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

Let’s think about this problem together, 2 over 3 or 2/3 times 4/5 We’ve seen it in the previous videos How to calculate these problems, This problem is equal to … We must first multiply the numerator. So 2 times 4 2 times 4, And we do the same process in the denominator, we have to multiply these two denominators, 3 times 5. 3 times 5. The numerator is equal to 8, The denominator equals 15. This resulting fraction cannot be reduced any further. 8 and 15 have no common factors except for 1. So this is the answer, Resulting fraction 8/15. but how? Why does this make any sense? Let’s think about it a little, There are two ways to visualize the issue. Let’s plot the fraction 2/3 We’ll draw 2/3 here …

I will draw it so that it is quite large, I’ll draw 2/3 and take 4/5 of it 2/3, I’ll draw it a lot like I said earlier Two thirds, As such, That’s a third of one, This is two-thirds, Wait I’ll try to draw the parts evenly, Not quite, but I’ll make them kind of equal. Here is the final drawing, Divided into thirds. I’ll draw it again, I drew thirds here, The fraction 2/3 represents two of these parts It represents, as we said, two of these three parts, And one way to think about the issue is to say 2/3 times 4/5, So how much of the fraction 4/5 do we have in the fraction 2/3? How do we divide the fraction 2/3 into fifths? Let’s try to divide one part into five parts. Let’s try it together, We’ll divide each of these parts, as I told you, into 5.

1, 2, 3, 4, 5. 1, 2, 3, 4, 5. And I can also split this last part if you like, 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 alert here Indicates that these parts are not fifths. We have 15 parts here In this format completely. That is, what needs to be said, how many of the fifteen parts do we have? So we’re gonna get this answer. 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, And I divided each third of those thirds To 5 fifths.

We have five times the number of limiting parts. 3 times 5 equals 15 But we want 4/5 of these two parts here, This shaded portion is 10/15, This is equivalent to the fraction 2/3. We’ll take 4/5 of one third, And in two thirds, we have 10 fifths, so we need to identify 8 of these 10 fifths. So we’ll 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 the problem in another way. Let’s start this time with fifths, not thirds, I’ll draw here I’ll draw a whole shape, Here is the look, I’ll try to divide it into five equal parts, as much as I can.

1, 2, 3, 4, 5. The fraction is 4/5, so we’ll shade 4 of these parts. 4 of these 5 equal parts. 3, 4. Now we want to take the fraction 2/3 of this diagram. How are we going to do that? We’ll 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 fraction 2/3 or put that fraction on this yellow region. We will not take 2/3 of the figure completely Rather, we will take the 2/3 of 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 of a shape or something, We want to take 2/3 of the yellow area, which is 8 parts. We’ll 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 out of 4/5.

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