Video: Solving Word Problems by Dividing Fractions by Whole Numbers

Amelia bought 1/2 a kilogram of apples. She wants to split it equally between herself and 4 friends. How much will each one of the 5 take?

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Video Transcript

Amelia bought half a kilogram of apples. She wants to split it equally between herself and four friends. How much will each one of the five take?

This problem is a division question. We can tell this because it talks about Amelia splitting up an amount of apples equally between herself and four friends. She divides up the amount. The first number in the division or the dividend is actually a fraction. We’re told that Amelia bought half a kilogram of apples. And this is the amount that split up. Now, it might be easy to see the number four in the question and think that we’re dividing half into four. But if we read the problem more carefully, we’re told that Amelia wants to split the amount equally between herself and four friends. That’s a total of five people altogether. And that’s why the final question asks us, how much will each one of the five take?

The problem is asking us to divide a fraction by a whole number: one-half divided by five. And to help us visualise what the answer might be, we can sketch a model to help. First of all, let’s represent our dividend, one-half. To do so, we could draw a rectangle to represent one whole. Then split it into two equal parts. And if we shade one of those parts, we can represent visually the half a kilogram of apples that Amelia has to begin with.

Now that we’ve found our starting number in the division, we know that we need to divide it by five. Amelia needs to divide her half a kilogram between herself and her four friends. And we can represent this on our model by drawing lines so that the part that represents one-half is split into five equal parts, like this. And the question asks us how much will each one of the five take. In other words, what’s one of these five parts worth? Is it one-fifth because it’s one out of a possible five. Or perhaps, we need to include the white part of the diagram too. And it’s one out of a possible six parts.

Well, neither of these two answers are correct. We know that to find what a fraction is worth, we need to divide a whole into equal parts. If we look at the whole rectangle, it’s not divided into equal parts at the moment. In order for us to understand what this fraction worth, it would help us to divide the whole model into parts that are the same size. So we can continue each line across the model. We’ve split the whole amount into 10ths. And so, one out of these 10 parts has a value of one 10th. And because we’re talking about the weight of apples, the answer is one 10th of a kilogram.

To find the answer, we knew that we had to divide one-half by five. To begin with, we drew a rectangle that represented one whole kilogram. And then, we shaded half of it. This gave us the first number or the dividend in our division. To help us understand what happens when we divide one-half by five, we then split that half into five equal parts. And we knew the answer to our question was going to be one of these parts. But what fraction was it worth? To find out, we needed to split that whole amount into parts of exactly the same size and there were 10 of them.

If Amelia bought half a kilogram of apples and wanted to share it equally between herself and four friends, each one of the five will have one 10th of a kilogram of apples.

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