Video: Solving Word Problems on Ratios and Proportions Involving Mixed Numbers

The actual size of a bracelet is 4 times larger than a photo of it in an advert. If the length of the bracelet in the photo is 1 1/6 inches, what is the actual length of the bracelet?

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Video Transcript

The actual size of a bracelet is four times larger than a photo of it in an advert. If the length of the bracelet in the photo is one and one-sixth inches, what is the actual length of the bracelet?

Our problem talks about the size of a bracelet. But we’re given two different sizes. The question talks about a photo of a bracelet in an advert. And we’re told that the length of the bracelet in the photo is one and one-sixth inches. The second size of the bracelet that’s mentioned is actually mentioned in the first sentence. And that’s the actual size of the bracelet, the size of the bracelet in real life. We’re not told this in inches. But we are told that the actual size is four times larger than the photo of it in an advert. We need to use the information that we’re given to calculate the actual length of the bracelet.

If we were to sketch the problem as a bar model, it might look like this. One bar is worth one and one-sixth inches. And so, the actual size of the bracelet could be represented by a much longer bar that’s worth four times one and one-sixth inches. So to calculate the answer, we need to multiply one and one-sixth by four. Now, one and one-sixth is a mixed number. It has a whole number part, which is the number one, and a fraction part. That’s the one-sixth on the end. To help us multiply this mixed number by four, let’s partition it.

First, we can multiply the whole number part, which is one. And then let’s multiply the fraction part, one-sixth. So first of all, four times one we know is four. And although multiplying fractions can be tricky at times, to find four lots of one-sixth is fairly easy. If we have four lots of one-sixth, we have four-sixths. Now, we have a whole number answer and a fraction answer. And if we combine these two together, we’re going to get another mixed number. Four plus four-sixths equals four and four-sixths. Now, we could write down this as the answer. The actual length of the bracelet is four and four-sixths inches. But it’s always a good idea to try to simplify a fraction, if we can. And we can simplify four-sixths.

To simplify a fraction, we need to divide both the numerator and the denominator by the largest possible common factor that they both have. In this case, the largest common factor of four and six is two. Four divided by two equals two. And six divided by two equals three. Four-sixths can be simplified and written as two-thirds. And so, if the length of a bracelet in an advert is one and one-sixth inches and the actual size of the same bracelet is four times larger than the photo. The actual size of the bracelet in real life is four and two-thirds of an inch.

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