Math formulas

Here you will learn about math formulas, including what math formulas are and how to use them.

Students will first learn about math formulas as part of expressions and equations in 6th grade and expand on that knowledge in high school algebra.

What are math formulas?

Math formulas are rules that connect two or more variables. They are used to work out the values of unknown variables by substituting in other known values.

Formulas will usually include coefficients, constants, variables, and an operator.

For example, here is a rectangle with base $b$ and height $h.$. You can use a math formula to find the value of the perimeter by substituting in the values for the length and width of the rectangle.

The formula for the perimeter $P$ of a rectangle is:

$P=2 \, (b+h)$

Literal equations

Literal equations are equations that have more than one variable in them. Literal equations are represented by formulas and equations.

These equations will all have more than one variable in them, and in order to solve them, you will need to isolate one of the variables. To do this, you will use the inverse operation.

Step-by-step guide: Literal equations

Kinematic equations

Kinematic equations are a set of equations that describe the motion of an object with constant acceleration. These equations can be used to predict the position, time, speed, and acceleration of an object. They are often used in precalculus, calculus, and physics classes.

The four main kinematic equations, where $v_o$ is the initial velocity (original velocity), $v$ is the final velocity, $a$ is the constant acceleration, $t$ is time, and $s$ is the displacement (change in position). These equations can look different depending on the class you are in.  For example, displacement, which is denoted by the variable s can be denoted by $x.$  

• Velocity-Time relation
  $v=v_o+a t$
  
• Displacement-Time relation
  $s=v_o t+\frac{1}{2} a t^2$
  
• Velocity-Displacement relation
  $v^2=v_0^2+2 a s$
  
• Average Velocity-Displacement relation
  $s=\frac{\left(v_0+v\right)}{2} t$

Step-by-step guide: Kinematic equations

List of important math formulas

The following formulas are considered important math formulas for students to know and understand, including geometry formulas.

What are math formulas?

Common Core State Standards

How does this relate to 6th grade math and high school math?

• Grade 6: Expressions and Equations (6.EE.A.2c)
  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas $V = s^3$ and $A = 6s^2$ to find the volume and surface area of a cube with sides of length $s = 1/2.$

• High School: Algebra (HS.A.CED.A.4)
  Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law $V = IR$ to highlight resistance $R.$

How to use math formulas

In order to solve with math formulas:

1. Use the formula given in the question.
2. Work carefully to answer the question, one step at a time.
3. Write the final answer clearly.

Math formulas examples

Example 1: perimeter of a rectangle

Find the perimeter of the given rectangle using the formula, $P=2 \, (b+h).$

1. Use the formula given in the question.

You will use the formula $P=2 \, (b+h)$ to find the perimeter of the rectangle.

The length of the rectangle is $13 \, cm$ and the width is $5 \, cm,$ so substitute the measurements into the formula.

$P=2 \, (13+5)$

2Work carefully to answer the question, one step at a time.

$P=2 \, (13+5)$

Solve the operation within the parenthesis first. Adding $13$ and $5$ gives you $18.$

$P=2 \times 18$

You will then multiply $2 \times 18.$

This can also be solved as $18 + 18$ to give the answer of $36.$

$P=36$

3Write the final answer clearly.

The final answer is $P = 36 \, cm.$

The perimeter of the rectangle is $36$ centimeters.

Example 2: area of a rectangle

Find the area of the rectangle given, using the formula $A = b \times h.$

Work carefully to answer the question, one step at a time.

Show step

$A=32 \times 17$

You will multiply $32$ by $17.$

$A = 544$

Example 3: area of a square

Find the area of the square given, using the formula $A=s \times s.$

Work carefully to answer the question, one step at a time.

Show step

$A=17 \times 17$

You will multiply $17$ by $17.$

$A = 289$

Example 4: volume of a rectangular prism

Find the volume of the rectangular prism using the formula, $V = b \times h \times d.$

Work carefully to answer the question, one step at a time.

Show step

$V=9 \times 6 \times 15$

First, multiply the first two numbers using the knowledge of your multiplication facts, $9 \times 6 = 54.$

Multiply $54$ by $15$ to calculate the volume of the rectangular prism.

$V=54 \times 15$

$V=810 \text { inches }$

Example 5: area of a triangle

Find the area of the triangle given, using the formula $A=\cfrac{1}{2} \, b h.$

Work carefully to answer the question, one step at a time.

Show step

$A=\cfrac{1}{2} \, (10 \times 15)$

Following the order of operations, you will multiply $10$ by $15$ first.

$10 \times 15=150$

$A=\cfrac{1}{2} \, (150)$

Finally you will multiply $150$ by $\, \cfrac{1}{2} \, ,$ or divide $150$ by $2.$

$A = 75$

Example 6: area of a parallelogram

Find the area of the parallelogram given, using the formula $A = b \times h.$

Work carefully to answer the question, one step at a time.

Show step

$A=27 \times 19$

To find the area, you will multiply $27$ by $19.$

$A = 513$

Teaching tips for math formulas

• Formulas can be difficult for students to memorize. Always have a way for students to refer back to the formula, such as an anchor chart or a reference sheet, until they get familiar and comfortable with each formula.

• These basic math formulas will prepare students for work in high school with more complex numbers and formulas, including linear equations, the quadratic formula, and other algebra formulas, such as the slope-intercept formula.

• While using quizzes to assess a student’s knowledge of the different equations is important, consider making the assessments real-life, and have students measure items within the classroom or school, and use the formulas to calculate the area of the classroom or playground.

Easy mistakes to make

• Substituting in the wrong number in the equation
  Learning the equation is important, but learning what each variable in an equation is equally important. In some basic math formulas, flipping the base and the height would still give students the same answer. However, as students move to more complex formulas, flipping of variables could result in incorrect answers.
  
  For example, when finding the area of a trapezoid, flipping of a side versus the height would result in the wrong answer because the sides are added together and divided by $2,$ and the height is not.

• Not clearly writing variables
  Neat writing is important. For example, the variables $v$ and $u$ can easily be muddled as they look similar and they both represent velocity in kinematic formulas.

The next lessons are

• Coordinate plane
• Types of graphs
• Graphing linear equations

Beyond elementary

You can use formulas in lots of different areas of math. One of the most famous formulas is the quadratic formula which we can use to solve quadratic equations.

$x=\cfrac{-b \pm \sqrt{b^2-4 a c}}{2 a}$

Quadratics are a type of polynomial and using coordinate geometry you can use them to produce a parabola shaped quadratic graph. We can use the graph to work out the solutions to the equation and the y-intercept of the graph.

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