Formula and Framing the Formula

In mathematics formula and framing the formula are discussed here how to frame the formula.

We have already learnt to frame algebraic expressions and solve them. We have also learnt to form linear equations and find solution to the equation. Using these, we will frame the formula and express the relation between the unknown quantities and know more about it.

Formula and Framing the Formula

We already know: An equation is the statement of equality which involves two the mathematical expressions, i.e., 2x - 1 = 4 - 3x

Formula:

It is an equation which expresses relationship between two or more qualities using literals and symbols. It is an equation that specifies how a number of variables are related to one another. Letters are used as symbols for the words. Letters that represent words have been standardized in many cases so that certain formulas may be written the same in various texts.

Framing of a formula:

In formula and framing the formula, we framed the formula by translating mathematical statements using symbols and literals. Look at the examples given below:

1. Mathematical statement: Amount (A) is equal to the sum of the Principal (P) and Interest (I).

Formula: A = P + I

2. Mathematical statement: The area of the rectangle (A) is equal to the product of the length (L) and breadth (B) of the rectangle.

Formula: A = L × B

3. Mathematical statement: The sum of the three angles (∠x, ∠y, ∠z) of a triangle is equal to two right angles (2 × 90° = 180°).

Formula: ∠x + ∠y + ∠z = 180°

4. Mathematical statement: One-fifth of a number subtracted from 5 gives 3.

Formula: 5 - ¹/₅ x = 3

5. Mathematical statement: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the remaining two sides.

Here H denotes the hypotenuse and P, B denote the remaining two sides.

Formula: H² = P² + B²

Examples on Formula and framing the formula:

1. Express the following as an equation.

Ravi’s father’s age is 5 years more than 3 times Ravi’s age. Father’s age is 44 years.

Solution:

Let Ravi’s age be x years.

Three times his age = 3x.

Father’s age 5 + 3x

Given father’s age = 44 years

Therefore, 5 + 3x = 44

2. Write the formula for the following statement.

One-fifth of the centigrade temperature is equal to one-ninth of the difference between Fahrenheit (F) temperature and 32.

Solution:

C/5 = (f - 32)/9

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

(a) Cost of a CD is Rs. P and Cost of a DVD is Rs. 3P

(b) Aditya’s age is x years. His brother’s age is (3x + 2) years.

Solution:

(a) In ordinary language we write it as:

The cost of DVD is three times the cost of CD.

(b) In ordinary language, we write it as;

Aditya’s brother’s age is two years more than three times his age.

4. A rectangular box is of height h cm. Its length is 3 times its height and the breadth is 7 cm less than the length. Express the length, breadth and height.

Solution:

Let the length, breadth and height of the rectangle be L, B, H.

Length of the rectangle is 3 times the height.

Therefore, Length of the rectangle = 3h

Breadth of rectangle is 7 cm less than the length

Therefore, Breadth of the rectangle = L - 7 but L = 3h

Therefore, Breadth of the rectangle in terms of height = 3h - 7