 Let's discuss proportions. What is a proportion? A proportion is a statement that has two equal ratio. In the previous session, we discussed what ratios are with that ratio is a method of comparing two numbers. Now we're going to take the two ratios and see if they are equal. One should be equal to the other. In a sense, when we use proportion, we try to make things equal or we try to make things to be fair. Okay, let's look at this example. Neo and Labo sells hair product for the total profit of 50,000. The profit is shared according to their ratio of number of products they sold. Labo sold 15 and Neo sold 32 products. How much should each receive? If we go back to that statement, it tells us that Neo and Labo sold those products and made a profit of about 50,000 rent. Both of them didn't sell the same quantity of products. Labo sold 15, Neo sold 32. It's not going to be fair to take the 50,000 and divide it equally between Labo and Neo because we know that Neo worked so much harder to make things equal and make sure that each and every one of them receives an equal proportion of their profit. We have to calculate their ratio. 15 plus 32 equals 47. These are the total product sold. Total products that they both sold, they were 47. So we're going to calculate the ratio of each and every one of them based on the total. Profit, let's first calculate the ratio for Labo. So how much will Labo receive? We first need to calculate the ratio which is 15 over or 15 divided by 47. The ratio of Labo to total product is 15 over 47. But we have to multiply that with the total profit. Because we want to get the ratio and that the ratio we multiplied with the 50 so that we can know how much Labo will receive and Labo will receive only 15,957. And we can do the same for Neo. Neo sold 32. So the ratio for Neo to total product will be 32 divided by 47. Multiply that with the 50,000 and Neo will receive the 4,042 red. And they will both receive an equal proportion of the amount that they sold for calculating the ratio. Let's say Mary is a strict hookup. She buys a box of 48 Fritos Zimba chips. In that box it contains 48 Fritos Zimba chips and she buys that for 58 run at the Giants store. Then she goes on a train and she sells this two packets of Fritos Zimbas for five ring. She sells two packets for five ring. So it means she makes a combo. But we need to know how much profit she make after selling everything from the box. To do that, we can use the ratio and find out how much one packet actually costs. So we're going to calculate the ratio of two packets of Zimba chips to five rent the cost. And that will be two divide by five rent, which means for every one packet of chips, she sells it two run fifties there. Okay. Now we know that a packet is two run 50. We can take the two run 50, multiply by the total packet of chips that are in the box. If she sold everything, she would have made two run 50 multiplied by 48 gives us 110 to each. To calculate the profit, which we want to know, we're going to use the formula, revenue minus cost. Because we know the formula for profit is how much you sold minus half of the profit. So minus how much you bought for. So she sold everything, 48 packets of Zimba chips and she made 120 rent revenue. But a giant, she bought the packet, that box of 48 Fritos chips for 58 rent. That is the cost. So we go into subtract our cost from our revenue. And that will give us the profit of 62. This is one way of calculating the profit using the ratio. The other way you can use is this method. If we know that the ratio of selling two is to five, so two packets cost five rent, two is to five. So the ratio of the quantity to price is two is to five. Then what will be the ratio of all total Zimba chips? What will be the cost of Zimba chips? The total sale of Zimba chips. And we don't know the total sale of all Zimba chips. So we need to calculate that, which is our X. Then we're going to make X the sum of the formula. By multiplying with X the size and multiplying with X the size, remember? What you do on the right, you must do on the left. So if we multiply by X and we use another shade, we're going to use the darker green. So if I multiply this side by X, I must do the same here by X. Therefore, the X and the X will cancel out the side and you will be left with 48 on this side. And this side, you will have X times two, which is two X. We also have the five Z. We need to get rid of the five. So I will use another color, we'll use the purple. If I multiply this side by five and multiply this side by five, the five this side and the five that side will cancel and this side will be left with the five. And that is why I will have two X times two, which gives us two X is equals to five times 48 or 48 times five. And that's when we do the cross multiplication. And now we need to make X the side of the formula. So it means we need to be remaining with X on one side, on the left hand side, and we remove two and divide it on the other side, on the right hand side. So we do that by dividing by two, this side by dividing by two. Two and two will cancel out and you'll be left with X is equals to five times 48 is 240 divided by two. And that will give you 110 quick. And we still do the same formula for profit, it's revenue minus cost. And we know that the revenue is 120 minus the cost of 58 grand and we still receive the same amount of 62.