Succeed with maths – Part 2
Succeed with maths – Part 2

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Succeed with maths – Part 2

3.1 Volume: the imperial units

To measure volume, the imperial system uses, amongst other units, gallons and pints. You may also have heard of a gill and a quart. As with length and mass in the imperial system there are no constant relationships between all these units, although there is more similarity with these than with some!

There are:

  • 4 gills in 1 pint
  • 2 pints in 1 quart
  • 4 quarts in 1 gallon.

For our purposes it is most useful to know that:

  • 8 pints = 1 gallon.

As the methods used to convert between different units of volume are just the same as those already covered for both length and mass, you can move straight on to an activity to complete. Bear in mind what you have already learned over this week and the last. You can always look back at the previous sections or click on ‘reveal comment’ for some hints if you need them!

Activity _unit3.3.2 Activity 6 Imperial units of volume

Timing: Allow approximately 5 minutes

For each of the following scenarios, use the appropriate operation and unit to determine the answer.

  • a.At the beginning of the month a garage purchases 240 pints of motor oil. Each week it uses 44 pints. Assuming that there are four weeks in this month, how many pints of oil will be left over at the end of the month? What is this value in gallons?

Discussion

Write down all the information from the question in a list and think about the size of the answer that you expect.

Answer

  • a.There are 44 pints used each week.

    So the total volume used in a month equals 44 pints prefix multiplication of four equals 176 pints

    The garage started with 240 pints.

    Remaining volume of oil equals 240 pints negative 176 pints equals 64 pints

    There are 8 pints in a gallon.

    So, 64 pints in gallons equals 64 division eight equals eight gallons

    Therefore there are 8 gallons of oil remaining at the end of the month.

  • b.A large barrel holds 50 gallons of beer. If in one week 14.5 gallons of beer are sold from the barrel and the next week 15.5 gallons are sold, how many pints of beer will have been sold in total and what will be left in the barrel (in pints)?

Answer

Number of gallons sold equals 14.5 gallons prefix plus of 15.5 gallons equals 30 gallons

There are 8 pints in a gallon.

So, number of pints sold equals left parenthesis 30 multiplication eight right parenthesis pints equals 240 pints

Gallons left in the barrel equals 50 gallons prefix times of negative 30 gallons equals 20 gallons

So pints left in the barrel equals 20 multiplication eight equals 160 pints

To double-check the answer add the pints sold to the pints left in the barrel and then convert back to gallons. This should be the same as the original capacity given:

Total number of pints equals 240 pints prefix plus of 160 pints equals 400 pints

one gallon equals eight pints

So total volume in gallons equals 400 division eight equals 50 gallons

You can now confidently state that 240 pints were sold and there were 160 pints remaining in the barrel.

Finally, you need to know how these two measurement systems relate to each other for volume. This is the subject of the next brief section.

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