Gary has guitar lessons every 5 days and band practice every 4 days . his first band practice is in 4 days and his first guitar lesson is in 5 days . in 100 days , how many times will Gary have had guitar lessons and band practice on the same day ? explain your answer

In order to find out how many times Gary will have guitar lessons and and band practice on the same day, we have to find the least common multiple (LCM) for 5 and 4.

5 : 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100

4: 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60,64,68,72,76,80,84,88,92,96,100

So, the last common multiple for both numbers is 20, which means that every 20 days he has band practice and guitar lesson. As we can see, the number of times he has had band practice and guitar lessons in the same day out of 100 days is 5 times. Therefore, the number of times Garry will have guitar lessons and band practice is 5 times on the same day out of 100 days.

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.