Question

How do you write an algebraic expression that models the word phrase “The sum of 57 and a number b”?

Answer 1

Hint: We use the meaning of each word given in the expression and write the expression step-by-step according to the sequence of words given in the expression. Assume the number as the variable ‘b’ and form the expression accordingly.
* Sum of any two numbers is given by the addition of the two numbers. Example: If ‘x’ and ‘y’ are two numbers then their sum will be written as \[x + y\]

Complete step-by-step answer:
We have to form an expression for the word phrase: The sum of 57 and a number b.
We use the definitions of the sum of two numbers to form the expression.
Let us assume the number stated in the word phrase in the question as a variable.
Let the number be ‘b’ … (1)
Then the sum of any number and the number ‘57’ can be written as \[57 + \] required number … (2)
Now we are given in the word phrase the sum of 57 and ‘b’, so the second number is ‘b’.
i.e. Add value ‘b’ to number ‘57’ from equation (2) , i.e. \[\left( {57 + b} \right)\] … (3)

\[\therefore \]The expression: The sum of 57 and a number ‘b’ can be written as \[\left( {57 + b} \right)\].

Note:
Many students make the mistake of substituting the values of ‘b’ in the equation formed in the answer one by one and then write the answer as some numerical values. Keep in mind we don’t need final answers as numerical values here we only need an algebraic expression that states the meaning of the word phrase. Also, students using commutative property can also write the final sum or expression as \[\left( {b + 57} \right)\]