Question Video: Dividing a Quantity into a Two Part Ratio Mathematics

David and Isabella share 30 cupcakes in the ratio 2 : 3. How many do they each get?

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Video Transcript

David and Isabella share 30 cupcakes in the ratio two to three. How many do they each get?

One way we have to answer this question is the add-divide-multiply method. But there is another method which is equally valid. And that involves thinking about bar modeling and fractions. The first step is the same as the add-divide-multiply method. We look at our ratio. That’s the ratio two to three. We then add the numbers in our ratio. Two plus three is equal to five, meaning we’re looking at a total of five parts in this question. And so a bar model will be made up of five parts, as shown.

Remember, order is important. So David gets two of these parts. That’s represented by the yellow bits. And Isabella gets three. That’s represented by the pink parts. Now, we can think about this in terms of fractions. And we can see that the portion of the bar that I’ve shaded yellow represents two-fifths of the whole, whereas the portion that I’ve shaded pink represents three-fifths of the total.

We can extend this into the number of cupcakes and say that, well, if there are 30 cupcakes, David gets two-fifths of these. Similarly, Isabella will get three-fifths of these. By recalling that “of” can quite regularly be interchanged with the multiplication symbol, we see that we can answer this question either by finding two-fifths of 30 and three-fifths of 30 or by multiplying two-fifths by 30 and three-fifths by 30.

Let’s multiply two-fifths by 30. We’ll write 30 as a fraction. It’s 30 over one. Next, we cross cancel. We divide the denominator of our first fraction by five and the numerator of our second by five. Two times six gives us 12, and one times one gives us one. But 12 ones is simply 12. And so we see that David gets 12 of the cupcakes.

To find the number that Isabella gets, we could subtract this from 30. But let’s multiply again. We do three-fifths times 30 over one and, once again, divide through by five. This gives us three times six, which is 18 over one, or simply 18. David gets 12 cupcakes, and Isabella gets 18.

Note that, of course, we can check our answer by checking that 12 and 18 do add up to 30, which they do. Note also that at this stage, we could have found the value of one-fifth by dividing 30 by five. Then whatever value we get, we double to find the value of two-fifths. Either method is perfectly valid.

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