In order to translate the above sentence into an algebraic expression, let's consider each part of the sentence:

"The product of an unknown number and the reciprocal of 5."

"The product of an unknown number and..." means that we're going to multiply whatever follows the "and" by an unknown number, which we'll call .

"...the reciprocal of 5" is another way of saying  divided by , or .

Putting all of the above together, we get  or .

In order to translate the above sentence into an algebraic expression, let's consider each part of the sentence:

"The reciprocal of the quantity 8 minus an unknown number."

"The reciprocal of..." means that we divide  by whatever follows in the sentence.

"The quantity 8 minus an unknown number" means that we are considering the full operation  minus an unknown number that we can call . 

 Putting all of the above together, we get .

In order to translate the above sentence into an algebraic expression, let's consider each part of the sentence:

"The quotient of an unknown number and the quantity 4 minus the same unknown number."

"The quotient of..." means that we are going to divide the numbers that follow in the sentence.

"An unknown number" refers to a variable that we'll refer to as .

"...and the quantity 4 minus the same unknow number" means that we'll subtract  by the unknown number , or 

 Putting all of the above together, we get  .

In order to translate the above sentence into an algebraic expression, let's consider each part of the sentence:

"Six times the quantity seven plus an unknown number".

"Six times..." means that we are going to multiply the remainder of the above sentence by .

"The quantity..." means that we're going to holistically consider the numbers that follow, in this case by putting them in parentheses. 

"Seven plus an unknown number" means that we're going to add an unknown number  to , or .

 Putting all of the above together, we get .

In order to translate the above sentence into an algebraic expression, let's consider each part of the sentence:

"The reciprocal of the quantity two times an unknown number."

"The reciprocal of..." means that we're going to divide  by the numbers that follow this phrase.

"The quantity..." means that we're going to holistically consider the numbers that follow.

"Two times an unknown number" means that we're going to multiply  by an unknown number that we'll call .

 Putting all of the above together, we get .

When something is more than , that means we are dealing with addition. That something is twenty. So our expression is 

When something is less than , that means we are dealing with subtraction. This also means  will come before the subtraction sign. That something is seven. So our expression is . 

When we see times, we are dealing with multiplication. It doesn't matter which comes first since multiplication is commutative. Our expression is .

When we see divided, we use division. When something is divided by eighty-eight, the eighty-eight is the denominator and  in this case is in the numerator. Our expression is .

Raising to a power means exponents. In this case we are raised to an exponent of  and our base is nine. Our expression is .