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# Multiplying fractions and whole numbers visually

CCSS.Math:

## Video transcript

we've already seen that the fraction two fists or fraction like the fraction two fists can be literally represented as two times 1/5 2 times 1/5 which is the same thing which is equal to literally having two 1/5 so 1/5 plus 1/5 and if we wanted to visualize it let me make a hole here and divide it into five equal sections and so this represents two of those fifths this is the first of the fifths and then this is the second of the fifths literally 2/5 2/5 2/5 now let's think about something a little bit more interesting what would 3 times 2/5 represent 3 times 2/5 and I encourage you to pause this video and based on what we just did here think about what you think this would be equivalent to well we just saw that 2/5 would be the same thing as so let me just rewrite this as instead of 3 times 2/5 written like this let me write 2/5 like that so this is the same thing as 3 times 2 times 1/5 3 times 2 times 1/5 times 1/5 and multiplication we could multiply the 2 times the 1/5 first and then multiply by the 3 or we could multiply the 3 times the 2 first and then multiply by the 1/5 so you could view this literally as being equal to 3 times 2 is of course 6 so this is the same thing as 6 times once 6 times 1/5 6 times 1/5 and if we were to try to visualize that again so that's a whole that's another whole each of those holes have been divided into five equal sections and so we're going to color in we're going to color in six of them so that's the first fifth second fifth third fifth fourth fifth fifth fifth and that gets us to a hole and then we have Fifth's just like that so literally 3 times 2/5 can be viewed as six fifths and of course six times 1/5 or six fifths can be written as so this is equal to literally six let me do the same color six fifths six over six over five now you might have said well what if we instead of viewing two fifths says this as we just did in this example we view 2/5 as 1/5 plus 1/5 what would happen then well let's try it out so 3 times 2/5 I'll rewrite it 3 times 2/5 2 over 5 2/5 is the same thing as 3 times 3 times 1/5 plus 1/5 2/5 is the same thing as 1/5 plus 1/5 so 3 times 1/5 plus 1/5 which would be equal to well I just have to have literally 3 of these added together so it's going to be 1/5 plus 1/5 plus 1/5 plus 1/5 plus I think you get the idea here plus 1/5 plus 1/5 well what's this going to be well we literally have 6 fifths here we could ignore the parentheses and just add all these together we once again have 1 2 3 4 5 6 fifths so once again this is equal to 6/5 so hopefully this shows that when you multiply that 2/5 we saw already represents 2 1/5 we already saw that or 2 times 1/5 and 3 times 2/5 is literally the same thing as 3 times 2 times 1/5 or in this case that would be 6 fifths