Video instructions and help with filling out and completing How Form 2220 Amounts

Instructions and Help about How Form 2220 Amounts

Hi I'm Rob welcome to math antics in this lesson we're going to learn how to add mixed numbers if you're not quite sure what mixed numbers are then you should definitely watch our video called mixed numbers first as you remember a mixed number is a combination or sum of a whole number and a proper fraction and for this lesson it's going to be important to remember that even though the plus symbol isn't usually shown between those two parts of a mixed number they're being added together 3 and 1/4 means 3 plus 1/4 2 and 5/8 means 2 plus 5/8 and here's why that's so important to remember let's say you're given a problem we need to add the whole number 2 to the mixed number 3 and 1/4 if you know that 3 and 1/4 is the same as 3 plus 1/4 then you can see that the problem is really 2 Plus 3 plus 1/4 well that's easy all you have to do is add the 2 and the 3 to get 5 and you'll have 5 plus 1/4 which is the mixed number I have been 1/4 so if you need to add a whole number to a mixed number you can just add the whole number parts and you're done ok but what if you need to add a mixed number to a fraction like in the problem 1 and 3/8 plus 1/8 again if you remember that 1 a 3/8 means 1 plus 3/8 then you can see that this problem is really 1 plus 3/8 plus 1/8 that looks pretty easy also 3/8 and 1/8 are what we call like fractions they have the same denominator and can be added easily 3/8 plus 1/8 equals 4 eighths so our answer is simply the mixed number 1 and 4 eighths oh but you might notice the fraction part can be simplified for eighths simplifies to 1/2 so we should write our answer as 1 and 1/2 instead it's not mathematically wrong if you don't simplify a fraction but teachers and tests usually require you to simplify it whenever you can so it's a good habit to get into notice that in each of those examples we just added whole numbers to whole numbers and fractions to fractions and it works the same way when adding a mixed number to a mixed number like 2 and 1/5 plus 4 and 2/5 again let's show our mixed numbers with the plus signs so you can see the real problem two plus one-fifth plus four plus two-fifths because all of these parts are being added an addition has the commutative property it really doesn't matter what order we do the addition that means we can rearrange this problem to make it simpler now we have two plus four plus one-fifth plus two-fifths adding the whole numbers is easy two plus four equals 6 and adding these like fractions is easy to 1/5 plus 2/5 equals 3/5 that leaves us with 6 plus 3/5 which is the mixed number 6 and 3/5 so when you add mixed numbers you can just add the whole number parts to get the whole number of the answer and you add the fraction parts to get the fraction part of the answer that's why in a lot of math books you'll see the addition of mixed numbers written in a stacked form like this this is similar to the way you would stack multi digit numbers up to add them and it helps you remember that you can add the fraction parts and the whole number parts and two separate columns and write your answer below the answer line just like a multi-digit addition and do you remember how in multi digit addition if a column of digits added up to 10 or more you had to carry or regroup to the next column well something similar to that can happen when adding mixed numbers sometimes adding the fraction parts of two mixed numbers actually affects the whole number part of the answer to see what I mean by that let's say you hosted a massive pizza party for all your friends this is a great party we got some really cool friends hey thanks you should hang out with those more often I think you'd really fit in and after the party ended you had 1 and 3/8 cheese pizzas leftover and 1 and 5/8 pepperoni pizzas leftover what's the total amount of leftover pizza well we just need to add those two mixed numbers together let's stack them like I just showed you and add them column by column 3/8 plus 5/8 equals 8/8 and 1 plus 1 equals 2 so the answer is 2 and 8/8 ah but do you see what happened the fraction parts of the two mixed numbers combine to form what I call a whole fraction 8 over 8 and we know that 8 over 8 simplifies to 1 so having 2 eight over eight is the same as having two plus one which is three we added two mixed numbers together and ended up with the whole number three and our leftover pizza shows us that we got the answer right here's another example that shows how the fraction parts can affect the whole number part of the answer when adding mixed numbers one in 3/7 plus 2 and 5/7 this time we'll use the commutative property to rearrange the addition and then we add the whole number parts 1 plus 2 equals 3 and then we'll add the fraction parts 3/7 plus 5/7 equals 8 sevenths so the answer we get is 3 & 8 sevenths but do you notice something funny about the fraction part of that answer it's an improper fraction which means that its value is greater than 1 and it's really bad form to leave an improper fraction in a mixed number like this because