In this article I am going to explain evaluating the algebraic expressions. You must read my previous articles on order of operations and algebra to better understand this article or you should have good knowledge of order of operations and basic algebra. Evaluating the algebraic expression is grade 7 topic and next step from writing the algebraic relations from the word phrases.
As you already know that variables take many number values, or in other words variables are just different number values at different conditions or circumstances.
So, a variable can take different number values. By giving the variable a number value in an expression and solving it according to order of operations is called evaluating the algebraic expression.
Consider the simple word phrase "twice a number added to 10". The algebraic relation for this phrase is given below;
2n + 10
Where "n" is any number, two is its coefficient (as twice means 2 times) and 10 is the constant term. Now "n" represent any number, which means, "n" can take any value from the countless numbers in the real number system. Let's evaluate this expression by giving some number values to "n";
Please note that algebraic relation and algebraic expression are one and same thing.
For example, when the number is 3 i.e. n = 3 the relation is evaluated as follows;
2(3) + 10
= 6 + 10
= 16
Note that, instead writing 2n, I wrote 2(3), by replacing (plugging) "n" by "3" as the value of "n" is "3" now. Also, always use open brackets when plugging in the variable values in an algebraic relation.
When the number is "- 5" i.e. n = - 5, the expression is evaluated as follows;
2(- 5) + 10
= -10 + 10
= 0
Let's try the following examples to understand the concept further.
Evaluate the algebraic expression, - 5y - 7, where "y" having the values, y = 1, -1, 4, - 6
1. Plug y = 1 in the expression;
- 5(1) - 7
= - 5 - 7
= - 12
2. Plugging y = -1, the relation becomes;
- 5(- 1) - 7
= 5 - 7
= - 2
3. When y = 4 the solution is;
- 5(4) - 7
= - 20 - 7
= - 27
4. If y = - 6, the value of the solution comes to;
- 5(- 6) - 7
= 30 - 7
= 23
Hence, you saw that same variable took different values in an algebraic relations. This should be clear now that variables are simply numbers, but they can take many number values in the algebraic relations or equations.
You can try more values of "y" in the same algebraic expression above for more practice. Stay tuned, as more algebra is on its way.
