let's think a littlebit about what it means to multiply2/3 times 6. one way to think about itis to literally take six 2/3 and add them together. this is six 2/3 right over here.
How To Add Fractions With Regular Numbers, and if we wanted toactually compute this, this would be equalto-- well, we're going to take these six2's and add them together. so we could view itas 2 times 6 over 3.
2 times 6 over 3, whichis the same thing, of course, as 2, 4,6, 8, 10, 12, 12/3. and what is 12/3 equal to? well, we could rewrite12 as-- so this is equal to-- we could rewrite 12as 3 plus 3 plus 3 plus 3 over the yellow 3. let me do it likethis so i don't have to keep switching colors. this is going to bethe same thing as 3/3
plus 3/3 plus 3/3 plus 3/3. and each of these areobviously a whole. each of these equal 1. that's 1 and that's 1, so thisis going to be equal to 4. so that's one way toconceptualize 2/3 times 6. another way to thinkof it is as 2/3 of 6. so let's think about that. let me draw a number line here. and i'm going to drawthe number line up to 6.
so what i care about is thesection of the number line that goes to 6. so that looks pretty good. so this is 1, 2, 3, 4, 5, and 6. so if we want totake 2/3 of 6, we can think of this wholesection of the number line between 0 and6 as the whole. and then we want totake 2/3 of that. so how do we do that?
well, we divide it into thirds,to three equals sections. so that's one equalsection, two equal sections, and three equal sections. and we want two of those thirds. so we want 1/3 and 2/3. now where does that get us? that gets us to 4. so we get, obviously,to the same answer. we would be in a toughsituation if somehow we
got two different answers. either way, 2/3times 6 or 6 times 2/3, either way, that isgoing to be equal to 4. but there are two differentways of viewing this. this first way is literallyviewing it as 2/3 six times. and this way is we're takinga fraction of the number 6. we're going 2/3 of the way to6, which would get us to 4.
No comments:
Post a Comment