Question

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

Answer 1

you just cross sinplify and then multiply the numerators by themselves and denominators by themselves and get your answer

Answer 2

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
`(3)/(2)` and
`(1)/(8)` so multiply across and get
`(3)/(16)` 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
`(27)/(80)`. 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.
`(16)/(21)` and
`(7)/(8)` 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
`(1)/(1)` and
`(2)/(3)` multiply across and get just
`(2)/(3)`. prime factorization is the best way to do this but, more effective with larger numbers.
`(2*2*2*2*7)/(3*7*2*2*2)` 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
`(2)/(3)`.

I really hope this helps you!!