Subtracting mixed numbers: 7 6/9 - 3 2/5

let's try to evaluate seven and six nines minus three and two-fifths so like always I like to separate out the whole number parts from the fractional parts this is the same thing as seven eight plus six nine minus three minus two-fifths and the reason why I'm saying minus 3 minus two-fifths is this is the same thing as minus three plus two-fifths and so you distribute the negative sign you're subtracting a three and then you're subtracting the two-fifths and so now we can worry about the whole number parts seven minus three well seven minus three is going to give us four so that's going to give us four and then we're going to have six ninths minus two-fifths so let me think about what six ninths minus two-fifths are six nine minus two-fifths well we're going to have to find a common denominator so this is going to be the same thing and I think the least common multiple of nine and five is going to be 45 literally then multiply they have no common factors so it's going to be over 45 then we'll from 9 to 45 to multiply by five so I'm gonna have to multiply the numerator by five so 6 times 5 is 30 and I'm going to subtract to go from 5 to 45 had to multiply by 9 so after multiply the numerator by nine if I don't want to change the value so 2 times 9 is 18 and 30 over 30 40 50 minus 18 45th so it's going to be something over 45 30 minus 18 is 12 so this is if I if I subtract these two fractions right over here I get 12 12 40 fifths so it's 4 plus 12 forty fifths or if we wanted to write it as a mixed number this is equal to 4 and 12 forty fifths but we're not done yet we can simplify this further 12 and 45 have common factors they are both divisible by they're both divisible by three so we can say that this is actually they're both divisible by well we can I think we can divide more after that so let's see if we divide the numerator by 3 and the denominator by 3 we end up with 4 and 12 divided by three is 4 and 45 divided by 3 45 divided by 3 is 15 4 and 4 15 actually we're done these two what can't be simplified any more for and for 15