We're asked to plot each of the following fractions on the number line, and we're
told to use the length from zero to one
to represent the unit.
Beginning with the fraction one-half,
because the denominator is two, we will cut
the length from zero to one into two equal parts, or two equal lengths. So here's zero,
and here's one. If we cut this length into two equal parts, that would be here,
each of these shorter lengths is one-half of a unit.
So starting at zero and counting to the
right, the location of one-half on the
number line is here, half the distance
between zero and one.
Next we have the fraction two-thirds. Because the denominator is three,
we will cut the length from zero to one into three equal parts, or three equal lengths.
So starting at zero and ending at one, we cut this into three equal lengths, or three
equal parts. Each of the shorter lengths is equal to one-third, and because
two-thirds is two copies of one-third,
starting at zero and counting to the
right, we have one third, and then two-thirds. Next would be three-thirds, which is equal to
one. This blue point is the location of two-thirds on the number line.
Next we have five-fourths. Because the
denominator is four,
we will cut the length from zero to one into four equal parts, or four equal lengths.
Each of these shorter lengths is equal to
one-fourth.
So starting at zero, we have one-fourth, two-fourths, three-fourths, four-fourths,
which equals one. But we want five-fourths, so now we'll cut the length from one to two
into four equal parts as well.
So again, going back to zero we have
one-fourth, two-fourths, three-fourths, four-
fourths, which equals one. And then we have five-fourths.
This is the location of five-fourths on
the number line.
Notice how we can also express
five-fourths as one and one-fourth.
I hope you found this helpful.
