### Video Transcript

Madison is saving up to buy a bike
that costs 99 dollars. She gets 12 dollars each week in
pocket money. How many weeks will she have to
wait until she has enough money to buy the bike? Which calculation will help us
answer this question? Is it A) 99 minus 12 equals 87? B) 99 plus 12 equals 111? C) 12 divided by 99 is equal to
four over 33? D) 99 divided by 12 is eight
remainder three? Or E) 99 divided by 12 is equal to
eight?

And there are two further parts to
this question which we’ll consider in a moment.

We have been told the total cost of
the bike, and we know that Madison gets 12 dollars each week in pocket money. Our aim is to work out the total
number of weeks she will have to wait until she has enough money to buy the
bike. And it can be difficult to decide
whether you need to add, divide, multiply, or subtract, so let’s think about what’s
happening here. In week one, Madison gets 12
dollars. In week two, she gets another 12
dollars. In week three, once again, she gets
12 dollars. So, to work out, for example, the
amount of money Madison has after three weeks, I could perform some addition. I could add 12 dollars and 12
dollars and 12 dollars. This is called repeated
addition. But an alternative, this is to take
this value and multiply it by three. Similarly, to work out how much
money Madison has after four weeks, I could multiply 12 dollars by four. After five weeks, I could multiply
12 dollars by five, and so on.

This isn’t necessarily the most
efficient way to perform this calculation, though. Instead, we can use something
called inverse operations when we’re problem-solving. We know that, to work out how much
money Madison has at the end of a given week, we multiply 12 dollars by the number
of weeks. So, at some point, there’s going to
be a number of weeks for which when I multiply that number by 12, I get 99
dollars. And in fact, that number might not
be an integer. It might not be a whole number. If that’s the case, we’re going to
need to do some roundings to decide the exact number of weeks it’s going to
take.

So, to work out this value, we’re
going to perform the inverse operation. We’re currently multiplying. But what’s the inverse or the
opposite to multiplying? The opposite to multiplying is
dividing. So to work out the number of weeks
it’s going to take Madison to save up to buy that bike, we’re going to do 99 dollars
divided by 12 dollars. And if we go over to our answer
selections, we can see that’s either D or E. D says that 99 divided by 12 is
eight remainder three. And E says that 99 divided by 12 is
eight. So, which one is it? Well, if we work out 12 multiplied
by eight, we get 96. That’s not quite 99. So, how many are left over? Well, 99 minus 96 is three. So that tells us that 99 divided by
12 must be eight with a remainder of three. We need eight 12s to make 99 plus
an extra three.

The second part of this question
says that, to find the number of weeks she has to wait, should we ignore the
remainder or round it up? A) Round it up. B) Ignore it. Well, let’s go back to what we were
saying earlier. To work out the remainder when we
divided 99 by 12, we did the opposite. We said what’s 12 multiplied by
eight. And that was 96. So, after eight weeks, Madison is
going to have 96 dollars. She can’t go to the shop and say,
“Well, I’ve only got 96 dollars. Please give me the bike.” The shopkeeper is certainly not
going to ignore the missing money. Madison is going to have to wait
one extra week till she can afford that bike. So, it’s A. We’re going to round this number up
to nine.

The final part of this question
asks us why. Is it A) Do not use the congruence
symbol? B) Because the remainder is less
than five dollars? C) Because she needs to wait an
extra week to earn the remaining three dollars? D) Because she does not need to
wait any further weeks? E) Because the remainder is less
than 99 dollars? And in fact we’ve already answered
this. We said Madison is going to need to
wait an extra week to earn the last little bit of pocket money that will help her
pay for the bike.