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

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Succeed with maths – Part 2

2.2 Mass: imperial units

To measure mass in the imperial system, ounces (abbreviated to ‘oz’), pounds (lb) and stones (st) are used. These are listed in increasing order of size and you can see the relationship between these units below:

  • 16 ounces in 1 pound
  • 14 pounds in 1 stone

It's easy to confuse the two!

These relationships can in part be explained by the fact that an ounce was originally based on the mass of that very useful item, the barleycorn, with 480 barleycorns to the ounce (although it couldn't have been much fun counting 480 of them!). Having 16 ounces to the pound was useful because 16 can be divided into halves (8, 4, 2, 1) easily, which was very useful for shop keepers measuring out and selling their wares.

The same logic also applies to changing, or converting, between these different mass units as with any others. So, if you convert a value from ounces to pounds, you would expect the final number to be smaller, and hence need to divide by 16 (16 ounces in 1 pound). Using the knowledge you have already gained this week you may be able to work out this next example without looking at our workings. See how you get on!

Let’s suppose you were moving boxes of electronic equipment. The first box has a mass of 14 pounds 11 ounces and the second, 17 pounds 8 ounces. You want to find the total mass of both boxes in stones, pounds and ounces to ensure they can be moved safely.

First, add the pounds together:

14 pounds plus 17 pounds equals 31 pounds

Next add up the ounces:

11 ounces plus eight ounces equals 19 ounces

Since there are 16 ounces in 1 pound, this means:

19 ounces equals 16 ounces plus three ounces equals one pound plus three ounces

multiline equation line 1 Thus comma the total mass equals 31 pounds plus one pound plus three ounces times line 2 equals 32 pounds plus three ounces

There are 14 pounds in 1 stone.

So, 32 pounds equals 32 division 14 equals two stones and four pounds full stop

So the total mass is 2 stones, 4 pounds and 3 ounces.

Now, have a go at this next activity yourself.

Activity _unit3.2.3 Activity 3 Mass in imperial

Timing: Allow approximately 10 minutes

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

  • a.At birth, Samuel’s mass is 7 pounds 4 ounces. After one week, he has gained 13 ounces. What is Samuel’s mass at the end of the week in pounds and ounces?

Answer

multiline equation line 1 Samuel apostrophe s mass equals seven pounds plus four ounces plus 13 ounces equals seven pounds 17 ounces

There are 16 ounces in 1 pound, so you can convert 17 ounces in pounds and ounces.

17 ounces postfix times times equation left hand side equals right hand side 16 ounces postfix times times plus one ounce postfix times equation left hand side times equals right hand side one pound postfix times prefix times plus of one ounce postfix times

So, Samuel apostrophe s mass equals seven pounds plus one pound plus one ounce

The correct way to say this is that Samuel’s mass is now 8 pounds 1 ounce.

  • b.When he started dieting, Derek’s mass was 203 pounds. He lost 37 pounds. What is Derek’s mass now in stones and pounds?

Answer

  • b.multiline equation line 1 Derek apostrophe s new mass equals 203 pounds minus 37 pounds equals 166 pounds

    There are 14 pounds in a stone. So, this means that our final answer needs to be smaller, and that it is necessary to divide by 14 to achieve this.

    multiline equation line 1 166 pounds equals open 166 division 14 close stone equals 11 stone and 12 pounds full stop

    So, now Derek’s mass is 11 stone and 12 pounds.

As with length, you need to be able to relate the two different systems of measurement to each other for mass – this is the subject of the next section and will help give you an idea of the size of the different units.

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