When
, we have


and of course 3 | 6. ("3 divides 6", in case the notation is unfamiliar.)
Suppose this is true for
, that

Now for
, we have

so we know the left side is at least divisible by
by our assumption.
It remains to show that

which is easily done with Fermat's little theorem. It says

where
is prime and
is any integer. Then for any positive integer
,

Furthermore,

which goes all the way down to

So, we find that

QED
Answer:
He can fill 3 bags
Step-by-step explanation:
You would first make them have a common denominator so you would have 2/8 instead of 1/4 then you would do 6/8 divided by 2/8 to get 3
1/4 = 2/8
6/8 divided by 2/8 = 3
Answer: $11,600
Step-by-step explanation:
$2000 * 10% = $200
y = 200x + $2,000
12 * 4 = 48
48 = x
y = 200(48) + $2,000
y = $9,600 + $2,000
y = $11,600
Answer:
hiiii
Step-by-step explanation:
To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate.
(Table)
In a unit rate, the denominator is always 1. So, to find unit rate, divide the denominator with the numerator in a way that the denominator becomes 1. For example, if 50km is covered in 5.5 hours, the unit rate will be 50km/5.5 hours = 9.09 km/hour. ( equation)
To find the unit rate, divide the numerator and denominator of the given rate by the denominator of the given rate. So in this case, divide the numerator and denominator of 70/5 by 5, to get 14/1, or 14 students per class, which is the unit rate. ( Graph)