WEBVTT mathematics/basic-math/pyo
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This lesson, we are going to be adding and subtracting mixed numbers.
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Remember a mixed number is a fraction with a whole number in the front.
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If I have a whole number with a proper fraction, then I have a mixed number.
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When I am adding mixed numbers together, the main thing here is the fraction.
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We are look at fractions here.
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Whole numbers, 3 and 1, we can just add them together.
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For the wholes, we have 4 wholes.
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Then we have the fractions that we have to worry about.
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In this case, I am going to just add the whole numbers and I am going to add the fractions.
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3 plus 1, the whole numbers, that is going to become my new whole number.
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Then 3/5 plus 1/5.
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Again from the last few lesson in adding fractions, we have to make sure that they have a common denominator.
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In this case, this fraction and this fraction both have a denominator of 5.
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We can go ahead and add those fractions.
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It is going to be 3 plus 1; I am adding the numerators; 3 plus 1 is 4.
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My denominator stays the same as always as a 5.
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This mixed number plus this mixed number equals this mixed number.
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When you have your answer, when you find the answer,
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you have to make sure that this fraction here is a proper fraction.
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Meaning the top number must be smaller than the bottom number.
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If that is the case, then that is your answer, 4 and 4/5.
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Let's do a few problems; we are adding 2 and 1/2 plus 2 and 2/3.
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Again I am going to add the whole numbers together, this whole number and this whole number.
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That is going to become 4.
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Then I am going to add my fractions together, 1/2 plus 2/3.
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But there is a problem; our denominators are different.
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Whenever you have fractions with different denominators,
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then you can't add them or subtract them until you make the denominators the same.
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In order to make the denominators the same,
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you have to look for the least common denominator or the least common multiple.
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Between 2 and 3, the least common denominator will be 6.
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The multiples of 2 would be 2, 4, 6, 8, so on.
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For 3, 3, 6, 9, and so on; the least common multiple is 6.
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I have to change these fractions.
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I have to convert the fractions so that the denominators will become a 6.
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1/2, I am going to multiply this 2 by 3 to get a 6.
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2 times 3 is 6.
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Whatever I do to this part, I have to do to the top.
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1 times 3 is 3.
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Again you have to multiply the top and the bottom by the same number.
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If you don't, then it is going to be wrong because these fractions have to stay the same.
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All you are doing is changing the numbers, but it is still the same fraction.
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Then we have to do this next one, 2/3.
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2/3, I have to change this so the denominator will become a 6.
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3 times 2 became 6.
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I have to multiply the top number by the same number.
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It is going to be 4.
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This mixed number could be the same thing as 2 and 3/6.
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This one can change to 2 and 4/6.
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They might look different; but they are the same thing.
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This problem is the same problem as this one as long as you did everything correctly.
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All you did was just change the fractions so that their denominators would be the same.
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Again I am going to add the whole numbers.
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It is 2 plus 2 which is 4.
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Then since their denominators are the same for the fractions, I can add them.
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It is going to be 3 plus 4 which is 7 over...
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The denominator always stays the same; it is going to be 6.
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Let's look at this answer right here; I have a problem.
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Because I have 4 and 7/6, remember my mixed number, this is supposed to be a mixed number.
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The mixed number has to be a whole number with a proper fraction.
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But since my numerator is bigger than my denominator, this is actually an improper fraction.
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I have to change this so that this will no longer be an improper fraction.
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Let's just look at just this part right here, 7/6.
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7/6, since it is an improper fraction, we can change this so that it becomes a mixed number.
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Remember I ask myself how many times can 6 fit into the top number 7?
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I know that 6 can only fit into 7 one time.
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If 6 fits into 7 one time, how many do I have left over?
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I only have 1 because I have 7; 7 minus 6 would be 1.
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Again my denominator stays the same.
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This right here, 7/6, became 1 and 1/6.
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But then again I have a 4 right here; I have another whole number, 4.
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I have a whole number 4; I have a whole number of 1.
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Since this 4 and 7/6 is the same thing as 4 plus 7/6,
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I can just take this whole number and add them together.
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This will become 5 and 1/6.
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Again if your answer, your mixed number, has an improper fraction, you have to take out the whole number,
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change your improper fraction into a mixed number, and then add your whole number to it.
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7/6 became 1 and 1/6.
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I have a whole number 4 that I have to consider.
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I am going to add that 4 to that mixed number.
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It is going to be 5 and 1/6; that is my answer.
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Another example here, I have 6 and 5/7 minus 2 and 1/5.
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The main problem here is my fraction.
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I have to look at my fractions, 5/7 and 1/5; my denominators are different.
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I have to make sure to make a common denominator.
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Normally you can do the factor tree to find the least common denominator.
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But for 7 and for 5, they are both prime numbers.
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If they are both prime numbers, then you can just list out all the multiples
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or the first few until you find the common multiple--7, 14, 21, 28, 35.
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For 5, the multiples are 5, 10, 15, 20, 25, let me continue right here, 30, 35.
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I found one, 35.
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You have to make sure when you find the least common denominator that it is the smallest one.
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They are going to have more than one common denominator or common multiple.
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You just have to make sure it is the least common multiple.
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It is the smallest common multiple; in this case, it is 35.
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I am going to change just this fraction.
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I am going to ignore my whole number for now.
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I am just going to change the fractions.
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5/7, I want to make the denominator become 35.
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7, what did I multiply by 7 to get 35?--multiplied 5.
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Then I have to multiply this top number by 5; this becomes 25.
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Then I am going to look at this fraction right here, 1/5.
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5 times 7 became 35; multiply this top number by 7; get 7.
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I am going to rewrite my mixed numbers, my problem, so that I will have common denominators for each of these.
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This becomes 6 and 25/35 minus 2 and 7/35.
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Now that I have common denominators, I can go ahead and subtract these two fractions.
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Let's do 6 minus 2; the whole number is 6 minus 2 which is 4.
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Then I can take my numerator here, subtract it by this numerator.
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25 minus 7 is 18; my denominator stays the same as 35.
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My answer here is 4 and 18/35.
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Again you have to look at this fraction right here, this mixed number.
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Make sure that this is a proper fraction.
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Your top number, your numerator, is going to be smaller than the denominator.
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This next example, 3 and 3/4 plus 4 and 1/10.
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Again I have to look at my fractions because I can't add them until I have a common denominator.
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In this case, you can either, just like the other examples, to find the LCD, you can list out their multiples.
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Since these are not prime numbers, you can do factor trees.
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I am just going to do the factor tree; this is 2 and 2.
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For 10, it is going to be 5 and 2.
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There is a common number of 2; cross one out.
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My LCD, my least common denominator... I am going to write out all the remaining circled numbers.
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2 times 2 is 4; times 5 is 20; my LCD is 20.
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I am going to change these two fractions so that my denominators will become 20.
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3/4; 4, I multiplied it by 5 to get a 20.
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I am going to do the same thing to the top, 15.
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The other fraction, 1/10; 10 times 2 became 20; 1 times 2 is 2.
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Again this fraction 3/4 is the same thing as 15/20 and 1/10 is 2/20.
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I am going to rewrite this problem, 3 and 15/20 plus 4 and 2/20.
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I add my whole numbers together; it is going to be 7.
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Then I have to add my fractions.
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They have a common denominator so I can add them together.
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I am going to take my numerators, 15 and 2; add them up.
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I get 17 over... guess what my denominator is going to be?
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20, your denominator has to stay the same.
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I look at this answer.
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Is my top number in my fraction smaller than my bottom number?
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If it is, then it is a proper fraction.
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This is going to be my answer, 7 and 17/20.
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This next example, 12 and 9/11 minus 12 and 3/22.
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Before I begin here, I have to make sure that the denominators for these fractions are the same.
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I am looking at this fraction here and this fraction here.
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Here I have an 11 as my denominator; this one, I have a 22.
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I have to change these denominators so that they are the same in order for me to be able to subtract these fractions.
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I need to find the least common denominator.
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I am going to write out the multiples of 11--11, 22, 33, and so on.
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For 22, it is going to be 22, 44, and so on.
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My least common multiple is 22.
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Since they are denominators, it becomes the least common denominator.
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Make sure, if you are going to list out the multiples to find the LCD,
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then you have to find the one that is smallest.
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It has to be the smallest common multiple because these two numbers,
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they are going to have more than one common multiple.
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It has to be the smallest one.
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Now that I have my LCD, I have to make sure that these fractions
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will be converted so that I will have my denominator as 22.
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This fraction right here, 9/11... I know that I have whole numbers here.
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But I am just going to worry about my proper fractions first.
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9/11, I want to make that denominator 22.
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I take this number, 22, divide it by 11.
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Or I can just figure out 11 times 2 gave me 22.
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Whatever I do to that number, I have to do to the top number.
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I have to multiply the top number by 2 as well.
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9 times 2 is 18.
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This next fraction, 3/22, the denominator is already 22.
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We don't have to change it; we can just keep it the way it is.
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I know that 9/11 is the same thing, is the same fraction as 18/22.
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I can just rewrite this whole problem so that they will have common denominators.
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12 and 18... let me erase that.
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12 and 18... it has to change to this fraction right here.
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12 and 18/22 minus 12 and 3/22; again double check your denominators.
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Make sure that they are the same; then we can go ahead and subtract those.
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For this, my whole numbers, 12 minus 12, is going to be 0.
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Then I don't have to worry about my whole numbers for now.
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I have to subtract my numerators; 18 minus 3 is 15.
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My denominator again, it is the same as 22.
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My denominator for my answer has to also stay the same; it is 15/22.
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I don't have a whole number because 12 minus 12 gave me 0.
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I don't have a whole number here.
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Here I have to make sure when I have my fraction that this top number is smaller than the bottom number.
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This is a proper fraction.
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I can't simplify it because 15 and 22 do not have any common factors.
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There is no number that can go into both the top number and the bottom number.
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Once I ask myself all those questions and I can't simplify, then this would be my answer.
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12 and 9/11 minus 12 and 3/22 became 15/22.
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That is it for this lesson; thank you for watching Educator.com.