The ten by ten grid represents the unit or one whole. We're asked to shade the grid to
represent the given value, write the equivalent fraction for each percent and the
equivalent percent for each fraction. In the first example we are given a
fifty percent. Remember percent means per hundred so to show fifty percent we shade
fifty out of the one hundred pieces that make up this unit.
This model represents fifty percent. And now we're asked to write the percent as a fraction.
Again because the percent is a number compared to one hundred,
as a fraction fifty percent is equal to fifty hundredths.
But this fraction does simplify, which means you can represent one-half using
smaller pieces, or smaller parts. If we go back to our model notice how if we cut
the unit into two equally sized parts or pieces,
one of the two parts is shaded, which shows fifty-hundredths is equal to one-half. A more
traditional way to simplify the fraction would be to divide fifty and one hundred by fifty. Notice fifty divided by fifty
is equal to one. One hundred divided by fifty is equal to two, giving us the simplified fraction of one-
half. Next we're asked to model thirty seven percent and therefore we'll shade thirty-seven of the
one hundred parts that make up the unit.
So we'll shade three columns and then seven more small pieces.
Here's the model for thirty-seven percent. As a fraction
thirty-seven percent equals thirty-seven hundredths. Again a percent is always a number
compared to one hundred. And this faction does not simplify. In the next two examples
we're given a fraction. And again this ten by ten grid is our unit, or one whole. And
because the fraction is one-fourth,
we want to shade one-fourth of this unit. Because the denominator is four, we'll divide this
into four equally sized parts, or pieces.
And because the fraction is
one-fourth, we shade one of the four equally sized pieces that make up one whole.
This is the model for one-fourth. And now we're asked to write one-fourth as a percentage. Because
this is a ten by ten grid and we see that twenty-five of the smaller parts are shaded, this
shows that one-fourth is equal to twenty-five hundredths. Twenty-five hundredths is equal to
twenty five percent. So one-fourth as a percentage is equal to twenty-five
percent.
Next we have the fraction three-twentieths. Because the denominator is twenty we'll
divide the unit into twenty equally sized parts or pieces. And then because the
numerator is three, we will shade three of them.
Now that we have one unit divided into twenty
equally sized parts or pieces, we will shade three of them to represent the
model three-twentieths. And now we're asked to write the fraction as a percentage.
So beginning with three-twentieths, if we look at the one hundred parts that make up
one whole, notice how fifteen of them are shaded, which shows three-twentieths is equal
to fifteen-hundredths.
Notice how we can also obtain this fraction with a denominator of one hundred by
multiplying the numerator and denominator of three-twentieths by five.
Now that we know three-twentieths is equal to fifteen-hundredths,
we know three-twentieths is equal to fifteen percent.
Let's look at two more examples.
Here we're given the fraction five-fourths.
Five-fourths means five copies of one-fourth. Because denominator is four, we'll
divide each unit, or each ten by ten grid into four equal parts and then shade
five of them. Notice how because we have more than four parts we know this is
equal to more than one.
Now that each unit is divided into four equally sized parts or pieces we know
which part is equal to one-fourth and therefore, to model five-fourths we'll
shade five parts.
Looking at the model this also shows us how five-fourths is equal to one
and one-fourth as a mixed number.
It doesn't ask about this, but this is a nice connection to make. Well we are asked to write
the fraction as a percentage. Looking at the model notice how this would be one
hundred percent, plus twenty-five percent, which equals one hundred twenty-five percent.
We're looking at the fraction five-fourths. To create an equivalent
fraction with a denominator of one hundred,
notice how we'd have to multiply the numerator and denominator by twenty-five, which does
give us one hundred twenty-five hundredths, which equals one hundred twenty-five percent. Again we have one hundred
percent here, plus twenty-five percent, which gives us one hundred twenty-five
percent. Next we have one hundred fifty percent, which is equal to one hundred
percent plus fifty percent, so we'll shade one hundred percent of this unit and fifty
percent of this unit. So shading this unit would be one hundred percent and
then shading fifty percent of this unit will give us a total of one hundred
fifty percent.
And now need to write the percent as a fraction. A percent is the number
compared to one hundred and therefore, one hundred fifty percent is equal to one hundred fifty
hundredths. If we take a look at the model when we divide this unit into two equal parts,
each part is equal to one-half and we have one, two, three copies of one-half,
which equals three-halves. So this shows the fraction of one hundred fifty hundredths simplifies to three-
halves. More traditionally we can simplify this fraction by dividing the
numerator and denominator by fifty, which is the greatest common factor of one hunded fifty and
one hundred. I also want to point out how as a mixed number we can see one hundred
fifty percent is equal to one whole plus one half, or one and a half.
So it asks for the fraction, not the mixed number, but it's also true
one hundred fifty percent equals three-halves, which also equals one and a half.
I hope you found this helpful.