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## Adding and subtracting fractions with unlike denominators

Current time:0:00Total duration:3:46

# Visually subtracting fractions: 3/4-5/8

CCSS Math: 5.NF.A.1

## Video transcript

- Let's see if we can figure
out with 3/4 minus 5/8 is. And we have 3/4 depicted right over here. You could view this entire bar as a whole, and we see that it is divided into four equal sections, and that three of them are shaded in. So those three that are shaded in, those represent 3/4 of the whole. So you see that right over there, and then this bar down
here, you could view this as another whole. This is another whole right over here and you could see this divided
into eight equal pieces, and five of them are shaded in. So that represents,
that represents the 5/8. So we want to have 3/4,
this green shaded area, and we want to take away the 5/8. So how could we do it? And even when you look at it visually, it might jump out at you. Whenever we add or subtract fractions, we like to think in terms of
having the same denominator. Are we going to deal in
fourths or eighths or 16s, or whatever else? So let's think about having
a common denominator. And a good common denominator is going to be a common
multiple of the two denominators right over here, and ideally
their least common multiple. And one way that I like to tackle that, there's many ways to do it, is look at the larger
of the two denominators, look at eight, and then keep
looking at increasing multiples of eight until you find one
that's also divisible by four, perfectly divisible by four. But with eight, you immediately say, "Well, eight is divisible by four," and that's clearly
divisible by itself as well, so eight is actually the
least common multiple of four and eight. So you can rewrite both of these, both of these fractions
as something over eight. So the 3/4, you can write
it as something over eight, and then subtracting from that, the 5/8, if you want to write
that as something over eight, well, that's just going to be 5/8. And then you can figure
out your actual answer. So how can we rewrite 3/4
to something over eight? Well, there's a couple of
ways to think about doing it. One way, look. I had four in the denominator, now I'm going to have twice
as many equal sections. I'm multiplied by two,
so I'm going to have twice as many of the
sections actually shaded in. So times two, 3/4 is
the same thing as 6/8. And we can also see that visually. If we're going to have twice
as many equal sections, here we have everything in fourths, but I'm going to divide,
I'm going to turn this into twice as many equal
sections so I have eighths. So let's do that. So let me... So you have this right here. Let me divide that. Let me divide that. Let me divide that, and
then let me divide that, and now I went from fourths to eights. I have one, two, three, four, five, six, seven, eight equal sections, and we see that six of them are shaded in, that 3/4 is the same thing as 6/8. But regardless, now we can subtract. We have 6/8 and we want to
take away five of the eighths. So we have 6/8, and we want to take away one, two, three, four, five of them, and those five of them
correspond to these purple five right over here. We're taking away one,
two, three, four, five. We're taking these away. So if you're just looking at the green, we started with 6/8, we're taking away one, two, three, four, five of them, and you can see that
corresponds to the 5/8 down here and what are you left with? Well, you're just going to be left with, you're just going to be left
with this 1/8 right over there. So it's just going to be 1/8. And you could see that
numerically up here. If I have six of something,
in this case it's 6/8, and I want to subtract
five of that something, in this case 5/8, I'm going to be left with one
of that something, or 1/8.