Sarah is filling bags with
rice. The capacity of each bag is
two-thirds of a cubic decimeter. One cubic decimeter of rice has a
mass of 1.45 kilograms. Work out the mass of 30 bags filled
with rice. The mass of the bags can be
Let’s begin by highlighting the
important pieces of information in this question. We’re told that each bag has a
capacity of two-thirds of a cubic decimeter. That’s how much rice each bag can
hold. We know that one cubic decimeter
has a mass of 1.45 kilograms although that’s not going to be hugely useful just
yet. We also know that Sarah is going to
be filling 30 bags with rice.
To answer this question then, we’ll
begin by calculating the total amount of rice that will fit into those 30 bags. Then, we’ll calculate the mass of
all of the rice that fits into those bags. One bag has a capacity of
two-thirds of a cubic decimeter. We can, therefore, work out the
total amount of rice that 30 bags will hold by multiplying two-thirds by 30.
Remember when working with a
mixture of fractions and integers, those are whole numbers, it’s sensible to turn
the integers into a fraction. We do that by adding the
denominator of one since 30 is the same as 31 wholes. Next, we could multiply the
numerator of each fraction and the denominator of each fraction and then simplify
We could, however, do something
called cross cancelling. This is where we look diagonally to
see if the numbers have any common factors. In fact, both 30 and three have a
factor of three. So we can simplify our problem by
dividing each of these by three. 30 divided by three is 10 and three
divided by three is one. The only common factor that two and
one have is one. They’re called coprime. So we can’t simplify these two
numbers any further.
Now, we perform the multiplication
as normal. Two multiplied by 10 is 20 and one
multiplied by one is one. We can spot that 21 wholes is just
20. So the total capacity of all 30
bags is 20 cubic decimeters.
Next, we’ll use the information
that one cubic decimeter of rice weighs 1.45 kilograms. Once again, we can scale this
information up to work out the mass of 20 cubic decimeters. This time, we’ll multiply by
20. So to work out the total mass of
the 20 cubic decimeters and therefore the 30 bags of rice, we’ll multiply 20 by
1.45. 20 is two multiplied by 10. So it’s actually easier to work out
two multiplied by 1.45 and then multiply that by 10.
We can use a number of formal
written methods to multiply 1.45 by two. And in fact, you might be able to
do it in your head. But it’s certainly useful to check
with a written method of thoughts. Let’s look at the column
method. When multiplying a decimal by an
integer, we can include a decimal point in the answer directly below the one in the
question. Then, we multiply as normal.
Five multiplied by two is 10. So we put a zero in the units
column and we carry the one. Four multiplied by two is
eight. And then, when we add that carried
one, we get nine. And one multiplied by two is
two. So 1.45 multiplied by two is 2.90,
which is actually just 2.9. We’re going to now need to multiply
this by 10.
Remember to multiply by 10, we move
each of the digits to the left one space. The two moves from the units into
the tens column and the nine moves from the tenths into the units column. That tells us that 2.9 multiplied
by 10 is 29 and 1.45 multiplied by 20 is 29.
We’re assuming the mass of the bags
themselves can be neglected. So we’re done. The mass of 30 bags filled with
rice is 29 kilograms.