Does this verbal phrase translate into the algebraic expression correctly?

Yes.

The sum of ten and the quotient of a number xxx and 666.

Translate into an algebraic expression six times the diffrence of a and b

Yes, the verbal phrase "The quotient of seven times a number and three" is correctly translated into the algebraic expression " (7x) / 3".

To understand how to translate the verbal phrase into an algebraic expression, let's break it down:

1. "Seven times a number": This means that we have a variable, which we can represent as "x", and it is multiplied by 7. So, we have 7x.

2. "Divided by three": This means that the result of multiplying the number (x) by 7 should be divided by 3. Therefore, we divide 7x by 3, resulting in (7x) / 3.

So, the expression (7x) / 3 is the correct algebraic representation of the verbal phrase "The quotient of seven times a number and three".