Video Transcript
Comparing Fractions Using Models:
Same Denominator
In this video, we will learn how to
use models to compare proper fractions that have the same denominator and explain
how the size of the numerator affects the size of the fraction.
Each of these models shows an
amount of fifth. We know this because each model has
been divided into five equal parts: one, two, three, four, five. When we divide a shape or a number
into five equal parts, we call each part a fifth. And we write this as one over
five. Did you notice that the number at
the bottom of the fraction is a five? We call this number the
denominator.
The denominator tells us the number
of equal parts. In this model, one of the parts has
been shaded pink. This model represents
one-fifth. We call the number at the top of
the fraction the numerator. This tells us the number of
selected parts. In this case, one out of five equal
parts is shaded. So this model which has two out of
five parts shaded shows two-fifths. The denominator stays the same,
because we still have five equal parts, but the number of parts selected is two.
So this model shows
three-fifths. Three parts have been shaded out of
five. Three over five is
three-fifths. And the last of our models shows
four-fifths. Four parts out of five are
selected. So we write this as four over
five.
Which of our four fractions is
worth the most? Which has the greatest value:
one-fifth, two-fifths, three-fifths, or four-fifths? Two-fifths are worth more than
one-fifth. Three-fifths are worth more than
two-fifths. And four-fifths are worth more than
three-fifths. So the fraction which is worth the
most is four-fifths.
When we’re comparing fractions with
the same denominator or the same number of equal parts, the fraction with the
highest numerator is worth the most. Four-fifths are worth more than
three-fifths. Four-fifths are worth more than
two-fifths. And four-fifths are worth more than
one-fifth.
In this video, we’re going to be
comparing fractions with the same denominator. Let’s put into practice what we’ve
learned so far by answering some questions.
Complete the following using less
than, equal to, or greater than. Is four-sixths less than, equal to,
or greater than five-sixths?
In this question. we’re being asked
to compare two fractions: four-sixths and five-sixths. We have to use the symbol less
than, equal to, or greater than. Both of our models show an amount
of sixths. This is because the bar models have
been divided into six equal parts. The denominator, or the number at
the bottom of the fraction, is the same. Both models show an amount of
sixths.
But the numerators, or the numbers
on the top of the fractions, are different. The numerator on our first fraction
is a four. And we can see that four out of the
six equal parts have been shaded. The numerator in our second
fraction is a five. This is because five out of the six
equal parts are shaded.
We can tell by looking at the model
and by comparing the numerators that four-sixths is less than five-sixths. Four equal parts is less than five
equal parts. We completed the comparison using
the symbol less than. Four-sixths is less than
five-sixths.
Complete four-ninths what
seven-ninths using less than, equal to, or greater than.
In this question, we’re being asked
to compare two fractions. And both fractions have the same
denominator. The denominator is the bottom
number in the fraction. Both of these fractions are an
amount of ninths.
Let’s model these fractions on a
number line. Our number line has nine
divisions. So the first division represents
one-ninth. When we divide into nine equal
parts, we call each part a ninth. Our next division represents
two-ninths. And the next division is
three-ninths. Did you notice that the denominator
stays the same? And the numerator is increasing by
one each time.
Next is four-ninths, five-ninths,
six-ninths, seven-ninths, eight-ninths, and nine-ninths. Nine-ninths is equal to one or one
whole. Now we’ve got our number line, we
can compare our fractions four-ninths and seven-ninths. As we count along the number line,
the number of parts increases. The numerator increases by one each
time. Since four comes before seven on
the number line or four-ninths comes before seven-ninths, we can say that
four-ninths is less than seven-ninths. So the missing symbol is less
than. Four-ninths is less than
seven-ninths.
Complete five-ninths what
four-ninths using the symbol less than, equal to, or greater than.
In this question, we’re being asked
to compare two fractions: five-ninths and four-ninths. We can see that both fractions have
the same denominator. That’s the number on the bottom of
the fraction. It’s a nine. So this means nine equal parts.
Here’s a bar model. It’s been divided into nine equal
parts. Each part is worth one-ninth. If we shade five of our nine equal
parts, our model shows five-ninths. And if we shade four out of our
nine equal parts, the model shows the fraction four-ninths. Since five is greater than four and
both of our fractions are ninths, we can say that five-ninths is greater than
four-ninths. The missing symbol is greater
than. Five-ninths are greater than
four-ninths.
What have we learned in this
video? We’ve learned how to compare
fractions with the same denominator using models. We also learned that the greater
the numerator, the top number on the fraction, the bigger the fraction.
