Jacob cuts four metres of ribbon
into three pieces. The length of the first piece is
1.28 metres. The length of the second piece is
1.65 metres. Work out the length of the third
We can draw a bar model to help us
understand what we need to do to solve this problem. The first piece of information
we’re told is that Jacob starts off with four metres of ribbon and that he cuts
these four metres into three pieces: one, two, three.
We’re also told some facts about
the different lengths. The first piece of ribbon is 1.28
metres long. And then we’re told the length of
the second piece is 1.65 metres long. So we need to use all of these
facts to help us work out the length of the third piece. How can we find out the length of
the final piece of ribbon?
One method we could use is to
subtract twice. Start with four metres; take away
1.28, which is the length of the first piece; then subtract 1.65, which is the
length of the second piece. And then this will leave us with
the length of the third piece.
Another method we could use
involves subtracting once, adding first and then taking away. First, we need to add together the
length of the first and second pieces, 1.28 add 1.65, and then comes the
subtraction. Need to take away this amount from
the four metres of ribbon that Jacob had to begin with. And whatever’s left is the length
of the third piece.
Let’s use this second method to
find the answer. First, we need to add to find the
total length of the first and second pieces. We can use column addition to do
this. Notice that we’ve made sure that
the decimal points are lined up so that all the digits have the correct values.
To make sure that we don’t make a
mistake with the answer, let’s put a decimal point in there before we start. First, add the hundredths. Eight hundredths plus five
hundredths equals 13 hundredths. So we can write the three digit in
the hundredths column and then exchange 10 of those hundredths for one-tenth.
Now we can add the tenths
column. Two-tenths plus six-tenths equals
eight-tenths, not forgetting the one-tenth underneath leaves us with
nine-tenths. And finally, if we add the ones in
the ones, one plus one equals two. And let’s include the units of
measurement, which is metres, to remind us what this stands for. This is the value of the first and
the second pieces of ribbon.
Now all we need to do is to find
the difference between 2.93 and four. Because 2.93 is very close to three
whole metres, we can count on. Start with 2.93 and then label the
whole amount that we need to get to, which is four. First, add to get to the nearest
whole number. 2.93 plus seven hundredths or 0.07
takes us to three. And then add whole numbers to get
to our target. Three plus one whole equals
four. So the total difference between
2.93 and four is 0.07 plus one, which equals 1.07 metres.
So although we could’ve found the
answer by starting with four metres and then subtracting twice, the way that we did
eventually find the answer was to start by adding together the lengths of the first
and the second pieces of ribbon. Once we found this total amount, we
could subtract it from four to find the difference. But because 2.93 was very close to
three, we decided to count on instead. The length of the third piece of
ribbon is 1.07 metres.