# Math Lesson 8.1.2 - What is a Formula? How do we Write Formulas?

Welcome to our Math lesson on What is a Formula? How do we Write Formulas?, this is the second lesson of our suite of math lessons covering the topic of Writing Formulas and Substituting in a Formula, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

## What is a Formula? How do we Write Formulas?

A formula is a fact or a rule written in mathematical symbols. It contains a set of instructions on how to calculate an unknown quantity in terms of one or more known ones. The unknown quantity (otherwise known as the independent variable) is related to the known ones (dependent variables) through the equal sign '='. Therefore, in a certain sense, a formula is a kind of equation (we will explain this concept in the next chapter) where variables are not just mathematical symbols but they have a more concrete and practical meaning. Hence, a formula is a kind of scientific "recipe" where the known variables are like the ingredients, which when combined give the final product (the unknown quantity).

As we said earlier, variables in formulas are combined with each other through mathematical operators such as addition, subtraction, multiplication, division, raise in power, logarithm, exponentiation, etc. Only the multiplication symbol ('·' or '×') is not written in a formula but is implied. Likewise, the division symbol (÷) is replaced by the fraction bar ('' or '/').

### Example 1

Write down the following mathematical sentences as formulas using the given rules.

1. Volume V of a cylinder is the product of base area Ab and height H, where the base area is a circle of radius R, and is obtained by raising the base radius to the second power and multiplying it by the Archimedes Constant π. You can use the Cylinder Calculator to see full calculations and formula in practice.
2. Acceleration a of a moving object is the change in velocity in a given time t, where v0 is the initial velocity and v the final velocity of the moving object. You can use the Uniformly Accelerated Motion Calculator to see full calculations and formula in practice.

### Solution 1

1. From the description given in words, we obtain the following formula of cylinder volume:
V = Ab∙H = πR2 H
(You can see that multiplication symbol is obsolete, as explained earlier.)
2. Since the term "change" means "difference" and it implies subtraction of the initial quantity from the final one, we obtain the following formula for acceleration:
a = v - v0/t

We can also complete the inverse to interpret a formula and express the phenomenon described by it in words. Let's consider the example below to clarify this point.

### Example 2

Describe in words the meaning of the following formulas.

1. Formula of percentage of a substance A in a compound:
%A = m(A)/m(tot) × 100%
where m stands for 'mass' of substance.
2. Formula of the heat energy Q dissipated by an electric device connected to a circuit operating at the current I:
Q = I2 Rt
where R is the resistance of the device and t is the operating time.

### Solution 1

1. The first formula indicates the ratio of the substance A to the total amount of the compound expressed as a percentage. In words, it means, "The percentage of a given substance to the total amount in a compound expressed as a percentage is obtained by dividing the mass of the given substance to the total mass of the compound and then multiplying the result by 100."
2. This formula indicates that the heat energy dissipated by an electric device is the product of the square of operating current in the circuit, resistance of the device and the operating time.

## More Writing Formulas and Substituting in a Formula Lessons and Learning Resources

Formulas Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
8.1Writing Formulas and Substituting in a Formula
Lesson IDMath Lesson TitleLessonVideo
Lesson
8.1.1Mathematical vs Word Sentences
8.1.2What is a Formula? How do we Write Formulas?
8.1.3Expressing Events in a Shorter Way using Formulas
8.1.4Substituting into a Formula
8.1.5Substituting in Formulas derived from Wordy Problems
8.1.6Finding the Inverse Formula

## Whats next?

Enjoy the "What is a Formula? How do we Write Formulas?" math lesson? People who liked the "Writing Formulas and Substituting in a Formula lesson found the following resources useful:

1. Formula Definition Feedback. Helps other - Leave a rating for this formula definition (see below)
2. Formulas Math tutorial: Writing Formulas and Substituting in a Formula. Read the Writing Formulas and Substituting in a Formula math tutorial and build your math knowledge of Formulas
3. Formulas Video tutorial: Writing Formulas and Substituting in a Formula. Watch or listen to the Writing Formulas and Substituting in a Formula video tutorial, a useful way to help you revise when travelling to and from school/college
4. Formulas Revision Notes: Writing Formulas and Substituting in a Formula. Print the notes so you can revise the key points covered in the math tutorial for Writing Formulas and Substituting in a Formula
5. Formulas Practice Questions: Writing Formulas and Substituting in a Formula. Test and improve your knowledge of Writing Formulas and Substituting in a Formula with example questins and answers
6. Check your calculations for Formulas questions with our excellent Formulas calculators which contain full equations and calculations clearly displayed line by line. See the Formulas Calculators by iCalculator™ below.
7. Continuing learning formulas - read our next math tutorial: Types of Formulas. Rearranging Formulas