 Succeed with maths: part 2

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# 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.

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

There are 14 pounds in 1 stone.

So,

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?

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

So,

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?

• b.

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.

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.