How many ounces are there in one and two-fifths tons?
Now just before we answer this let’s quickly recap US tons, pounds, and ounces.
The same weight, one ton, is called two thousand pounds or the abbreviation we use for that is lbs. And each pound is made up of sixteen ounces, so for every one of those two thousand pounds there’s sixteen times as many ounces. So that means there are two thousand times sixteen ounces, and the abbreviation we use for that is oz, and so that means that there are thirty-two thousand ounces.
So the process of converting from tons to ounces is, first of all, to multiply by two thousand because there are two thousand times as many pounds as there are tons, and then to take that answer and multiply it by sixteen to convert pounds in ounces because there are sixteen times as many ounces as there are pounds.
So our calculation is gonna be to take that one and two-fifths then multiply it by two thousand then multiply that by sixteen. Well if this was a two-mark question, we’d have just got one of our marks because we’ve shown clearly how we’re going to do the calculation.
Now it’s just a matter of trying to, as efficiently as possible, complete that calculation Now if you’ve got a calculator, it’s just a matter of typing in the numbers and out pops our answer: forty-four thousand eight hundred ounces.
But if we don’t have a calculator we’ve got to do this calculation manually, so let’s look at a couple of different ways of doing that calculation.
Now remember one and two-fifths means one plus two fifths, so I can rewrite my calculation like this. And using the distributive property, I can say that it’s two thousand times sixteen times one plus two thousand times sixteen times two-fifths.
And one times two thousand times sixteen well two times sixteen is thirty-two, so two thousand times sixteen is thirty-two thousand, and likewise on the other part of the calculation. Well two-fifths times thirty-two thousand seems a little bit more complicated. But if we notice that two-fifths could be written as four-tenths, if I double the numerator and double the denominator, and thirty-two thousand is the same as thirty-two thousand over one, so I’ve got four times thirty-two thousand on the top of the fraction and ten times one on the bottom, so the ten is going to cancel. So this ten will cancel with one of those zeros. So I’ve got four times three thousand two hundred. Well to multiply by four, I can double it and double it again.
Well doubling three thousand two hundred gives me six thousand four hundred, and then doubling that again gives me twelve thousand eight hundred. And thirty-two thousand plus twelve thousand eight hundred is forty-four thousand eight hundred ounces.
So that gives us one way of looking at it. So let’s look at it a slightly different way. Multiplication is commutative, so it doesn’t matter which way round we multiply things together. So I could rewrite that as two thousand times one and two-fifths times sixteen. Now one and two-fifths is one plus two-fifths. And one whole one is five-fifths, so effectively one and two-fifths is five-fifths plus two-fifths, which is seven-fifths.
And again if I wanted to, I could write two thousand as two thousand over one and sixteen as sixteen over one. Now I’ve got two thousand times seven times sixteen on the top and one times five times one on the bottom. Well I can see straight away that the fives cancel with two thousand. So fives into five go once and fives into two thousand go four hundred times, so I’ve now just got the calculation four hundred times seven times sixteen. Well I’m gonna do seven times sixteen first.
And seven times ten is seventy, and seven times six is forty-two, so seven times sixteen is the same as seventy plus forty-two. So this is equivalent to four hundred times a hundred and twelve.
And four hundred is the same as a hundred times four, and four is the same as two times two. So a hundred times two times two is the same as four hundred. Now this makes it slightly easier for me to do my calculation because I can do a hundred and twelve times two; I can take that answer and multiply by two and take that answer and multiply it by a hundred.
And two times a hundred and twelve is two hundred and twenty-four. And if I take two hundred and twenty-four and multiply that by two, I get four hundred and forty-eight. And if I multiply that by a hundred, I’ve got four four eight zero zero: forty-four thousand eight hundred. In other words the same answer as I got using the calculator and using my other mental method
So just to summarise, the main thing that we had to remember was that one ton consists of two thousand pounds and one pound consists of sixteen ounces. So to convert from tons to pounds, I need to multiply by two thousand. And to convert pounds to ounces, I need to multiply by sixteen because there are sixteen times as many ounces as there are pounds. So to convert tons to ounces, I need to multiply by two thousand and by sixteen.