Video: Solving Word Problems by Dividing Two Whole Numbers

Victoria has $112 and spends $14 each day. How long will it be until she has no money left?

04:35

Video Transcript

Victoria has 112 dollars and spends 14 dollars each day. How long will it be until she has no money left?

Victoria is starting with 112 dollars and she spends 14 dollars each day. This means that she loses or subtracts 14 dollars each day. So maybe you think that we should use subtraction. Something like this, 112 minus 14, that would be for day one. Then, we’ll have to subtract 14 from day two and day three. We were just keep subtracting over and over and over again until there was no money left, until we got to zero.

There’s actually a better way for us to solve this. Instead of using repeated subtraction, let’s use division. Let’s take the 112 dollars Victoria has, divide that by the 14 dollars she spends every day; that will give us the number of times she can spend 14 dollars — the number of days she can spend 14 dollars. We start by asking the question, how many times does 14 go into 11? But 11 is smaller than 14. We can make zero groups of 14 out of 11.

Then, we ask the question, how many times could 14 go into 112? How many groups of 14 can we make out of 112? We know that 14 times 10 equals 140, so 10 is too bigger number. We could try nine: 14 times nine. Let’s see if we can make nine groups of 14 out of 112. We’ll need to multiply 14 times nine. Four times nine is 36, nine times one is nine, plus three is 12. Bring down the 12. 14 times nine is 126, But 126 is bigger than 112. So nine is too big a number.

Back to the drawing board, if nine was too big, perhaps eight will be the right amount. So we multiply 14 times eight. Eight times four is 32. Write down your two, carry your three. Eight times one is eight plus three, nine, 10, 11. Look at that! 14 times eight is 112. So we write 14 times eight in our division box, we subtract 112 from 112, we get a remainder of zero.

But what does this eight mean? What’s this division told us? It’s saying that 112 can be put in groups of 14 eight times. This means that Victoria could spend 14 dollars eight times before she had no money left. And since she spends 14 dollars every day, she can only do this for eight days before she ran out of money. By dividing 14 into 112, we were able to determine how many days it would be until Victoria ran out of money. Victoria would ran out of money in eight days.

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