Chad buy peanuts in 2-pound bags. He repackages them into bags that hold 5/6 pound of peanuts. How many 2-pound bags of peanuts should Chad buy so that’s can fill the 5/6 pound bags without having any peanuts left over?
2/(5/6)
every 2lb bag fill 2 small bags, with 2/6 left over
So, 3 big bags will fill 6 small bags, plus 6/6, or 7 small bags
To get the answer, we need to find the least common multiple (LCM) of 2 and 5/6.
First, let's convert 5/6 to an equivalent fraction with a denominator of 6. We multiply the numerator and denominator by 6, which gives us 5/6 * 6/6 = 30/36.
Now, we find the LCM of 2 and 30/36. The LCM is the smallest number that is divisible by both 2 and 30/36.
The prime factors of 2 are 2.
The prime factors of 30/36 are 2, 3, and 5.
To find the LCM, we take the highest power of each prime factor that appears in either number.
LCM = 2^1 * 3^1 * 5^1 = 2 * 3 * 5 = 30.
So, Chad should buy 30 bags of 2-pound peanuts in order to fill the 5/6 pound bags without any peanuts left over.