Fractions: Finding The Common Denominator.

[Music] thank you [Music] this class is busy finding common denominators for the example Mrs Clark has helped the students discover ways of doing this Greg doesn't seem to be able to do the work we'll come back to him later but do you know what a common denominator is here are some of the examples the class is working look at this example one-fourth plus two-fourths each fraction has four as a denominator four is called the common denominator and the two fractions are called like fractions you add only like fractions by adding their numerators keeping the denominator the same but let's look at one of these examples one half plus one-fourth these fractions are called unlike fractions because their denominators are different they don't have a common denominator so you must change the fractions to like fractions but Greg can't remember how to do this turning your papers on your way out class dismissed [Music] Greg haven't you finished not yet is something wrong well Mrs Clark I'm not sure you haven't worked any of the examples with the unlike fractions I know I can't remember how to find the common denominator well if you can stay for a few minutes I think we can find out how to do it that it'd be fine Mrs Clark I'll be right back use your fraction cutouts while I'm gone all right let's see one half plus one-fourth it shouldn't be too hard to figure out it isn't what who said that I did where are you are you out there no let's not waste time looking for me what's giving you trouble this one half plus one-fourth the denominators are different two and four so if I'm going to add them I have to find the common denominator but I can't remember how to do it what are those cutouts for on your desk oh we use them to help us change fractions how do you do that see each of these cutouts is a fraction of a whole circle one half 1 4 1 8 one-third and one-sixth C well can you change a half to eighths let's see one-half equals one two three four eighths can you change a half to fourths one half equals one two fourths say if I change one-half to two-fourths in the example I can add the fractions because they have the same denominator four four is the common denominator you see you've changed the unlike fractions to like fractions two-fourths plus one-fourth equals three-fourths but we discovered something in class about dividing one denominator into another now I remember Mrs Clark was standing right there when she said when you work with unlike fractions ask yourself well the smaller denominator divide into the larger denominator without a remainder if it will the smaller one is a factor of the larger one then the larger denominator can be used as a common denominator [Music] yes that's it and look it works two is a factor of four so I can use 4 for a common denominator when I changed one-half to two-fourths I could add the two fractions because I made them like fractions very good now look over there and use your imagination [Music] here's the problem for you Greg an area this piece of material is 1 6 of a square yard in area how much material do I have altogether how would you write that out as an example one-third Plus one-sixth say that's what I have here to get the answer you have to find the common denominator now let's see is three a factor of six yes so I can use six as a common denominator now I have to change one-third to sixths how are you going to do that I'll use the fraction cutouts here is one-third and these are six one-third equals two-sixths 2 6 plus 1 6 equals 3 6 3 6 equals one-half one-half now the fraction is in its lowest terms what about my problem Greg how much material do I have exactly one half yard one half square yard Greg thank you [Music] watch and listen carefully now I'm going to give you another imaginary problem Greg I have just measured the amount of paint in these gallon cans this can is half full and this can is one third full if I pour the paint from this can into that one how full will it be one half plus one third oh look here it is in my paper I need a common denominator but I can't use three because three is not a factor of two and I can't use two because two is not a factor of three so how can I find a common denominator say well those sets of fractions on the board help me let's look at them and see you know that these sets show different ways of writing one-half and one-third all these fractions are equal and all these are equal to your answer to how to add one-half and one-third is right there I don't see it well let's look at the paint cans again let's suppose the paint cans were measuring cups now let's put all the paint in one cup how full is the cup now I guess it's 5 6 full but is that right is one half plus one-third five-sixths I can't tell I'm not working with sixth but you can work with sixths look at the sets of fractions on the board can you change halves and thirds to sixth oh sure one-half equals three-sixths and one-third equals two-sixths so I can use six for my common denominator notice that 3 times 2 equals 6. the product of two denominators is always a common denominator for two fractions I see now 3 6 plus 2 6 equals 5 6 so 5 6 is right you have five sixths of a can of paint in that can thank you [Music] now I remember we discovered how to find the common denominator this way too Mrs Clark explained to us what we did like this when you're working with unlike fractions and you can't use the larger denominator for a common denominator look for the smallest number that both denominators will divide into without a remainder this is called the least common denominator [Music] I think I'm beginning to understand it now that's very good Greg oh hi Mr Clark weren't you talking to me oh oh sure do you really understand how to find the common denominator yes I know how to do the work now Mrs Clark it won't take me long to finish fine Greg has made a good beginning in discovering how to find the common denominator he has learned to use the larger denominator as a common denominator if the smaller one will divide into it without a remainder if it won't Greg has learned to look for the smallest number that may be divided by the denominators without a remainder he has also learned that the product of two denominators is always a common denominator for those fractions working with unlike fractions is easy when you know how to find the common denominator isn't it Greg thank you [Music]