Multiplying and Dividing Mixed Numbers

hi I'm Tiffany today I'm going to show you how to multiply and divide with fractions and mixed numbers multiplying and dividing mixed numbers when multiplying mixed numbers you want to make both numbers into improper fractions then multiply like normal for dividing mixed numbers you want to make both numbers like improper fractions then divide remembering to keep it change it flip it here's example number one we need to make these mixed numbers into improper fractions so we are going to multiply here add here and go in a clockwise direction 5 times 1 is 5 5 plus 3 is 8 8 becomes my new numerator and 5 remains my denominator now I'm going to multiply that by whatever this improper fraction will be 4 times 2 is 8 8 plus 3 is 11 my denominator remains 4 now the really good thing about multiplying fractions is you do not need to get a common denominator you multiply straight across you multiply your numerators together and then your denominators together so 8 times 11 is 88 then 5 times 4 is 20 now I need to divide here to get a mixed number because right now my numerator is larger than my denominator so I'm going to divide 20 into 88 20 goes into 88 4 times which is 80 now I subtract and I get 8 the way you write your answer is in the order that you got your numbers here you wrote down the 4 first and it becomes your whole number the eighth is your numerator because it's the remainder or how much you had left over and twenty is your denominator it remains the same it was already twenty I could have really done this in my head but I wanted to work it out so you understood how we got there but 20 goes into 88 four times I know that 20 would go into 89 88 so there would be a difference of eight that's my numerator a my denominator remains the same so if you understand what you're doing you can do all of that step in your head without actually having to do the division now I need to simplify the fraction portion the four my whole number it remains the same but my eight and my 20 can be simplified for can go into both 8 and 20 so 8 divided by 4 is 2 and 20 divided by 4 is 5 my answer is 4 and 2/5 let's move on to example number two example number two I need to get improper fractions again meaning I need to convert this 2 times 3 is 6 6 plus 1 is 7 my numerator for example number one is 7 my denominator is 2 I need to multiply that by the improper fraction that I get over here 9 times 4 is 36 36 plus 2 is 38 38 is my numerator 9 is my denominator now it's time to multiply straight across 7 times 38 is 266 and 2 times 9 is 18 this is an improper fraction so for my answer I need to make it into a mixed number that means I need to divide again this one's a little more tricky so I'm actually going to divide it I'm going to divide by 18 into 266 I don't know what this is off the top of my head 18 goes into 26 one time and it is 18 I'm going to subtract I get eight bring down my six 18 goes into 80 six four times and it's 72 when I subtract I get 14 I have nothing left to bring down so that means this will be my numerator so this is my top number then I will swoop down here and I end here with my 18 so 14 is my whole number 14 is also my numerator and 18 is my denominator now my answer can be simplified my whole number 14 remains the same and then I just figure out something that can go into both 14 and 18 2 can go into both 14 and 18 because they're even 14 divided by 2 is 7 18 divided by 2 is 9 so the answer to example number 2 is 14 and seven ninths let's move on to example number three example number three it's time for me to make these mixed numbers into improper fractions 7 times 5 is 35 35 plus 2 is 37 the denominator remains 7 I'm going to multiply that by whatever I have over here 4 times 6 is 24 24 plus 1 is 25 now I need to multiply straight across 925 is my numerator and my denominator is 28 now if I divide 28 into 925 I get 33 with the remainder of 1 so that means my answer is 33 and 128 that's the answer for example number 3 let's move on to example number four example number four this time we're working with division we're working with division there's something we need to keep in mind we need to remember to keep it change it and flip it I like to write these numbers directly on top of my fraction so that I don't forget what to do with each problem before I can keep it change it flip it I need to fix these numbers so they're in a form that works for me right now I'm going to make them improper fractions just like I did with the multiplication examples multiply here and add here 4 times 2 is 8 8 plus 3 is 11 11 is my numerator 4 is my denominator over here I have 6 times 1 which gives me 6 and then 6 plus 5 gives me 11 11 over 6 now what we need to do is keep it change it flip it keep it means keep this fraction the same 11 over 4 change means change the sign to multiplication instead of division and flip means make your last number the reciprocal of itself the reciprocal means you switch the position of your numerator and denominator that means instead of 11 over 6 I'm going to have 6 over 11 so now what I've done really is set all of this up to give us a regular ol multiplication problem so really you never actually divide fractions you only multiply them when you see a division sign just keep that in mind to remind you that you need to correctly set up your problem for multiplication 11 times 6 is 66 4 times 11 is 44 now I need to divide here and I'm going to get 1 and 22 over 44 22 over 44 can be simplified to 1/2 so this answer is the same as 1 and 1/2 let's move on to example number 5 example number 5 multiply here add here 2 times 3 is 6 6 plus 1 is 7 9 times 4 is 36 36 plus 7 is 43 denominator remains the same and if you remember we are keeping it changing it and flipping it this number remains the same because we want to keep it the same we want to change this to multiplication sign and we want to flip this to 9 over 43 now we're going to multiply straight across 7 times 9 is 63 2 times 43 is 86 so your answer to example number 5 is 63 over 86 let's move on to example number stick let's make this improper fraction 15 times 5 is 75 75 plus 2 is 77 and that goes over 15 10 times 6 is 60 60 plus 3 is 63 you put that over 10 remember we want to keep it change it flip it so we are keeping my first fraction the same changing the sign to multiplication from the original division side and flip the last fraction to its reciprocal 77 times 10 is 770 the denominator is 945 I can simplify 770 by 5 as well as 945 so I'm going to simplify to get a little more room I've just cleared the slide but rewritten the answer that we had at our last point we have 770 over 945 five can go into both of these and now I'm still able to simplify my fraction by dividing the numerator and the denominator by 7 so after simplifying by 7 I end up getting 22 over 27 so the answer to example number 6 is 22 over 27 that's my last example thanks for watching you

Channel: Super Easy Math

Views: 824,361

Rating: 4.760325 out of 5

Keywords: math, basic math, mathematics, math help, MULTIPLYING MIXED NUMBERS, DIVIDING MIXED NUMBERS, MULTIPLYING AND DIVIDING MIXED NUMBERS

Id: 56aYsGpwQvQ

Length: 12min 56sec (776 seconds)

Published: Thu Jul 31 2014