# Number and Quantity Formulas for the PRAXIS® Core Academic Skills for Educators Mathematics Test

The “PRAXIS Core Academic Skills for Educator: Mathematics” Test (5733) used to be a scary test, but not anymore. The math section underwent significant revision so that it now only tests skills that will *actually* be used by educators in the regular classroom. The Number and Quantity section remains to be the most important one, comprising approximately 36% of the whole exam. The following chart has the essential formulas you’ll need to ace this part of the test.

Also, look for our charts covering the other three types of math questions on the PRAXIS® Test:

Algebra Formulas for the PRAXIS® Core Academic Skills Test

Geometry Formulas for the PRAXIS® Core Academic Skills Test

## Number and Quantity Formulas

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

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

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

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

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

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

Number and Quantity |
\(\dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \cdot d)+(c \cdot b)}{(b \cdot d)}\) | a, b, c, d = any real number |
Remember to simplify the fraction if possible. |

Number and Quantity |
\(\dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{a \cdot c)}{(b \cdot d)}\) | a, b, c, d = any real number |
Remember to simplify the fraction if possible. |

Number and Quantity |
\(\dfrac{a}{b} \div \dfrac{c}{d}=\dfrac{a \cdot d)}{(b \cdot c)}\) | a, b, c, d = any real number |
Remember to simplify the fraction if possible. |

Number and Quantity |
\(a\dfrac{b}{c}=\dfrac{(a \cdot c)+b}{c}\) | a, b, c = any real number |
Remember to simplify the fraction if possible. |

Number and Quantity |
\(\%a = \frac{a}{b} \cdot 100\) | %a = percentage of a in ba, b = any real number |
Remember to simplify the fraction if possible. |

Number and Quantity |
\(r=\dfrac{Q}{t}\) | r = rateQ = quantityt = time |
Remember to simplify the friction if possible. |

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