Find the result of one-half
multiplied by one-third.
There are two ways we can answer
this. One method involves using a bar
model and recalling that a half times one-third is the same as finding a half of
one-third. We can represent our fraction
one-third by shading one bar out of three equally sized bars. Then in the opposite direction, in
this case, going downwards, we represent a half of this same model by shading one
bar out of two equally sized bars. We can now see we have one
rectangle shaded out of a possible of three times two, which is six rectangles.
And so this means that a half of
one-third which is the same as a half times one-third is simply one out of six;
that’s one-sixth. Of course, there is a slightly
quicker way we could’ve done this. We know that, to multiply a pair of
fractions, we multiply their numerators together, then separately multiply their
denominators together. So a half times one-third is one
times one over two times three. One times one is one and two times
three is six. So once again, we see that a half
times one-third is equal to one-sixth.