If five over two 𝑎 plus four over
three 𝑏 is equal to 12, what is the value of 15𝑎 plus eight 𝑏?
So if we’re looking to solve this
problem, the first thing we want to do is we want to remove the fractions because
then we’ll be able to see how we can get to 15𝑎 plus eight 𝑏. So to be able to get rid of our
fractions, what we need to do is find the least common multiple of two and
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 it’s in both of the lists of our times tables for two and
three. And now we found the least common
multiple, what we’re gonna do is multiply our whole equation by six. Because if we do this, what we’re
going to do is remove the fractions because we’re gonna create a whole number
coefficient for 𝑎 and 𝑏.
What we’ll remember though is if
you’re 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 we’re gonna get 30 over two
𝑎. And we get that because we have
five multiplied by six is 30 and then 30 over two 𝑎 plus 24 over three 𝑏. Again, six multiplied by four is
24, so 24 over three 𝑏, and then is equal to 72. And that’s 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, it’s 60. Six by two is 12. Add them together, we get our
72. Well, now what we’ve done is we’ve
divided. So we’ve got 30 divided by two
which gives us 15. So we got 15𝑎 plus and we got 24
divided by three. So that’s eight. So we get eight 𝑏 is equal to
Well, if we take a look at what
we’ve got, we can see that the 15𝑎 plus eight 𝑏 is what we’re looking to find the
value of in the question. So therefore, we can say that if
five over two 𝑎 plus four over three 𝑏 is equal to 12, the value of 15𝑎 plus
eight 𝑏 is 72.