{1}{4 \times 7} + \frac{1}{7 \times 10}={1\over{4}}+{1\over28}+{1\over{70}}$

To add fractions, multiply the denominator by a certain number so that the three denominators have a "common multiple".

From the factors, we can see that the Least Common Multiple of 4 = 2^2, 28 = 2^2 * 7, 70 = 2*5*7, is 2^2 * 5 * 7 = 140 (taking the highest exponents--- all this is basic and stuff that you should know already).

So: $={35\over140}+{5\over{140}}+{2\over140}={35+5+2\over{140}}={42\over140}={3\over{10}}$