Types of Formulas. Rearranging Formulas - Revision Notes

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In these revision notes for Types of Formulas. Rearranging Formulas, we cover the following key points:

  • What are some of the fields in which formulas are abundantly used?
  • What are some typical examples of formulas use in each field of science?
  • How to rearrange formulas to make a given variable its subject?

Types of Formulas. Rearranging Formulas Revision Notes

Depending on the subject and purpose they are used for, formulas are classified into algebra, geometry, physics, chemistry, spreadsheet (excel), banking, engineering, etc.

Algebra formulas are used in equations, inequalities, wordy problems, etc. The eight basic algebraic identities, all properties of indices, roots, ratios and proportion, the formula of percentage, etc., are all examples of algebraic formulas. Other types of algebraic formulas include: the quadratic formula; arithmetic and geometric series formulas by which we calculate the value of n-th term or the sum of n terms of such series; and so on.

Geometry formulas extend from perimeter and area of various shapes to volume of solid objects; from trigonometry to polygons; from plane to space geometry and so on.

Physics formulas. Physics is another field of science that contains a very large number of formulas. From kinematics to dynamics; from work and energy to momentum and impulse; from electricity to magnetism and electromagnetism; from optics to modern physics etc., all these sub-branches of Physics contain a significant number of formulas in their theories.

Chemistry formulas. Chemistry is also a branch of science that contains many formulas, where the most notorious are the molecular formula that show how atoms are combined in molecules; stoichiometric formulas that are mostly based on Formula Mass, i.e. in the sum of the atomic weights of each atom present in the molecule of the substance; element percentages formulas in compounds, etc.

Spreadsheet formulas. A spreadsheet formula, like those used in Microsoft Excel, is an equation that performs a calculation on the numbers, functions and values of one or more cells. A formula is associated with a cell or a cell range. In the formula bar, we must write the 'equal to' sign first, then the name of formula; then we open the brackets where the name of the first and the last cell separated by a semicolon are written. After closing the brackets, we click on the cell in which we want the result to appear, then we press ENTER and the result appears in the designed cell.

Banking formulas include, among others, those of simple and compound interest. Thus, if the principal (original amount deposited or borrowed) if P and the simple interest rate is r, the formula used for calculating the total amount A(t) to be received or paid after a period t is

A(t) = P(1 + rt)

As for compound interest, we use the formula

An (t) = P(1 + r/n)nt

where n is the number of compounds in a year.

Engineering formulas. Engineering is a branch of science that consists in the application in practice of science and math to solve problems. Engineers figure out how things work and find practical uses for scientific discoveries. In this sense, engineering is the combination of math and other natural sciences. Calculations and formulas in engineering are usually more complicated than in physics or math. There are many engineering sub-branches, such as mechanical engineering, civil engineering, computer engineering, electrical engineering, etc., which contain a large number of formulas.

When the quantity to the left part in the original formula is known and we are interested in finding any of the quantities in the right part of the formula, we can isolate the variable required by completing inverse operations. It is a known fact that the inverse operation of addition is subtraction, the inverse operation of multiplication is division and the inverse operation of raise in power is finding the root. Moreover, sending a number or variable from left to right or vice-versa makes it change the sign to its opposite (plus becomes minus and minus becomes plus).

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