Let's solve this atomic mass ratio problem step by step. We are given copper-64 and silver-108, which means copper has an atomic mass of 64 and silver has an atomic mass of 108. We need to find the mass ratio of 7 copper atoms to 9 silver atoms.
Now let's calculate the total mass for each element. For copper, we multiply 7 atoms by the atomic mass of 64, giving us 448 atomic mass units. For silver, we multiply 9 atoms by the atomic mass of 108, giving us 972 atomic mass units.
Now we calculate the mass ratio by dividing the mass of 7 copper atoms by the mass of 9 silver atoms. This gives us 448 over 972. To simplify this fraction, we find the greatest common divisor, which is 4. Dividing both numerator and denominator by 4, we get the final simplified ratio of 112 to 243.
Let's verify our calculation step by step. Seven times sixty-four equals four hundred forty-eight. Nine times one hundred eight equals nine hundred seventy-two. The fraction four hundred forty-eight over nine hundred seventy-two simplifies to one hundred twelve over two hundred forty-three. Therefore, the mass ratio of 7 copper atoms to 9 silver atoms is 112 to 243, which is approximately 0.461 in decimal form.