Math problems, please help?

this is subtracting fractions

it says of D dogs, to make it easy, I will pick 100 dogs, but it doesn't really matter

1/3 are large

so 33 dogs are large

there are 67 dogs leftover

1/4 of those dogs are medium (because of the word remainder, it says to look at the group after you have taken out the large dogs)

so 1/4 of 67 is (grab your calculator) about 17 dogs

so now you only have 50 dogs left

so 50/100 = 1/2

answer = A

1/3 = large dogs

which leaves 2/3 of "remaining" dogs

you need to find the number of medium dogs in order to find the number of small dogs, so...

1/4 of the 2/3 remaining dogs are medium dogs:

multiply 1/4 and 2/3 = 2/12 (reduced to 1/6)

add 1/3 (lg dogs) plus 1/6 (med dogs) = (2/6) + (1/6) = 3/6 = reduced to 1/2

when using fractions, use 1 to represent 100% or (1/1, 2/2, 3/3...)

1 - (1/2) = 1/2 are small dogs.

(1/3) + (1/6) + (1/2) = 1 (or 100%)

(2/6) + (1/6) + (3/6) = (6/6) or 1

the correct answer is (a)

to help understand, use real numbers:

the kennel has 99 dogs

of the 99, (1/3) or 33 are large dogs

of the remaining (2/3) or 66 dogs, 1/4 (25%) are medium dogs

66 divided by (1/4) or 25% is approx 16 dogs

66 - 16 = 50 (or 1/2 or 50%)

out of 99 dogs, approximately 50 are lg and med dogs combined, which leaves about 49 dogs or 1/2 of 99 dogs remaining and they must be the small dogs.

1/3 are large

(2/3)(1/4) = 2/12 = 1/6 are medium

1/3 + 1/6 = 3/6 = 1/2 are large or medium

1 - 1/2 = 1/2

1/2 are small

1/2 D

1/3 + 1/4(2/3) change all to twelfths 4/12+2/12 = 1/2 so the remaining 1/2D will be small dogs

1/3 = l

1/4*2/3 = m = 1/6

l+m+s=1

1/3 + 1/6 + s = 1

s= 1/2

or the other way to look at it is 3/4 of 2/3 = 6/12 = 1/2

D/3 + (1/4)(2D/3) is the total of large and medium degus.

i.e. D/3 + D/6 = D/2

So, D/2 remain and are the small degus.....................so, (a)

:)>