Answer:
24
Step-by-step explanation:
24 is the lowest number that can be divided by both.
So 1/2 of 3/4 is 3/8 which is equal to 6 cookies ( or 3/8 of a packet has 6 cookies)
So if we say a packet of cookies = X
and we know 8/8 of a packet of cookies = 1 full packet of cookies
( 8/8 of a packet or 1 full packet has X cookies )
Then 3/8 divided by 8/8 = 6/X
3/8 = 6/X
X = 6 divided by 3/8
X = 16
So there should be 16 cookies in a full packet
If 'a' is a rational number and c is rational, then
a = p/q
c = r/s
where p,q,r,s are integers (q and s can't be zero)
Subtracting c-a gives
b = c-a
b = (p/q) - (r/s)
b = (ps/qs) - (qr/qs)
b = (ps - qr)/(qs)
The quantity pq - qr is an integer. The reason why is because ps and qr are both integers (multiplying any two integers leads to another integer). Subtracting any two integers results in another integer.
So we have (ps - qr)/(qs) in the form (integer)/(integer) = rational number
Therefore, b is a rational number, but this contradicts the given info that b is irrational. If b is irrational, then we CANNOT write it as a ratio of integers.
This contradiction proves the assumption "a+b = c and c is rational" is incorrect
The sum is irrational.
Therefore, if a+b = c, where 'a' is rational and b is irrational, then c is irrational.
1/4 times 2 2/3 = 2/3
Change from a mixed number to improper fraction: 1/4 times 8/3
Multiply across so 1x8/4x3 to get 8/12
Simplify to 2/3