 Hello and welcome to the session. In this session we are going to discuss how to solve first degree equations including those involving fractions, decimals, ratio, proportion and percent. Now we are already familiar with method of solving a first degree equation. Now steps of solving an equation in first degree in X are as follows. First of all we shall open the brackets if exist in the equation. Then we add and subtract to get all terms within X on one side of the equation and everything else on the other side. Then we multiply or divide to solve for X. Now we shall solve first degree equations involving decimals, fractions, ratio, proportion and percent. Now we shall consider an example. Suppose we have to solve the proportion for X and that is X upon 3.5 is equal to 2.4 X plus 1 whole upon 4. So first we will cross multiply it and we get 4 X is equal to 3.5 into 2.4 X plus 1 the whole. Now we shall open the brackets and we get 4 X is equal to 3.5 into 2.4 X that is equal to 8.4 X plus 3.5 into 1 that is equal to 3.5. Now we bring all the terms of X on one side and the constants on the other side of the equation and we get 4 X minus 8.4 X is equal to 3.5. This implies that minus of 4.4 X is equal to 3.5. Now we divide both sides by minus 4.4 and we get X is equal to 3.5 upon minus 4.4 that is equal to minus of 0.79. So X is equal to minus of 0.79. Similarly we can solve equations involving percent. Suppose we have to find 14 percent of what number is 7. Now here let X be the number whose 14 percent is equal to 7. So we write 14 percent of X is equal to 7. This implies 14 by 100 into X is equal to 7. Now this is an equation in first degree. To solve it we multiply both sides by 100 and we get 14 into X by 100 is 14 X by 100 into 100 is equal to 7 into 100. This implies that 14 X is equal to 700. To find the value of X we divide both sides by 14 and we get 14 X upon 14 is equal to 700 by 14 which implies that X is equal to 700 by 14. Here 14 into 1 is 14 and 14 into 50 is 700. So this implies that X is equal to 50. So we say that the number is 50 whose 14 percent is 7 Now let us consider one more example if one fourth of all hibernating animals in US are in danger of becoming extinct. This means 6348 hibernating animals are in danger. We need to find how many hibernating animals are there in US. First we form its equation. Let number of all hibernating animals in US be X and it is given that one fourth of X are in danger of becoming extinct and that is equal to 6348. So equation is 1 by 4 of X that is 1 by 4 into X is equal to 6348. To find the value of X we multiply by 4 on both sides and we get 1 by 4 X into 4 is equal to 6348 into 4. This implies that X is equal to 25392. So number of hibernating animals in US are 25392. Thus we can solve the first degree equations involving percent, fraction, decimal and proportion. This completes our session. Hope you enjoyed this session.