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

Current time:0:00Total duration:2:41

CCSS.Math:

divide simplify the answer and write as a mixed number and we have two and one-fourth divided by one and three-fourths so the first thing we want to do since both of these are mixed numbers is to convert them both into improper fractions so let's start with two and one-fourth so we're still going to have four in the denominator but instead of two and one-fourth remember two is the same thing as eight forts so we have eight forts and then we have another 1/4 that gives us nine fourths or another way to come up with this 9 you take 4 you take 4 times 2 which is 8 plus 1 that gives you 9 and then the 1 and 3/4 same process you're going to have 4 in the denominator and then the numerator is going to be 4 times 1 which is 4 plus 3 which is 7 so this is the exact same problem here 2 and 1/4 divided by 1 and 3/4 is the same thing as 9 fourths divided by 7/4 and we saw in several videos already that dividing by a fraction is the same thing as multiplying by its reciprocal so this is equivalent to this is equivalent to so these are all equivalent this is equivalent to 9/4 x times the reciprocal of this we're taking changing the division operation to a multiplication and we're taking the reciprocal of the 7/4 the reciprocal of 7/4 you swap the numerator denominator or the top number in the bottom number and you get 4 over 7 now we could just multiply these we could just say this is 9 times 4 which would be 36 over 4 times 7 which is 28 and then try to put it in lowest terms or we could do it right now because it'd be simpler we have a 4 in the numerator we have a 4 in the denominator that will eventually be in the denominator so let's divide our eventual numerators on our debt ventral denominators both by 4 so you divide this 4 by 4 you get 1 this 4 by 4 you get 1 so now when you multiply it you get 9 times 1 which is 9 over 1 times 7 which is 7 so we have our answer but it's writ right now it's an improper fraction they want us to write it as a mixed number and to figure out as a mixed number we can do it in our now I think we've seen this enough times we say how many times does 7 how many times does 7 go into 9 what goes into it exactly one time but when you take 7 into 9 one time what do you have left over we're going to have 2 left over right 7 times 1 is 7 and you're gonna have 2 left over you need 2 more to get to 9 so you're going to have 2 left over so this is one and two sevens and we're done