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Formula and Framing the Formula are the concepts used to explain the relationship between different variables. Let us discuss deeply every individual concept of Formula and also Framing the Formula. It is easy to find the relation between two variables by framing a formula with simple steps. Every concept is clearly explained with the solved examples in the below article. Therefore, completely read the entire article and follow every step to get complete knowledge on Formula and Framing the Formula.

## List of Topics for Formula and Framing the Formula

- Change the Subject of a Formula
- Changing the Subject in an Equation or Formula
- Practice Test on Framing the Formula

### Formula

A formula is a relation between different variables. The formula can be written as an equation with the help of variables and also mathematical symbols. When you look at the equation, it is clearly stating how a variable is related to another variable.

**Example:**

1. Let us consider a square which is of side a and the perimeter of it is p, then the formula will be p = 4a.

Here the formula shows the exact relation between the perimeter of a square and also the side of a square. It is easy to find the unknown quantity using the known quantity when the values of all the quantities are known.

2. If the perimeter of a rectangle p is twice the sum of its breadth b and length l, then the formula will represent as p = 2(l + b)

3. The volume of a cube is V and its side is a. Then, the formula is V = a^3.

4. We can also write a formula to express the relation between force, mass, and acceleration. Force of an object F is the product of mass “m” and acceleration “a” of that object. The formula is F = ma.

5. If the sum of two unknown variables is 15, then the formula is a + b = 15, where a and b are unknown variables.

### Framing a Formula

Framing a formula is arranging the formula of the given mathematical statements with the help of symbols and literals.

1. Firstly, select variables need to form an equation. Also, decide the symbols that need to use for the equation. Some of the symbols and letters are already in the use to represent certain quantities. For example, p is used to represent the principal.

2. Finally, understand the conditions to write an equation and frame the formula.

#### Subject of a formula

When a quantity is expressing in terms of other quantities, then that particular quantity expressed is defined as the Subject of a formula. Generally, the Subject of the formula is written on the left-hand side and other constants are written on the right-hand side of the equality sign in a formula.

Example:

If z = x + y, then z is expressed in terms of the sum of the x and y. Here, z is the subject of this formula.

x = z – y. Here x is the subject of this formula.

#### Substitution in a formula

If the variable of an algebraic expression is assigned with certain values, then the given expression gets a particular value. This process is known as substitution.

1. Note down the unknown quantity as the subject of the formula.

2. Substitute different values of the known quantity in the formula to find the value of the subject.

Examples of Framing of a Formula:

1. The total amount A is equal to the sum of the Interest (I) and Principal (P).

Solution:

Formula: A = I + P

2. One-third of a number subtracted from 4 gives 2.

Solution:

Formula: 4 – 1/3 x = 2

3. The sum of the three angles (∠a, ∠b, ∠c) of a triangle is equal to two right angles.

Solution:

Formula: ∠a + ∠b + ∠c = 180°

4. The area of the rectangle (A) is equal to the product of the breadth (B) and length (L) of the rectangle.

Solution:

Formula: A = B × L

### Solved Examples on Formula and Framing the Formula

1. Express the following as an equation. Arun’s father’s age is 3 years more than 4 times Arun’s age. Father’s age is 39 years.

Solution:

Given that Arun’s father’s age is 3 years more than 4 times Arun’s age. Father’s age is 39 years.

Let Arun’s age is s years.

Four times his age = 4s.

Father’s age 3 + 4s

Given father’s age = 39 years

3 + 4s = 39

The final equation is 3 + 4s = 39

2. Write the formula for the following statement. One-fourth of the weight of an apple (A) is equal to one-fifth of the difference between Orange (O) and 2.

Solution:

Given that One-fourth of the weight of an apple (A) = 1/4

Difference between Orange (O) and 2 = O – 2

One-fifth of the difference between Orange (O) and 2. = 1/5(O – 2)

One-fourth of the weight of an apple (A) is equal to one-fifth of the difference between Orange (O) and 2.

1/4 = 1/5(O – 2)

3. Change the following statement using expression into a statement in ordinary language.

(a) Cost of a Desk is Rs. X and Cost of a Box is Rs. 4X

(b) Sam’s age is p years. His brother’s age is (5p + 2) years.

Solution:

(a) Given that Cost of a Desk is Rs. X and Cost of a Box is Rs. 4X

The Cost of a Box is 4 times the Cost of a Desk.

(b) Sam’s age is p years. His brother’s age is (5p + 2) years.

Sam’s brother’s age is two years more than five times his age.

4. A rectangular box is of height h cm. Its length is 7 times its height and the breadth is 5 cm less than the length. Express the length, breadth, and height.

Solution:

Given that A rectangular box is of height h cm. Its length is 7 times its height and the breadth is 5 cm less than the length. Express the length, breadth, and height.

Height = h, length = l, breadth = b

The length of the rectangle is 7 times the height.

The Length of the rectangle = 7h

The breadth of the rectangle is 5 cm less than the length

The Breadth of rectangle = l – 5

As l = 7h, b = 7h – 5.

Height h

Length l = 7h

Breadth b = 7h – 5