We want to place the fractions of one-fourth, one-half,
one-eight and three-fourths on the number line.
Notice how the number line below shows zero here on the left, and
one here on the right. So all of these fractions are between zero and one.
And therefor, they will fit on this number line. Let's first work on placing
a fraction of one-half
on the number line. Because the denominator is two, we're going to cut, or partition
the number line from zero to one into two equal pieces.
So we would divide it here. Each of these pieces, or partitions
has a length of one-half. So we have zero,
then we have one-half, this would be two-halves, which is equal to one.
Which means one-half would be here on the number line,
right between zero and one.
Now let's work on placing the fractions of one-fourth and
three-fourths on the number line.
Now because the denominator is four,
we're going to cut, or partition the number line between zero and one into four equal pieces.
So because we already cut it into half into two equal pieces,
we'll divided it again here and here, so each of these lengths
is equal to one-fourth. So we have zero,
one-fourth, two-fourths, which equals one-half,
three-fourths and fourth-fourths, which is equal to one.
Which means one-fourth would be here, and three-fourths would be here.
And this would be one-fourth and this would be three-fourths.
Notice how this also shows us that one-fourth is half
of one-half. And now our last fraction
is one-eighth. So because our denominator is eight,  we're now going to cut, or partition
the number line from zero to one into eight equal pieces, or eight equal partitions.
So because we already have it divided into four equal pieces, we divide each of
these pieces in half
here, here, here and here.
Each of these lengths is equal to one-eighth. So we have zero,
one-eighth, two-eighths, which equals one-fourth,
three-eighths, four-eighths, which equals one-half,
five-eighths, six-eighths, which equals three-fourths,
seven-eighths and eight-eighths, which equals one.
Which means one-eighth would be here
on the number line.
Noticed how this also shows us that one-eighth
is half of one-fourth.
I hope you found this helpful.
