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# Dividing fractions: 3/5 ÷ 1/2

CCSS.Math:

## Video transcript

divide and write the answer as a mixed number and we have three fifths divided by one half now whenever you're dividing any fractions you just have to remember that dividing by a fraction is the same thing as multiplying by its reciprocal so this thing right here is the same thing as 3/5 as 3/5 times so this is our 3/5 right here and instead of a division sign you want a multiplication sign and instead of a 1/2 you want to take the reciprocal of 1/2 which would be 2 over 1 so times 2 over 1 so dividing by 1/2 is the exact same thing as multiplying by 2 over 1 and we just do this as a straightforward multiplication problem now 3 times 2 is 6 so our numerator is 6 5 times 1 is 5 so 3/5 divided by 1/2 as an improper fraction is 6 fifths now they want us to write it as a mixed number so we divide the 5 into 6 forgot how many times it goes that'll be the whole number part of the mixed number and then whatever is left over will be the remaining numerator the remaining numerator over 5 so what we'll do let's take 5 into 6 5 goes into 6 one time 1 times 5 is 5 subtract you have a remainder of 1 so 6 over 5 is equal to 1 is equal to one whole or 5 fifths and 1 over 5 and 1 and 1/5 this one comes from whatever is left over and now we're done 3/5 divided by 1/2 is 1 in 1/5 now the one thing that's not obvious is why did this work why is dividing by 1/2 the same thing as multiplying essentially by 2 2 over 1 is the same thing as 2 and to do that I'll do a little side fairly simple example but hopefully it gets the point across if I were to take let me pick take 4 objects so they have 4 objects one two three four so I have four objects and if I were to divide it into of two so I want to divide it into groups of two so that is one group of two and then that is another group of two how many groups do I have well 4 divided by 2 I have 2 groups of 2 so that is equal to 2 now what if I took those same four objects 1 2 3 4 so I'm taking those same four objects instead of dividing them into groups of two I want to divide them I want to divide them into groups of 1/2 which means each group will have half of an object in it so let's say that would be one group right there that is a second group that is a third group I think you see each group has half of a circle in it that is the fourth that's the fifth it's the sixth that's the seventh and then that's the eighth you have eight groups of 1/2 so this is equal to 8 and notice now each of the objects became two groups so you could say how many groups do you have well you have four objects and each of them each of them became two groups each of them I'm looking for a different color each of them became two groups and so you also have eight so dividing by 1/2 is the same thing as multiplying by two and you can think about it with other numbers but hopefully that gives you a little bit of an intuition