An algebraic expression is a mathematical statement consisting variables, constants and their related operations. But the base fact is, an algebraic expression is not generated by itself nor it is created randomly. It is formed by translation of a given situation in verbal form so that a solution can be arrived algebraically because algebraic methods of solutions are easier and convenient. Subsequently the algebraic solution is translated back to verbal form for the conclusion.Hence it is imperative that one should be familiar in translating verbal statement to algebraic expression and vice versa.
Translate the phrase to an algebraic expression
Normally a real situation is described as word problems. When we express in words, we need to follow certain grammar and also in some cases explain the background. But an algebraic expression is just a code and has minimal number of items which are only required. Therefore, one must be very good in interpretations of statements and know which part is to be considered and which part is to be ignored. For an example, let us consider a world problem as follows. In 1998, during a wild fire in a park, 10 trees were gutted and only 22 trees, including 3 pine trees survived. Find how many trees were there in the park before the fire?
In this statement, the parts, ‘In 1998, during a wild fire in a park’ is only the background situation. In the mathematical expression they have no part to play.
Similarly the part ‘including 3 pine trees’ is an extra information because the question is not on the number of trees in different categories. It might have been mentioned for use in different context but not relevant to the given question.
The first step is identify which has been asked and assume that as ‘x’. In this case the number of trees prior to the wild fire is x.
The next step is to pick up the phrases one by one and translate step by step.
’10 trees were gutted’ means 10 must be reduced from the original number of trees to determine the number of trees remaining.
Algebraically the number of remaining trees can be expressed as an algebraic expression ‘x – 10’.
Now it says ‘only 22 trees, including 3 pine trees survived.
Ignoring ‘including 3 pine trees’,. as mentioned earlier, we can figure out the actual number of trees left were 22.
This is another algebraic expression (though it is a constant). Hence the two expressions we derived are ‘same’. In other words, the ‘equation is x – 10 = 22.
Translate an algebraic expression to word form
As explained earlier, when you get a solution by solving an algebraic expression or equation, your answer will be in algebraic form. To report back that in verbal form you must correctly. In the example we described in the previous section we ended up with x – 10 = 22.
By solving algebraically, we get x = 32.
Now you must report the final answer not just be saying x = 32. You must express in verbatim as ‘the number of trees before the fire was 32’
All the time the answer may not be this simple.For example, you say John was 20 years old, 8 years back. What was his age 15 years back?
The approach is, if ‘x’ is present age, then his age 8 years back is given by the algebraic expression ‘x – 8’
Since it is stated as 20, x – 8 = 20 and hence x = 28.
In this case the final answer is not ‘x’ but ‘x – 15’, the age 15 years back.
That is, 28 – 15 = 13 (since x = 28). Therefore, the correct translation is ’15 years back John was 13 years old’.