# Formulas for Math on the ParaPro Test: Part 1—Number Sense and Algebra

Helping students learn math is awesome! And do you know who else is awesome?

**YOU!**

It’s great that you’re preparing to take the ParaPro Test so you can teach math in the future. And we want to help you reach that goal because our vision is a world full of people like you!

Here you’ll find the **essential formulas** you’ll need for the math questions that deal with **Number Sense and Algebra** on the **ParaPro Test**. Other questions on the ParaPro Test require additional formulas, so check out our charts for those:

Formulas for ParaPro Geometry and Measurement Questions

Formulas for ParaPro Data Analysis Questions

Use the three charts to solve these: free ParaPro math practice questions at Union Test Prep

## Number Sense and Algebra Formulas for the ParaPro Test

Category | Formula | Symbols | Comment |
---|---|---|---|

Number Sense and Algebra |
\(a + b = b+ a\) \(a \cdot b = b\cdot a\) |
\(a, b =\) any constant or variable | Commutative Property |

Number Sense and Algebra |
\(a + (b + c) = (a+b)+c\) \(a\cdot(b\cdot c) = (a\cdot b) \cdot c\) |
\(a,b, c =\) any constant or variable | Associative Property |

Number Sense and Algebra |
\(a\cdot(b+c) = a\cdot b + a\cdot c\) | \(a,b,c =\) any constant or variable | Distributive Property |

Number Sense and Algebra |
\(a+0 = a\) | \(a =\) any constant or variable | Identity Property of Addition |

Number Sense and Algebra |
\(a\cdot 1 = a\) | \(a =\) any constant or variable | Identity Property of Multiplication |

Number Sense and Algebra |
\(\frac{a}{b} + \frac{c}{d} = \dfrac{a\cdot d + c\cdot b}{b\cdot d}\) | \(a,b, c, d =\) any constant or variable | Remember to simplify the fraction (if possible) |

Number Sense and Algebra |
\(\frac{a}{b} \cdot \frac{c}{d} = \frac{a\cdot c}{b \cdot d}\) | \(a,b,c,d =\) any constant or variable | Remember to simplify the fraction (if possible) |

Number Sense and Algebra |
\(\frac{a}{b} \div \frac{c}{d} = \frac{a\cdot d}{b \cdot c}\) | \(a,b,c,d =\) any constant or variable | Remember to simplify the fraction (if possible) |

Number Sense and Algebra |
\(a \frac{b}{c} = \frac{a\cdot c + b}{c}\) | \(a,b,c =\) any constant or variable | Remember to simplify the fraction (if possible) |

Number Sense and Algebra |
\(a\cdot b\% = a \cdot \frac{b}{100}\) | \(a =\) any real number \(b \% =\) any percent |
Remember to simplify the fraction (if possible) |

Number Sense and Algebra |
\(x^a \cdot x^b = x ^{a+b}\) | \(a,b,x =\) any real number | |

Number Sense and Algebra |
\(\dfrac{x^a}{x^b} = x^{a-b}\) | \(a,b,x =\) any real number | |

Number Sense and Algebra |
\((x^a)^b = x^{a \cdot b}\) | \(a,b,x =\) any real number | |

Number Sense and Algebra |
\((x\cdot y )^a = x^a \cdot y^a\) | \(a,b,x,y =\) any real number | |

Number Sense and Algebra |
\(x^1 = x\) | \(x =\) any real number | |

Number Sense and Algebra |
\(x^0 = 1\) | \(x =\) any real number (\(x \ne 0\)) | |

Number Sense and Algebra |
\(x^{-a} = \dfrac{1}{x^a}\) | \(a,x =\) any real number (\(x \ne 0\)) | |

Number Sense and Algebra |
\(x+a = b \rightarrow x = b-a\) \(x-a = b \rightarrow x = b+a\) \(x\cdot a = b \rightarrow x= b \div a\) \(x\div a = b \rightarrow x = b \cdot a\) \(x^a = b \rightarrow x = \sqrt[a]{b}\) \(\sqrt[a]{x} = b \rightarrow x = b^a\) \(a^x = b \rightarrow x = \dfrac{ log \; b}{log \; a}\) |
\(a,b =\) constants \(x =\) variable |

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