Overview:
Some relationships between variables can be solved for in terms of common formulas. For example, the formula for the circumference of a circle is C=πd. This equation shows the relationship between the circumference of a circle and the diameter of the circle.
What Is a Formula?
A formula is an equation or inequality in which the relationships between variables are expressed in terms of others. It is a mathematical shorthand that often uses the first letters of the words for the objects that are represented. In the formula C = πd, the letter C stands for circumference and the letter d stands for diameter. The constant represented by the Greek letter pi is always the same irrational number.
How Can Formulas Be Solved?
Formulas are solved by substituting any of the values that are known for the variables in the formula, and then working the operations to solve for the others. For example, the profit of an item p equals the selling price s minus the cost of the item c. If the selling price of an item is $25.00 and the wholesale cost is $15.00, in order to find the profit, substitute the values as $25 – $15 and then subtract to solve the equation. The profit is $10.
How Are Formulas Related?
Because the relationships between variables are used within formulas, the formula can be used to solve for any value. The relationship between the length, the width, and the area of a rectangle can be expressed by the formula A=lw, when the length and the width are in the same type of units. One can find the area by multiplying the length by the width. If the area and the length is known, one can find the width by dividing the area by the length (w = A/l). If the area and the width is known, one can find the length by dividing the area by the width (l=A/w). There are three relationships expressed in that simple equation.
Why Are Some Letters Capital and Other Letters Small?
Capital letters in a formula often stand for different things than small letters in the same formula. They should not be changed within the formula. For example, suppose one side of a large square measures 1.6 cm. The area of the large square could be represented by S2, or 2.56 square centimeters. Inside the large square is a small square with a side that measures 0.6 cm. The area of the small square could be represented by s2, or .36 square centimeters. The area of the large square that is not part of the small square could be represented by a formula A=S2 – s2, where the S and the s stand for two different things.
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