Question

Write the given phrase as an algebraic expression: the sum of $8\,\,{\text{and}}\,\,y.$

Answer 1

Hint:Algebraic expressions are expressions which are made up of variables and constants along with mathematical algebraic operations which are addition, subtraction, multiplication, division etc.
Also Sum is the term given to the expression which is obtained by adding one term or number over another term or number or simply sum is the result of the mathematical process addition.
So by using the above two standard definitions we can solve the question given.

Complete step by step solution:
Given statement:
The sum of $8\,\,{\text{and}}\,\,y....................................\left( i \right)$
Now we know that in mathematics the algebraic expressions are those expressions which are made up of variables and constants along with mathematical algebraic operations which are addition, subtraction,multiplication, division etc.
Algebraic expressions are widely useful and popular since it represents the value of an expression for all of the values a variable can take on.
Now according to the basic definition of sum, it simply represents a number or a term obtained by adding one term or number over another term or number.
So according to the definition the mathematical process involved is addition and is represented by:
\[{\text{Sum}} = p + q..............................\left( {ii} \right)\]
Now on observing the given statement (i): The sum of$8\,\,{\text{and}}\,\,y$, we can say that here $p$ is $8$ and $q$ is $y$
Such that on comparison with (ii) we can write:
\[ \Rightarrow p + q = 8 + y....................................\left( {iii} \right)\]
Therefore the algebraic expression for the phrase the sum of $8\,\,{\text{and}}\,\,y$ is \[8 + y\].

Note:
While writing an algebraic expression some of the commonly used words and their corresponding mathematical operations are given below:
1. Addition : plus, sum, more than
2. Subtraction : subtracted, minus, less than, decreased by
3. Multiplication : times, product
4. Division : divided, quotient
Also while making an algebraic expression one must take care that the words and the operations used are mathematically correct or not.