Take every word and translate into math. 

 less than means that you need to subtract  to something.

That something is  so just combine them to have an expression of . 

Take every word and translate into math. Product indicates multiplication.

So we multiply  and  to get .

Is indicates equal something.

Difference is subtraction so we have .

Our final answer is .

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

"The square root of the sum of 5 and twice an unknown number"

"The square root of..." means that we are going to take the square root, , of the the expression that follows.

"The sum of ..." means that we're going to add one or more numbers to .

"Twice an unknown number" means that we're going to multiply  times an unknown number that, in this instance, we'll call . We can call this product .

 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:

"Two-fifths times the reciprocal of an unknown number"

"Two-fifths times..." means that we're going to take the product of  and everything that follows in the sentence.

"The reciprocal of an unknown number..." means that we divide  by an unknown number that we'll 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:

"Nine plus the quotient of an unknown number and six"

"Nine plus..." means that we're going to take the sum of  and everything that follows in the sentence.

"The quotient of an unknown number and six" means the value we get when we divide an unknown number  by , 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 difference between 7 and the quotient of an unknown number and 3"

"The difference between 7 and..." means that we are subtracting the remainder of the expression from 7, or ...

"The quotient of an unknown number and 3" means that we are dividing an unknown number - let's call it  - by , 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 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 .