Ok so I need help with multiplying fractions, this is the way my teacher did it but I have no idea how to do it the way he did it so if someone can, please explain to me on how to do it

example 1: this is basically reducing WHILE multiplying. since 5 and 10 have a greatest common factor and is able to be reduced by each other, we do so. hence the reason 5 went to 1 and 10 went to 2 because 5 goes into 5 once and 5 goes into 10 twice. it was a different case for 3 and 8. 3 obviously cant go into 8 and 3 is prime so nothing can be done with those. ONLY REDUCE WHILE MULTIPLYING DIAGONALLY you CANNOT do up and down or side to side. so our new fractions are and so multiply across and get which cant be reduced more.

example 2: this one in my opinion is pretty easy. you take the two fractions and multiply regularly across. you get . that fraction can be reduced. so we find the prime factorization of each number. 3 is a prime factor. 3x3x3=27 which is our top number. 2 and 5 are all prime numbers used to reach 80. 2x2x2x2x5=80. that's the prime factorization method its an easier way to check your work also.

example 3: this one is practically a combination of the two previous ones. and can be diagonally reduced on both diagonals. 7 goes into 7 once and 7 goes into 21 three times 8 goes into 8 once and 8 goes into 16 twice. now we have and multiply across and get just . prime factorization is the best way to do this but, more effective with larger numbers. now cross out the numbers that are the same on the top and bottom. three 2's cancel out, one 7 cancels out, and now we're left with .

I really hope this helps you!!

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step-by-step explanation:

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