Final answer:
To express the sum of the number of bass students and the number of violin students as a product, we can use the GCF (Greatest Common Factor) and the Distributive Property. The GCF is the largest number that divides both the number of bass students and the number of violin students without leaving a remainder. We can express the sum as the GCF multiplied by the sum of the number of bass students divided by the GCF and the number of violin students divided by the GCF.
Step-by-step explanation:
To express the sum of the number of bass students and the number of violin students as a product, we can use the GCF (Greatest Common Factor) and the Distributive Property.
Let's say the number of bass students is represented by 'b' and the number of violin students is represented by 'v'.
The GCF of 'b' and 'v' is the largest number that divides both 'b' and 'v' without leaving a remainder. Let's say the GCF of 'b' and 'v' is 'g'.
To express the sum of 'b' and 'v' as a product, we can write it as 'g' multiplied by the sum of 'b/g' and 'v/g'.
For example, if there are 10 bass students and 15 violin students, the GCF of 10 and 15 is 5. So, the sum of the number of bass students and the number of violin students can be expressed as 5 multiplied by the sum of (10/5) and (15/5), which is 5 multiplied by 2+3, resulting in 25.