Question Video: Rounding Remainders to Solve One-Step Word Problems Mathematics

Madison is saving up to buy a bike that costs $99. She gets $12 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? [A] 99 − 12 = 87 [B] 99 + 12 = 111 [C] 12 ÷ 99 = 4/33 [D] 99 ÷ 12 = 8𝑅3 [E] 99 ÷ 12 = 8. 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. Why? [A] Do not use the congruence symbol. [B] Because the remainder is less than $5. [C] Because she needs to wait an extra week to earn the remaining $3. [D] Because she does not need to wait any further weeks [E] Because the remainder is less than $99.

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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.

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