We have a problem involving atomic masses. We're given copper-64 and silver-108, and we need to find the mass ratio of 7 copper atoms to 9 silver atoms. Let's start by understanding what these numbers mean.
The numbers 64 and 108 represent the atomic mass of each element in atomic mass units. This means one copper atom has a mass of 64 u, and one silver atom has a mass of 108 u. To find the mass of multiple atoms, we multiply the number of atoms by the atomic mass.
Let's calculate step by step. First, the mass of 7 copper atoms is 7 times 64, which equals 448 atomic mass units. Next, the mass of 9 silver atoms is 9 times 108, which equals 972 atomic mass units. Now we can set up our ratio as 448 over 972.
To simplify the fraction 448 over 972, we need to find their greatest common divisor. We can factor both numbers and find that the GCD is 4. Dividing both numerator and denominator by 4, we get 112 over 243 as our simplified ratio.