# 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:

Data Interpretation and Representation, Statistics, and Probability Formulas for the PRAXIS® Core Academic Skills 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
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 b
a, b = any real number
Remember to simplify
the fraction if
possible.
Number and
Quantity
$$r=\dfrac{Q}{t}$$ r = rate
Q = quantity
t = time
Remember to simplify
the friction if
possible.