 What is 3 by 4 of 40? How do we solve this? Now remember this off here is signaling some operation here 3 by 4 of 40 is basically saying we need to take out 3 by 4 out of 40 So consider a grid of 40 squares. Now this 40 squares I am going to call it a whole. I'm just going to name it a whole. We see 3 by 4 is a fraction and I need to find out some fraction of a given wall because I just named this 40 as a wall What does that really mean is that we want to take out three parts out of four equal parts of 40 Now if all the squares are equal Can I say that this is one part? This is the second part. This is the third part and this is the fourth part Now out of these four parts. I want to take how many parts three parts so I just painted one of the parts in pink which we are not taking and We are interested in all the green parts. If you count all these squares, you get the answer as 30 So basically if 40 was a whole by saying 3 by 4 of 40 We have reduced 40 to 30. If you look closely once we say off It's always Implication in such cases when we are multiplying when we want to take out a fraction from a wall and that's why it Translates to 3 by 4 times 40 Now let us focus on 3 by 4 times 40. How do we do this? This is a fraction and this is a wall number So remember every wall number has a denominator as 1. Can I also write this as 3 by 4 times 40 by 1? And we know how we do multiplication of fractions We multiply numerators together and write it in a single numerator and then we also write denominators multiplication the denominator Why I like to do multiplication of fractions is because it allows me to perform multiplication or Division in any order. So if I want to multiply 3 and 40 together, I can do that I can also write this as 120 divided by 4 and then divide 120 by 4 which gives me 30 or I could simply divide 40 by 4 40 is 4 times 10 So I am remaining with 10 in the numerator and in the denominator I have 1 so I can also write this as 3 times 10 by 1 Which is nothing but 30 and in any order I can get to the answer 30 So remember whenever we have fraction of some whole it it translates to multiplication So what if I wanted to find 1 by 2 of 12? You just simply change this off into multiplication So 1 by 2 times 12 multiplied well in the numerator assuming that the denominator is 1 So we have 1 times 12 divided by 2 times 1 This is basically 6 and we are left with 6. So this is the answer What if we wanted to find 2 by 5 of 15 and this is again 2 by 5 times 15 that gives me 2 times 15 divided by 5 times 1 which gives me 6 and this is how whenever we have fraction of some whole number we can change this off into multiplication