# Multiplying two fractions: an explanation | Fractions | Pre-Algebra | Khan Academy

Let’s think about this issue, 2 by 3 or 2/3 times 4/5 We have seen it in previous videos The way these questions are calculated, This issue is equal to … We must first multiply the numerator, That is 2 times 4 2 times 4, And we do the same process in the place, we must hit these two stations, 3 times 5. The numerator here is 8, The denominator equals 15. And this resulting fracture cannot be simplified any further, There are no common factors between the numbers 8 and 15 except for the number 1. So this is the result, Resulting fraction 8/15. but how? Why is this logical? Let’s think about it a little bit, There are two ways to visualize an issue, Let’s draw the fraction 2/3 We’ll draw 2/3 here … I’m going to draw it somewhat big, I will draw 2/3 and take 4/5 2/3, I will draw it a lot as I said earlier Two thirds, Like this, This is one third, This is two thirds, Wait I’m going to try to draw the parts evenly, Not perfect, but I’ll make them somewhat equal. Here is the final drawing, Divided into three. I will draw it again, I drew three here, Fraction 2/3 represents two of these parts Acting as we said two of these three parts, And one way to think about the issue is to say 2/3 times 4/5, Ie, how many fractures 4/5 do we have in fraction 2/3? How do we divide the fraction 2/3 into one-fifth? Let’s try splitting one part into five parts. Let’s try this together. We will divide, as I told you, each of these parts into 5. 1, 2, 3, 4, 5. And I can also split this last part if you want, 1, 2, 3, 4, 5 We want to take 4/5 of these two parts. How many fifths do we have here? We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. We must be careful here Until these parts are not one-fifth. Here we have 15 parts In full shape. That is to say, how many parts of the fifteen do we have? And so we will get this output. But note 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, And 15. How do you think we got this? I have 3, I have three, I divided each third of these three To 5 fifths. We have five times the number of parts identified, 3 times 5 equals 15 But we want 4/5 of these two parts here, This shaded part represents 10/15, This equates to fraction 2/3. We will take 4/5 of the one third, And in the two thirds we have 10 fifths, that is, we have to define 8 of these 10 fifths. So we’re going to take 8 parts, Let’s shade 1, 2, 3, 4, 5, 6, 7, 8. 8 parts out of 15 parts, i.e. 8/15. We can think of it another way, Let’s start this time with a fifth, not a third, I will draw here I will draw a full shape, Here is the shape, I will try to divide it into five equal parts, as much as I can. 1, 2, 3, 4, 5. Fraction 4/5, that is, we will shade 4 of these parts. 4 of these 5 parts are equal. 3, 4. Now we want to take fraction 2/3 of this shape. How will we do that? We will divide each of these five parts into 3 parts. And again we have 15 parts. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. We want to take the 2/3 fraction or to limit this fraction to this yellow region. We will not take the full 2/3 of the figure We will take the 2/3 from the 4/5. So how many parts do we have? We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. If we have 12 shapes or something, We want to take 2/3 of the yellow area, i.e. 8 parts. We will take 1, 2, 3, 4, 5, 6, 7, 8 or 8 Of 15 parts. Either way, the answer will be the same. In the first method we will take 4/5 from 2/3, The second way is to take 2/3 of 4/5. 