Evaluation of Subject by Substitution

Wondering What does it mean to use substitution to evaluate an expression? and How do you evaluate a subject of a formula by substitution? Don’t worry at all as we need to follow some basic concepts for Evaluation of Subject by Substitution which are explained here elaborately.

Learning the Changing the Subject of a Formula Chapter help students to get a good grip on fundamental concepts like Establishing an Equation, Subject of a Formula, Change of Subject of Formula, etc. All these topics will guide kids to evaluate a formula using substitution.

From this article, you’ll learn how to evaluate a particular expression or formula by known quantities of an equation as well as find the solved problems on evaluating a formula using substitution and practice well.

Evaluating Formulas by Substitution

A formula holds with known and unknown variables. A dependent variable on one side and an independent variable on the other side will be involved in an expression. We evaluate the expression containing the independent variables on the other side of the equal sign. By substituting the values in the independent variables, the result will be the value of the dependent variable.

Thus, the process to evaluate a formula using substitution. Get confused with the concept, hold on and look at the below sample problem on Evaluating an expression by substitution.

Let’s consider the formula A = 4lb. Find A if l = 5 and b = 10.
Given that A is the dependent variable, that can be our result.
To find the value of it, we evaluate the expression on the other end of the equal sign ie., 5lb.
We know that, l = 5 and b = 10.
Now, get the A value by substituting the known values of an expression.
A = 4(5)(10)
A = 4(50)
A = 200
Finally, we know A value is 200.

Therefore, the above process is evaluating a formula by substitution. Learn Evaluation of subject by substitution from the further modules and practice more with our given solved questions on Evaluating simple expressions by substitution.

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How to do Evaluation of Subject by Substitution?

Evaluating a formula or expression by substitution is the same as solving a linear equation in one variable. Here, we will be discussing how to evaluate a particular subject of a formula using the substitution method. The main step to follow while performing the evaluation of the subject by substitution is to substitute the known values of an equation into the formula and then try to solve for the unknown quantity.

Below are the fundamental concepts that should be followed for evaluating a formula by substitution:

  1. By taking help from the given context hints about known and unknown quantities of a formula, calculate the subject of the formula.
  2. In case the given expression is directly in the form of an equation where the subject is at one side of the equation and the remaining known quantities are on another side of the equation, then you can immediately substitute the known values in the formula and get the result of the subject.
  3. If the given formula is not in the required form and wants to change the subject of the formula, then make the unknown quantitive on one side and other known quantities on another side. You can do this by applying simple mathematical operations or else look at the explanation from this article ie., Change of a subject of the formula.
  4. At this point, you just need to substitute the values of the known quantities into the equation which is formed above and evaluate the subject by substitution.

For understanding the above concepts very clearly, we have given some solved problems on evaluating a formula by substitution. Let’s practice the topic effectively by solving some questions on the Evaluation of subject by substitution.

Worked Examples on Evaluating Simple Expressions with Substitution

Example 1:
Express 25° celsius (C) as a temperature in degrees Fahrenheit (F) using the formula F = 9/5 C + 32?

Given that C = 25° and formula F = 9/5 C + 32
Now evaluate the formula by substitution of known values ie., C = 25
F = 9/5 C + 32
F = 9/5 x 25 + 32
F = 45 + 32
F = 77°
After Evaluating the Formula using Substitution Method the result of the unknown quantity is F = 77°.

Example 2:
A local hospital is holding a raffle as a fundraiser. The individual cost of participating in the raffle is given by the expression ie., 10a + 3, where a represents the number of applications someone purchases. Evaluate the expression by substituting the a value as 5 and 15.

Given expression is 10a + 3
(i) When a is 5
The expression becomes 10(5) + 3
= 50 + 3
= 53.
(ii) When a is 15
The expression becomes 10(15) + 3
= 150 + 3
= 153.

Example 3:
Find the length of a rectangular plot whose breadth is 40 m and the area is 120 m².

Given that area = 120 m² and breadth is 40 m
We know that the formula for the area rectangular plot is A = length x breadth
As the subject to find the formula is not an appropriate form, we have to change the subject of the formula.
So, length = area / breadth
Substitute the given known values in the above formula, to get the length of a rectangular plot.
length = 120 / 40 m = 3 m
Therefore, the length of a rectangular plot is 3 m.

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