Can someone explain to me how to divide fractions?

Question

Best answer for the first person to help me understand dividing the following types of fractions:
Whole number / fraction (3 / 4/5)
Mixed number / fraction (3 4/5 / 4/5)
Fraction / fraction (4/5 / 3/4)
Mixed number / mixed number (3 4/5 / 3 3/4)
Improper fraction / fraction (5/4 / 3/4)
Improper fraction / improper fraction (5/4 / 4/3)

Thank you!

Those aren't actual questions on the sheet I'm doing. Showing with numbers would be easier than words.
Thank you!!
(We learned it at school but I was at the optometrist, so I couldn't pay attention if I wanted to :) lol)

Am I on the right track? The question is 2/3 / 1/5, is the answer 10/3 (3 1/10)????

Answer 1

Ok that's a lot of information - you need to know the basic premise of division of fractions: You leave the first fraction as is, change the division sign to a multiplication sign, and flip the other fraction. That flipped fraction is a fraction's reciprocal.

For example, with two proper fractions:

4/5 (divided by sign) 3/4
becomes
4/5 x 4/3
and you solve by multiplying the numerators and denominators:
16/15
(and if you need too and can, simplifly)
1 and 1/15

Ok, for whole number and fraction:
3 is actually 3/1
3/1 (divided by sign) 4/5
becomes
3/1 x 5/4
15/4
(simplified to)
3 and 3/4

Ok, finally, for mixed fractions, turn the mixed fraction into an improper fraction:

3 and 4/5 (divided by sign) 3 and 3/4
becomes
19/5 (divided by sign) 15/4
which when you change the sign and use the reciprocal becomes
19/5 x 4/15 (and I use a calculator)
76/75
(simplified to)
1 and 1/75

The rest of the ones you offer are just combinations of those three rules. Try them.

Good luck!

------------added:

I don't mean to not do each example you typed out to be mean, nor do I not trust you. I'm just a teacher and want to see if you can apply this information to the other ones. Besides, the advice from an answerer above to turn them into decimals and use a calculator would be a pretty good check if you tried the others on your own.

Answer 2

OK...a whole number as a fraction is that number over 1. So, in your example 3 divided by 4 over 5...you put the 3 over 1 and flip the 4/5 over. Your problem is now 3/1 TIMES 5/4. If you can't cross out (reduce), multiply normally. You would multiply the 3 times the 5 and the 1 times the 4...this gives you 15/4. Reduced, you have 3 3/4.

For your mixed number, multiply the whole number times the bottom and add the top number. Place that number over the bottom. 3 4/5 will be (3x5+4) 19/5 and 3 3/4 will be 15 over 4. Flip the second fraction and multiply like before.

Fraction and fraction...flip the second one and multiply like before

Improper fraction...same thing. Flip, reduce where you can and multiply. OK...5/4 time 4/3....on paper you will see that the two 4s cross each other out leaving you with 5/1 and 1/3...now, multiply across and you end up with 5/3...reduced to 1 2/3 YOU don't worry about the fact it is improper until you have your answer. Take that answer and turn it into a mixed number by dividing the bottom into the top. See, 5/3..I divided the 3 into the 5 for 1 and I put the remaining 2 over the 3 for 5/3 = 1 2/3

Improper and improper would be the same way. 5/4 divided by 4/3 would be 5/4 times 3/4...giving you 15/16.

did that help???

Answer 3

The secret is that the top and the bottom must be fractions.
like a/b and c/d
then to divide you multiply but first flip the second one
so a/b x d/c
Whole number 3 / 4/5 becomes 3/1 x 5/4 = 15/4
Mixed 3 4/5 / 4/5 becomes 19/5 x 5/4 =95/20
Mixed mixed 3 4/5 / 3 3/4 becomes 19/5 x 4/15 = 76/75
Improper 5/4 / 3/4 becomes 5/4 x 4/3 = 5/3
Improper improper 5/4 /4/3 becomes 5/4 x 3/4 = 15/16
:)

Answer 4

With a whole number add a one under the # for example 3/1 mulitiply the number by the reciprocal of the next fraction for example 3/1 x 5/4+ 15/4

For the mixed # change the mix # into a fraction then do the same thing. If you get an answer for example like 12/2 you can reduce it to 6/1 or 6. Ok I'll help a little but I'm not going to do all of them. Good Luck.

Answer 5

Whole number divided by fraction.
Multiply it by the reciprocal.
Ex. 3/5 --> 5/3
( 3 / 4/5 )
3 ( 5/4 ) = 15 / 4, 15/4 = 3.75

Fraction divided by fraction.
Multiply first fraction by the reciprocal of the other.
( 4/5 / 3/4 )
4/5 ( 4/3 ) = 16/15 = 1.067

Answer 6

3/4 divided by 1/2 what you do is you change the division sign in the middle to a multiplication sign, and then you invert the '1/2' i.e. turn it upside down so now it is 3/4 x 2/1 and then you would multiply fractions as you normally do = 6/4 = 3/2

Answer 7

when there is a whole number times a fraction, put the fraction over 1then change the division to a multiplication sign and then flip the second fraction then multiply acr

when there is a mixed number/ fraction you multiply the whole number times the demoninator then add the numarator ( do to both mixed numbers) then change the division to a multiply sign, then flip the second fraction and then just multiply across

when there is a fraction times a fraction change the division sign to a multiplication sign, flip the second fraction, then mulitiply across

when there is a mixed number/ mixed number you multiply the whole number times the demoninator then add the numarator ( do to both mixed numbers) then change the division to a multiply sign, then flip the second fraction and then just multiply across

when there is a improper fraction/ fraction flip the second fraction then change division sign to multiplication sign then multiply across

when there is a improper fraction/ improper fraction flip the second fraction then change division sign to multiplication sign then multiply across

Answer 8

for example you have 3 and 4 fifth u line them up and u do 3x5=15 and and u had the numerator which is 4 so that ninteen. than u take that 19 and 5 and divide the top by the bottom

Answer 9

any time you are dividing fractions, just flip the second fraction upside down and mulitply across. for mixed number/ mixed number, divide the whole numbers into each other and then do the fliping thing with the other fractions.

Answer 10

Convert the fraction into decimal then do it on the calculater then convert it back.