How To Add Fractions With Different Denominators And Numerators

we've already seenthat fractions could be used torepresent parts of wholes. now we're going to extendthat idea a little bit to think about them as actualnumbers on the number line. so let me draw a numberline right over here.

How To Add Fractions With Different Denominators And Numerators, so that's my number line. let's say that thisis 0, this is 1, and let's say that this is 2. and let's say i wanted torepresent the fraction 3/4.

so one way to think about itis let's go between 0 and 1. so this fraction,the numerator here is less than the denominator. so the value of this isgoing to be less than 1. so this is going to besomeplace between 0 and 1. and one way wecould think about it is divide this sectioninto 4 equal spaces. so that would be dividingit into 2 equal spaces. so if i divide those again,now i've divided the space.

let me draw that alittle bit neater. now i'm dividing thespace between 0 and 1 into 4 equal spaces. now, 3/4 means that i've gone 3out of the 4 spaces towards 1. so i've gone 1, 2, 3. so this point right over hereon the number line, this is 3/4. this point right overhere, what do you think this is going to be? well, we've moved 1, 2of the spaces towards 4,

so this is 2/4. and this space right overhere, or this mark right over here on the number line,what is that going to be? well, we've moved 1 ofthe 4 spaces towards 1. so this is 1/4. what about this one? well, you could call this 0/4,which is the same thing as 0. so you normally wouldn'tcall that just 0/4. and now we have anotherinteresting question.

what could you alsocall this space? well, we already know basedon how we already marked the number line that this is 1. but using the 4'sin the denominator, we could say, hey, look. we've moved 1, 2, 3,4 out of 4 spaces. we could call that 4/4/ and that also makes sense. so let me make this clear.

4 parts out of 4 totalparts equals 1 whole. but this also makes sensefrom what we know of division. this little fractionsymbol that we keep using, this is the samething as divided by. this is 4 divided by 4. and we know that anynumber divided by itself-- except for 0. 0 is a little bit strange. but any non-zero number dividedby itself is going to be 1.

so this could be viewed as 4/4. so let's do a few exerciseswith our newfound knowledge of fractions on the number line. so let me get alittle exercise going. so here we have move the orangedot to 3/6 on the number line. so we already see thatthey've divided up the space between 0 and1 into 6 equal sections. 1, 2, 3, 4, 5, 6. so we need to move it to3 of those 4 sections.

1, 2, 3. let's check our answer. let's do a couple more of these. move the orange dot to2/4 on the number line. so we have 1, 2, 3,4 equal sections. we need to move itto 1, 2 of them. if they didn't divide itinto 4 equal sections for us, then it wouldn't have beenso easy to just count 2. the number of sections has to bethe number in the denominator.

and then the number in thenumerator's how many of those we move the dot to. let's do one more of this. this is a lot of fun. move the orange dot to1/4 on the number line. well, we already did thatwhen we were drawing it out. there's 1, 2, 3,4 equal sections. and we are going to move to 1/4.