Use division to simplify fractions

So we need to be able to simplify fractions, and that means we need to find equivalent fractions with smaller numbers – and the way to do that is to divide both the numerator and denominator of the fraction by a common factor. So, to simplify 6 eighteenths, we need to find a common factor of 6 and 18. Now, you might notice straight away that they’re both even numbers, so they’re both in the 2 times table: 2 is a common factor of 6 and 18. So if we []divide the numerator by 2, we get 3, and if we []divide the denominator by 2, we get 9. So we have simplified 6 eighteenths to 3 ninths, but we still haven’t expressed 6 eighteenths in its simplest terms: we can still simplify further. Both 3 and 9 are in the 3 times table, so we have another common factor, []which means we can simplify the fraction further. []3 divided by 3 is 1, and []9 divided by 3 is []3. So, in its simplest terms, 6 eighteenths can be expressed as 1 third. But rather than dividing by 2 and then dividing by 3, what could we do instead? Well, we could divide by 3 and then by 2, but to be able to write the fraction in its simplest terms as quickly as possible,[]
what we need to do is find the highest common factor of the numerator and denominator: so we need the highest times table which contains both 6 and 18. Because 6 and 18 are both in the 6 times table, we’ll get our answer of 1 third more quickly if we []divide both the numerator []and the denominator by 6, rather than dividing by 2 and then by 3.[]
And you can see here what simplifying fractions actually does: we can see that if we simplify 6 eighteenths to 1 third, we haven’t changed the value of the fraction; we still have the same amount of our rectangle shaded blue. But what we’re doing when we simplify fractions is that we make sure that they’re only split up into as many pieces as we need.[]
So how could you simplify 8 twelfths? Well, you might spot that both numbers are in the 2 times table, [][]so you can divide the numerator and the denominator by 2. But now, with 4 sixths, we can see that both numbers are still in the 2 times table, []so we can simplify this fraction further: [][]we can divide them both by 2 again. So 8 twelfths simplifies to 2 thirds.[]
But how could we simplify 8 twelfths more quickly? Rather than dividing by 2 and then by 2 again, we could divide by the highest common factor: so as both 8 and 12 are in the 4 times table, [][]we can divide them both by 4, and that way we’ve written the fraction in its simplest terms straight away.[]
And you can see, again, by simplifying the fraction, we haven’t changed its value: we’ve just made sure its only split up into as many pieces as we need to make the value of the fraction clear.[]
So now, pause the video and see if you can write 12 twentieths in its most simplified form. So both 12 and 20 are in the 2 times table, [][]so we could divide both by 2, but then, we can see with 6 tenths that both numbers are still in the 2 times table, []so we can simplify further, [][]and if we divide both the numerator and the denominator by 2 we get the fraction in its simplest form, 3 fifths.[]
But, if we look for the highest common factor, we might see that both numbers are in the 4 times table, []so 12 divided by 4 is 3 and []20 divided by 4 is 5, so we have 3 fifths.[]
And again, it’s really important to understand what we’re doing when we simplify fractions. Though we use division, we’re not really dividing the fraction – because if you divide both the numerator and the denominator, the fraction actually stays the same. And in some ways, what we’re doing is really the opposite of division: we’re making sure that the fraction is not divided up into more pieces than it needs: so here, to show the value of the fraction, we don’t need to split it up into 20 pieces: we just need to split it up into 5 pieces, and then our numerator of 3 tells us how many pieces we have.[]
So now, pause the video, and see if you can simplify these fractions. So, as 14 and 35 are both in the 7 times table, [][]we can divide both the numerator and denominator by 7 to simplify the fraction to 2 fifths. Now, for 7 and 28, again, both numbers are in the 7 times table, [][]so we can divide by 7 to get 1 quarter. And then, 25 and 30 are both in the 5 times table, [][]so we can divide by 5 to get 5 sixths.