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.

**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 '/').

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

- Volume V of a cylinder is the product of base area A
_{b}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. - Acceleration a of a moving object is the change in velocity in a given time t, where v
_{0}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.

- From the description given in words, we obtain the following formula of cylinder volume: V = A(You can see that multiplication symbol is obsolete, as explained earlier.)
_{b}∙H = πR^{2}H - 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 - v*_{0}*/**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.

Describe in words the meaning of the following formulas.

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

- 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."
- 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.

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- 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.
- Continuing learning formulas - read our next math tutorial: Types of Formulas. Rearranging Formulas

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