### Video Transcript

If five over two ๐ plus four over
three ๐ is equal to 12, what is the value of 15๐ plus eight ๐?

So if weโre looking to solve this
problem, the first thing we want to do is we want to remove the fractions because
then weโll be able to see how we can get to 15๐ plus eight ๐. So to be able to get rid of our
fractions, what we need to do is find the least common multiple of two and
three.

And to do that, what we can do is
we can list the first few multiples. So for two, we have two, four, six,
eight. For three, we have three, six. And we see that six is the least
common multiple because itโs in both of the lists of our times tables for two and
three. And now we found the least common
multiple, what weโre gonna do is multiply our whole equation by six. Because if we do this, what weโre
going to do is remove the fractions because weโre gonna create a whole number
coefficient for ๐ and ๐.

What weโll remember though is if
youโre multiplying the whole equation, that means the whole equation, so that means
multiply the left-hand side by six and the right-hand side by six. So weโre gonna get 30 over two
๐. And we get that because we have
five multiplied by six is 30 and then 30 over two ๐ plus 24 over three ๐. Again, six multiplied by four is
24, so 24 over three ๐, and then is equal to 72. And thatโs because six multiplied
by 12 is 72.

And we can do that quite easy with
some mental arithmetic because if we multiply six by 10, itโs 60. Six by two is 12. Add them together, we get our
72. Well, now what weโve done is weโve
divided. So weโve got 30 divided by two
which gives us 15. So we got 15๐ plus and we got 24
divided by three. So thatโs eight. So we get eight ๐ is equal to
72.

Well, if we take a look at what
weโve got, we can see that the 15๐ plus eight ๐ is what weโre looking to find the
value of in the question. So therefore, we can say that if
five over two ๐ plus four over three ๐ is equal to 12, the value of 15๐ plus
eight ๐ is 72.