If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

# Dividing a fraction by a whole number

CCSS.Math:

## Video transcript

let's see if we could figure out what to over 3 divided by 5 is equal to pause this video and see if you can figure this out well there's a couple of ways that we can approach it we can first do it in a conceptual way think about it visually and to do that let me represent 2/3 so let's say that this that what I'm drawing right over here is a hole this is a square and it represents a hole and now I could divide into 3 equal sections and I'm going to try to hand draw that so this is that looks pretty good three equal sections here each is a third and we have two thirds so we are really representing all of this stuff right over here that is two of my thirds now I want to divide those two thirds by five well the way I could do this is I could divide it into five equal sections but if I'm doing it I might as well just divide everything all the thirds into five equal sections so let me do that so one two three and then four and five equal sections so what is one of those five equal sections of my original 2/3 well this right over here is one of those five equal sections of my original 2/3 notice I could draw that I could draw another one here another one here another one there and another one there and I would have five equal sections that make up those two thirds but what does just one of them represent and if we figure out what this represents of the hole then we know what two thirds divided by five is well when I took my thirds and I divided them into five equal sections I essentially constructed 15 how do I know that well I had one to three thirds and then I divided it into one two three four five sections so each of these squares right over here is a fifteenth you have three times five and you could count them if you like and what we have called off in red is two of these 15 we have one fifteenth right over here and then to 15th right over there so this is going to be equal to two over 15 now another way that you could think about it and over time this is the way you will approach it but it's nice to think about it conceptually is when you divide by any number it's the same thing as multiplying by the reciprocal so five five is the same thing as five holes or five over one and so 2/3 divided by five is the same thing as 2/3 times the reciprocal of five or the reciprocal of 5 over one which is you just swap the numerator in the denominator which is 1 over 5 and so another way of thinking about this is this is 1/5 of 2/3 which is once again will be this section right over here and the way you could compute this conceptually you see that this is 215 but you could also say well I can just multiply it when I multiply fractions I can just multiply the numerators 2 times 1 is 2 let me do that same red color 2 times 1 is 2 and then I can multiply the denominators 3 times 5 is 15 and hopefully what we just drew out may helps make sense of why we can why dividing by something is the same thing as multiplying by the reciprocal and then when you multiply fractions it's the same thing as multiplying the numerators to get our new numerator and then multiplying the denominators to get our new denominator