(a) Write an algebraic expression for one-third of the sum of a number and seven:

One-third of indicates multiply by `1/3` , and the sum of indicates adding the number to seven.

**`1/3(x+7)` is the expression we seek.** **Note the use of parantheses: it is one third of the sum, so we must take the sum first. This is opposed to one-third of a number plus seven. **

(b) one-third of a number reduced by twice the same number:

One-third of the number indicates multiply by 1/3. Twice the number indicates multiplication by 2, while reduced by indicates subtraction.

**`1/3x-2x` is the required expression.**