Multiplying Three Fractions (Positive) Ex 1

Find the product of the three fractions we multiply three fractions, just like we multiply two fractions to multiply. We multiply the numerators and we multiply the denominators, but of course, you have to make sure the result is simplified, which means we have to simplify out all the common factors between the numerator and denominator. To multiply the three fractions. The numerator is three times four times 15, and the denominator is five times nine times twenty-four it’ll be easier to simplify before determining the products. One way to do this is to find the prime factorization of each factor. Let’S use this method to simplify before multiplying three is prime. The prime factorization of four is two times two and the prime factorization of 15 is 3 times 5 in the denominator. Five is prime. The prime factorization of 9 is 3 times 3. Let’S find the prime factorization of 24 using a factor. Tree 24 is equal to 4 times. 6 4 is equal to 2 times 2 and 6 is equal to 2 times 3. The prime factorization of 24 is 3 factors of 2 and a factor of 3. So we have 2 times 2 times 2 times 3. Now that we have the prime factorization of each factor, we can actually see the common factors between the numerator and denominator that will simplify to 1. Remember a fraction bar means division and therefore, 3/3 simplifies the 1. Here, as well as here 2/2 simplifies to 1 here, as well as here and finally 5/5 simplifies to 1 here, and that we’ve simplified out all the common factors between the numerator and denominator. We can multiply knowing the product will be in simplest form in the numerator notice. All the factors that simplified to 1 in the denominator were left with 3 times 2, which is 6. The simplified product is 1/6. So by determining the prime factorization of each factor, we can actually see all the common factors between the numerator and denominator. Let’S also take a look at a second method for simplifying before multiplying again multiplying the 3 fractions. The numerator is 3 times 4 times 15 and the denominator is 5 times 9 times 24. Let’S see if we can simplify this without determining the prime factorization of each factor. Notice 3 & 9 share a common factor of 3, where there’s 1 3 & 3 & 3 3 & 9. By simplifying this way, we just simplified out one common factor of 3 between the numerator and denominator. Notice, 5 and 15 share a common factor of 5. There’S one 5 & 5 & 3, 5 and 15. We just simplified out one common factor of 5 between the numerator and denominator and notice. 4 & 24 share a common factor of 4 there’s 1 4 & 4 & 6 fours and 24. We just simplified out the common factor of 4 between the numerator and denominator and notice here, there’s a common factor of 3 there’s 1 3 & 3. Here as well as here, we just simplified out another common factor of 3 between the numerator and denominator, and now we multiply 1 times 1 times. 1 is 1 and 1 times 1 times. 6 is 6, giving us the same product so notice. How? The second method is a little bit faster than determining the prime factorization of all the factors, but it may be a little more challenging to make sure we find all the common factors between the numerator and denominator. I hope you found this helpful

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