The rules just given for the addition and subtraction of fractions require that the given fractions have like denominators. When the denominators are unlike it is required, before adding or substracting, that the fractions be modified so as to make the denominators equal. For example: Let it be required to find the sum of 2/3 and 2/9. By reference to Fig.

275, we find that 2/5 on line A B is equal to 6/9 on line E F.

These being equal, we may therefore substitute 6/9 for 2/3.

Then we have -

6 /9+2/9=8/9

Now, it will be seen that the fraction - may be had by multiplying both numerator and denominator of the given fraction 2/3 by 3, for 2x3=6;

3x3=9

and we have seen (Art. 380) that this operation does not change the value of the fraction. From this we learn that the denominators may be made equal by multiplying the smaller denominator and its numerator by any number which will effect such a result.

For example: 1/3 + 7/15 = 5/15 +7/15 = 12/15;

and 2/5 + 7/35 = 14/35 + 7/35 = 21/35;

and 3/4 +3/12 + 7/16 = 12/16 + 4/16+ 7/16 = 23/16 = 1 7/16

In this example the second fraction is changed by multiplying by 1 1/3.