ChemistryPrep

Introduction

Chemistry requires the use of various math operations including algebra. A common reason why students struggle to be successful in chemistry is their math skills are not sufficient for chemistry. Students then have to learn complex chemistry concepts and calculations as well as math at the same time. This will help students learn the math fundamentals to be successful in chemistry.

Contents

  • Part A: Identification of the parts of an equation
    • Example A1: Identification of the part of an equation
      • Practice A1: Identification of the parts of an equation
    • Example A2: Infer the “hidden” parts of an equation
      • Practice A2: Infer the “hidden” parts of an equation
  • Part B: Isolate a variable
    • Example B1: Identify the math operation and opposite operation to isolate the variable
      • Practice B1: Identify the math operation and opposite operation to isolate the variable
    • Example B2: Solve for a variable (addition/subtraction)
      • Practice B2: Solve foer a variable (addition/subtraction)
    • Example B3: Solve for a variable (multiplication/division)
      • Practice B3: Solve for a variable (multiplication/division)

Part A: Identification of the parts of an equation

In chemistry we often use variables. A variable is usually a letter or symbol used in equations that can have different values. Example A1 shows an equation with various parts labeled. If there is no fraction bar, the number is considered to be a numerator with an imaginary fraction bar and a 1 in the denominator which is shown in example A2.

Example A1: Identification of the parts of an equation

yo yo \frac{x}{3}=\delta+4

  • x and LaTeX: \large \delta are the variables
  • x is in the numerator position
  • LaTeX: \large \delta is in the denominator position
  • there is a fraction bar between x and 3 which is a math operator that represents x divided by 3
  • there is a plus sign for the operation that represents the addition operation

Practice A1: Identification of the parts of an equation

LaTeX: \huge 41=\frac{7.3}{\Delta}+y

  • Identify the following:
    • variables
    • numerators
    • denominators
    • math operators

Example A2: Infer the “hidden” parts of an equation

Using the equation in example A1, we see there are 1’s in the denominators underneath the LaTeX: \large \delta and underneath the 4.

LaTeX: \huge \frac{x}{3}=\frac{\delta}{1}+\frac{4}{1}

  • the numerators are x, LaTeX: \large \delta, and 4
  • the denominators are 3, 1, and 1

Practice A2: Infer the “hidden” parts of an equation

Using the equation in practice A1, write in the 1’s in the denominators.

LaTeX: \huge 41=\frac{7.3}{\Delta}+y

  • put in the imaginary 1’s in the denominator positions
  • identify the numerators
  • identify the denominators

Part B: Isolate a variable

We routinely solve for variables in chemistry. This means get the variable by itself on one side of the equation symbol. This also means get the variable on top of the fraction bar in the numerator position. How do we get the variable “y” by itself on one side of the equation in the numerator position? To do this you must do the opposite of the operation it currently is associated with. Also, for the equation to remain correct, you must perform whatever opposite operation is needed to both sides of the equal sign. Table 1 shows a column of math operations on the left and the corresponding opposite operation.

Table 1: This is a table showing math operations and the inverse operations
Math Operation Opposite of Operation
addition (+) subtraction (-)
subtraction (-) addition (+)
multiplication (LaTeX: \large \times) or number in the numerator position division (LaTeX: \large \div)
division (LaTeX: \large \div) or number in the denominator position multiplication (LaTeX: \large \times) 
LaTeX: \large x^2 (squared) LaTeX: \large \sqrt[2]{} (square root) or LaTeX: \large x^{\frac{1}{2}} (raise to the LaTeX: \large \frac{}{}\frac{1}{2} power)
LaTeX: \large x^y (squared) LaTeX: \large \sqrt[y]{} (square root) or LaTeX: \large x^{\frac{1}{y}} (raise to the LaTeX: \large \frac{}{}\frac{1}{y} power)

Example B1: Identify the math operation and opposite operation to isolate the variable

This table shows operations and opposite operation
Equation Operation that the variable is involved in Opposite operation to isolate the variable equation and operation
LaTeX: \large y-3=6 3 is being subtracted from y you must add y to 3 and the other side of the equals sign LaTeX: \large y-3+3=6+3
LaTeX: \large 3.7=9+n 9 is being added to n you must subtract 9 from both sides of the equals sign LaTeX: \large 3.7-9=9+n-9
LaTeX: \large 7x=9 7 is being multiplied by x you must divide both sides by 7 LaTeX: \large \frac{7x}{7}=\frac{9}{7}
LaTeX: \large x^3=27 x is being raised to the 3rd power (cubed) you must take the cubed root or raise x to the LaTeX: \large \frac{1}{3} power LaTeX: \large \sqrt[3]{x^3} =\sqrt[3]{27} or LaTeX: \left(\large x^3\right)^{\frac{1}{3}}\large =\left(27\right)^{\frac{1}{3}}

Practice B1: Identify the math operation and opposite operation to isolate the variable

Fill in the blanks and show the operations, opposite operations, and the equations.
Equation Operation that the variable is involved in Opposite operation to isolate the variable equation and operation
LaTeX: \large 3=6+x
LaTeX: \large 3.7-z=15.372
LaTeX: \large 9.31=\frac{9}{t}
LaTeX: \large 51=m^2

Example B2: Solve for a variable (addition/subtraction)

This is an example of how to solve for a variable.
Equation/Operation Steps/Explanation
LaTeX: \large y +13=24 This is the starting equation.
LaTeX: \large y+13-13=24-13 Since 13 is being added to y, 13 must be subtracted from both sides of the equation.
LaTeX: \large y+0=11 Since y and y + 0 are the same, just leave the 0 out.
LaTeX: \large y=11 This is the final answer.

Practice B2: Solve for a variable (addition/subtraction)

This is a practice problem for solving for a variable.
Equation/Operation Steps/Explanation
LaTeX: \large -1.57=24.27-d

Example B3: Solve for a variable (multiplication/division)

This is an example of how to solve for a variable.
Equation/Operation Steps/Explanation
LaTeX: \large \frac{4.00{}}{u}=2.70 This is the starting equation.
LaTeX: \large \frac{4.00{}}{u}\times u=2.70\times u Since 4 is being divided by u and u is in the denominator position, u must be multiplied by both sides to get it into the numerator position on the right side.
LaTeX: \large 4.00=2.70u This is the new equation.
LaTeX: \large \frac{4{.00}}{2.70}=\frac{2.70}{2.70}u Since 2.7 is being multiplied by u, both sides must be divided by 2.7.
LaTeX: \large 1.48=1u Since 1 times u is the same as u, the one can be left out.
LaTeX: \large 1.48=u This is the final answer.

Practice B3: Solve for a variable (multiplication/division)

This is a practice problem for solving for a variable.
Equation/Operation Steps/Explanation
LaTeX: \large -13r=47.3