 We are going to learn about proportion. So let's say you are going to make an orange beverage for you and your friend and You have two glasses and you also know the recipe for that How do you make orange beverage is you take one part of the orange syrup? Let's say and then you take six parts of water and this is how you make orange beverage for your friend and you this is your glass and The ratio for orange syrup and the water is one by six here Now you take the another glass again You take one part of the orange syrup and you again take six parts of water And then you have another glass of the beverage where the ratio of orange syrup to water is One by six, but can you also make this beverage for two people in a single beaker? Yes, you can So let's say if you had this big beaker You already know the ratio of orange syrup to water for two people in that big beaker you can take two parts of the orange syrup and 12 parts of water by 12 parts now because you are making the beverage for two people in the single beaker and six parts of water for each part of the orange syrup and so the ratio of orange syrup To water in this case is going to be two by twelve here for the single person the ratio was one by six Do you notice something you can see that these two ratios are? Equivalent fractions and so we can safely write that one by six is equal to two by twelve and this is the concept of proportion when two ratios are equal Then we say that the numbers representing those ratios are in proportion So now going back to the earlier example. We saw one by six was equal to two by twelve So the ratio one was equal to this ratio two while describing the proportion We can say that one by six or the ratio of one to six is in proportion with the ratio two by twelve This can also be read as one six two and twelve are in proportion Please note this sign here the four dots placed in such a manner Show that the ratio on the left and ratio on the right are equal You can also write the four numbers using the comma and the order here is very important The numbers on the left show the numerator and denominator of the first ratio and numbers on the right Show the numerator and denominator of the other ratio now The problems are asked in a way that we are given with any four numbers like this and people ask whether These four numbers are in proportion So for four numbers to be in proportion for example the given numbers then one by two has to be equal to three by four Whether this is correct or not to see whether these are equal fractions We perform cross multiplication if the cross multiplication is equal then we say that two fractions are equal So the same principle goes here as well We multiply one with four and see if it is equal to the multiplication of three and two And if we look at the original number, let me just write those again We are multiplying one and four together Which are extreme numbers we are writing the multiplication of one and four And then we are checking if it is equal to the multiplication of the middle numbers Which are two and three the multiplication on the left is four Whereas multiplication on the right is six and since the multiplication is not equal We can say that the given numbers one two three four are not in proportion Let's take another example. So let's say we have three and nine and Four and twelve are these four numbers in proportion now. We will first multiply the extreme numbers Which gives us 12 times three and we will see whether this is equal to the the multiplication of the middle numbers Which is nine and four so the multiplication of extremes is 36 Whereas multiplication of middle numbers is 36 and both are equal And so we can say that the given numbers three nine four and twelve Are in proportion and this is how you test whether the given four numbers are in proportion Note that the order here is important If you change the order you will have to check the product of extreme and product of the middle numbers again