Learn About Multiplying Fractions In this lesson, let’s learn how to multiply a fraction by another fraction. We’re given two problems. We’re going to do them one by one. Let’s do the first part of the first problem first which is 1/3×3/5. When you’re multiplying fractions by fractions, what we do is we follow two steps. Step one, we multiply numerator one by numerator two and denominator one by denominator two. The step two is we write the fraction in the simplest form which may involve dividing both the numerator and denominator by the GCF or Greatest Common Factor. Let’s learn how to do this. 1/3×3/5= 1×3 is 3, 3×5 is 15, so it’s 3/15. 3/15 is actually an improper fraction. It’s not in simplest form. It is actually a proper fraction as I’m corrected but it’s not in simplest form. In order to write this in simplest form, what we will do is take 3/15, divide both numerator and denominator by their GCF which 3. 3÷3 is 1, 15÷3 is 5. The answer is 1/5. Let’s try the second problem which is 6/7×2/3. What we’re trying to do is 6/7×2/3. Again, I multiply the numerators, so it’s 12, 7×3 is 21. Again, is this in simplest form? No. Let’s divide both of this by 3 which is their GCF which gives me 12÷3 is 4, 21÷3 is 7. The answer here is 4/7. Let’s do problem two. Question on problem two says that on an average, people spend a third of their lives asleep and a fourth of the time they sense sleeping, they dream. What fraction of a lifetime does a person typically sleep dreaming? Let’s learn how to do this. We know that 1/3 of lifetime spent sleeping and we know that ¼ of sleep time is spent dreaming. If I want to figure out what percentage, what fraction of that time of lifetime I spent dreaming, I have to figure out ¼ of sleep time which is 1/3 of lifetime. ¼ of sleep time is the same as 1/3 of lifetime. The answer that I have to do is ¼×1/3. If I want to multiply it, 1×1 is 1, 4×3 is 12. The amount of time spent, 1/12 is the fraction of life spent dreaming. Quickly recapping what we’ve learned in this particular lesson. What we’ve learned is if we’re multiplying two fractions, 1/3 and 3/5 for example, we multiply the numerators and the denominators like we did here. 1×3, 3×5 gives me 3/15 and the end of the result fraction can be divided by the GCF to get the fraction in simplest form. Similarly, 6/7×2/3 is 12/21 which when simplified gives me 4/7. Now, a third of a lifetime is spent sleeping, a fourth is sleep time spent dreaming, what percentage or what fraction of a lifetime spent dreaming? Well, it’s actually the multiplication of ¼×1/3 which is 1/12.