### Video Transcript

Subtracting Proper Fractions Where
Denominators Are Multiples

In this video, we’re going to learn
how to subtract related fractions within one whole by finding a common
denominator. How would we subtract a third from
seven-ninths? When we’re subtracting fractions,
both fractions need to have the same denominator. We can’t take thirds away from
ninths. They’re not the same thing. Let’s use a model to help us
represent this calculation. The denominator in our first
fraction is a nine. This means we need to divide our
whole amount into nine equal parts. One, two, three, four, five, six,
seven, eight, nine. We divided the whole amount into
nine equal parts. Each part is worth one-ninth.

The numerator, which is the top
number in the fraction, is a seven. So we have to select
seven-ninths. There we go. We’ve shaded seven-ninths. So how would we subtract
one-third? Let’s draw a model to represent
one-third. This bar represents one whole. And because the denominator of our
fraction is a three, we need to divide our whole into three equal parts: one, two,
three. Each part represents one-third. And because our numerator is a one,
we need to shade one of our parts. These two models help us to see
that one-third is equal to three-ninths. So to subtract one-third from
seven-ninths, we just need to subtract three of our ninths. How many ninths do we have
left? Four-ninths. So seven-ninths subtract one-third
equals four-ninths. We used the model to help us work
out that one-third is equal to three-ninths.

There’s another way to work out how
many ninths are equal to one-third. To convert thirds into ninths, we
can multiply by three, because three times three is nine. And whatever we do to the
denominator, we need to do the same to the numerator to keep the fractions
equal. And we know that one times three is
three. Once we know that one-third is
equal to three-ninths, we can subtract. Seven-ninths subtract three-ninths
is four-ninths. If we have seven-ninths and we take
three of them away, we’ll be left with four-ninths. Let’s have a go at answering a
question now so we can put into practice what we’ve learned so far.

Using the given model, find
five-eighths subtract one-quarter. Give your answer in its simplest
form.

In this question, we have to find
five-eighths subtract one-quarter, and we’ve been given a model to help. The first model represents
five-eighths. The whole amount has been divided
into eight equal parts, and five of those eight parts have been shaded. We have to subtract one-quarter
from these five-eighths. Our second model represents
one-quarter. The whole amount has been divided
into four equal parts, and one of those four parts has been shaded.

By comparing these two models, we
can see that one-quarter is equal to two-eighths. So to subtract a quarter from our
five-eighths, we need to take away two-eighths. One, two. How many eighths do we have
left? There are three. So five-eighths take away
one-quarter is equal to five-eighths take away two-eighths. So if we have five-eighths and we
take away two, we’ll have three-eighths left. And the question says we have to
give our answer in its simplest form. We can’t simplify
three-eighths. Five-eighths take away one-quarter
equals three-eighths.

So far in this video, we’ve learned
how to subtract fractions with different denominators using models. Let’s have a go at subtracting
these fractions without a model.

What is five-sixths take away
two-thirds?

Straightaway, we can see that the
denominators in these two fractions are different. Before we can subtract two-thirds
from five-sixths, we need to make both denominators the same. In other words, we need to make
both of our fractions into an amount of sixths. We know six is a multiple of
three. If we multiply three by two, we get
six. And whatever we do to the
denominator, we need to do the same to the numerator. So we need to multiply two by
two. So two-thirds is equal to
four-sixths. Now, both of our fractions have the
same denominator. Now we’re ready to subtract.

We’ve got five-sixths, and we need
to take away four. And we know that five take away
four leaves us with one. Five-sixths take away four-sixths
equals one-sixth. So to help us subtract five-sixths
from two-thirds, we had to make both denominators the same. We know that six is a multiple of
three. So we multiplied three by two to
give us our denominator of six. Then we multiplied the numerator by
two, which gave us four-sixths. Once the denominators are the same,
we can subtract.

Let’s try answering some questions
now where we need to subtract two fractions with different denominators without
using a model.

Jackson has half of a chocolate bar
and he eats one-sixth of it. How much of the chocolate bar is
left over?

If Jackson has a half of a
chocolate bar and he eats a sixth of it, to find out how much of the chocolate bar
is left over, we need to subtract one-sixth from a half. Before we can subtract, both of the
denominators need to be the same. Six is a multiple of two, so we
could make both of the denominators a six. How many sixths are equal to
one-half? How do we get from two to six? Two times three is six. We multiplied the denominator by
three. Now we need to multiply the
numerator by three, and we know that one times three is three. Now that we know a half is equal to
three-sixths, we can subtract. Three-sixths subtract one-sixth
equals two-sixths.

If we have three-sixths and we take
one away, we’ll have two-sixths left. But we need to give our answer in
its simplest form. Two-sixths is equal to
one-third. If we divide two by two, we get
one. And if we divide six by two, we get
three. A half subtract one-sixth equals
two-sixths or one-third.

Sophia’s bottle contains
three-quarter liters of water. If she drinks one-eighth liters
from her bottle, how much water in liters is left over?

We know that Sophia’s bottle
contains three-quarter liters of water. If she drinks another eighth of a
liter, how much water will she have left? We have to find three-quarters take
away one-eighth. Before we can subtract, both of the
denominators need to be the same. We know that eight is a multiple of
four, so let’s see how many eighths are equal to three-quarters. Eight is the common
denominator. How do we get from four to
eight? We know that four times two is
eight, so we need to multiply our numerator by two. And we know that three times two is
six.

Now that we know that
three-quarters is equal to six-eighths, we can subtract. If we’ve got six-eighths and we
take away one of them, we’ll have five-eighths left. If Sophia’s bottle contains
three-quarters of a liter of water and she drinks an eighth of a liter from her
bottle, she will have five-eighths of a liter left over.

What have we learned in this
video? We have learned how to subtract
related fractions within one whole by finding a common denominator.